Newer
Older
"# Solving problems by Searching\n",
"\n",
"This notebook serves as supporting material for topics covered in **Chapter 3 - Solving Problems by Searching** and **Chapter 4 - Beyond Classical Search** from the book *Artificial Intelligence: A Modern Approach.* This notebook uses implementations from [search.py](https://github.com/aimacode/aima-python/blob/master/search.py) module. Let's start by importing everything from search module."
"from notebook import psource, heatmap, gaussian_kernel, show_map, final_path_colors, display_visual, plot_NQueens\n",
"\n",
"# Needed to hide warnings in the matplotlib sections\n",
"import warnings\n",
"warnings.filterwarnings(\"ignore\")"
"## CONTENTS\n",
"\n",
"* Overview\n",
"* Problem\n",
"* Simple Problem Solving Agent\n",
"* Search Algorithms Visualization\n",
"* Breadth-First Tree Search\n",
"* Breadth-First Search\n",
"* Hill Climbing\n",
"* Simulated Annealing\n",
"* Genetic Algorithm"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## OVERVIEW\n",
"Here, we learn about a specific kind of problem solving - building goal-based agents that can plan ahead to solve problems. In particular, we examine navigation problem/route finding problem. We must begin by precisely defining **problems** and their **solutions**. We will look at several general-purpose search algorithms.\n",
"\n",
"Search algorithms can be classified into two types:\n",
"* **Uninformed search algorithms**: Search algorithms which explore the search space without having any information about the problem other than its definition.\n",
" * Examples:\n",
" 1. Breadth First Search\n",
" 2. Depth First Search\n",
" 3. Depth Limited Search\n",
" 4. Iterative Deepening Search\n",
"* **Informed search algorithms**: These type of algorithms leverage any information (heuristics, path cost) on the problem to search through the search space to find the solution efficiently.\n",
" * Examples:\n",
" 1. Best First Search\n",
" 2. Uniform Cost Search\n",
" 3. A\\* Search\n",
" 4. Recursive Best First Search\n",
"*Don't miss the visualisations of these algorithms solving the route-finding problem defined on Romania map at the end of this notebook.*"
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For visualisations, we use networkx and matplotlib to show the map in the notebook and we use ipywidgets to interact with the map to see how the searching algorithm works. These are imported as required in `notebook.py`."
]
},
{
"cell_type": "code",
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import networkx as nx\n",
"import matplotlib.pyplot as plt\n",
"from matplotlib import lines\n",
"\n",
"from ipywidgets import interact\n",
"import ipywidgets as widgets\n",
"from IPython.display import display\n",
"import time"
]
},
"Let's see how we define a Problem. Run the next cell to see how abstract class `Problem` is defined in the search module."
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
"outputs": [
{
"data": {
"text/html": [
"<!DOCTYPE html PUBLIC \"-//W3C//DTD HTML 4.01//EN\"\n",
" \"http://www.w3.org/TR/html4/strict.dtd\">\n",
"\n",
"<html>\n",
"<head>\n",
" <title></title>\n",
" <meta http-equiv=\"content-type\" content=\"text/html; charset=None\">\n",
" <style type=\"text/css\">\n",
"td.linenos { background-color: #f0f0f0; padding-right: 10px; }\n",
"span.lineno { background-color: #f0f0f0; padding: 0 5px 0 5px; }\n",
"pre { line-height: 125%; }\n",
"body .hll { background-color: #ffffcc }\n",
"body { background: #f8f8f8; }\n",
"body .c { color: #408080; font-style: italic } /* Comment */\n",
"body .err { border: 1px solid #FF0000 } /* Error */\n",
"body .k { color: #008000; font-weight: bold } /* Keyword */\n",
"body .o { color: #666666 } /* Operator */\n",
"body .ch { color: #408080; font-style: italic } /* Comment.Hashbang */\n",
"body .cm { color: #408080; font-style: italic } /* Comment.Multiline */\n",
"body .cp { color: #BC7A00 } /* Comment.Preproc */\n",
"body .cpf { color: #408080; font-style: italic } /* Comment.PreprocFile */\n",
"body .c1 { color: #408080; font-style: italic } /* Comment.Single */\n",
"body .cs { color: #408080; font-style: italic } /* Comment.Special */\n",
"body .gd { color: #A00000 } /* Generic.Deleted */\n",
"body .ge { font-style: italic } /* Generic.Emph */\n",
"body .gr { color: #FF0000 } /* Generic.Error */\n",
"body .gh { color: #000080; font-weight: bold } /* Generic.Heading */\n",
"body .gi { color: #00A000 } /* Generic.Inserted */\n",
"body .go { color: #888888 } /* Generic.Output */\n",
"body .gp { color: #000080; font-weight: bold } /* Generic.Prompt */\n",
"body .gs { font-weight: bold } /* Generic.Strong */\n",
"body .gu { color: #800080; font-weight: bold } /* Generic.Subheading */\n",
"body .gt { color: #0044DD } /* Generic.Traceback */\n",
"body .kc { color: #008000; font-weight: bold } /* Keyword.Constant */\n",
"body .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */\n",
"body .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */\n",
"body .kp { color: #008000 } /* Keyword.Pseudo */\n",
"body .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */\n",
"body .kt { color: #B00040 } /* Keyword.Type */\n",
"body .m { color: #666666 } /* Literal.Number */\n",
"body .s { color: #BA2121 } /* Literal.String */\n",
"body .na { color: #7D9029 } /* Name.Attribute */\n",
"body .nb { color: #008000 } /* Name.Builtin */\n",
"body .nc { color: #0000FF; font-weight: bold } /* Name.Class */\n",
"body .no { color: #880000 } /* Name.Constant */\n",
"body .nd { color: #AA22FF } /* Name.Decorator */\n",
"body .ni { color: #999999; font-weight: bold } /* Name.Entity */\n",
"body .ne { color: #D2413A; font-weight: bold } /* Name.Exception */\n",
"body .nf { color: #0000FF } /* Name.Function */\n",
"body .nl { color: #A0A000 } /* Name.Label */\n",
"body .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */\n",
"body .nt { color: #008000; font-weight: bold } /* Name.Tag */\n",
"body .nv { color: #19177C } /* Name.Variable */\n",
"body .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */\n",
"body .w { color: #bbbbbb } /* Text.Whitespace */\n",
"body .mb { color: #666666 } /* Literal.Number.Bin */\n",
"body .mf { color: #666666 } /* Literal.Number.Float */\n",
"body .mh { color: #666666 } /* Literal.Number.Hex */\n",
"body .mi { color: #666666 } /* Literal.Number.Integer */\n",
"body .mo { color: #666666 } /* Literal.Number.Oct */\n",
"body .sa { color: #BA2121 } /* Literal.String.Affix */\n",
"body .sb { color: #BA2121 } /* Literal.String.Backtick */\n",
"body .sc { color: #BA2121 } /* Literal.String.Char */\n",
"body .dl { color: #BA2121 } /* Literal.String.Delimiter */\n",
"body .sd { color: #BA2121; font-style: italic } /* Literal.String.Doc */\n",
"body .s2 { color: #BA2121 } /* Literal.String.Double */\n",
"body .se { color: #BB6622; font-weight: bold } /* Literal.String.Escape */\n",
"body .sh { color: #BA2121 } /* Literal.String.Heredoc */\n",
"body .si { color: #BB6688; font-weight: bold } /* Literal.String.Interpol */\n",
"body .sx { color: #008000 } /* Literal.String.Other */\n",
"body .sr { color: #BB6688 } /* Literal.String.Regex */\n",
"body .s1 { color: #BA2121 } /* Literal.String.Single */\n",
"body .ss { color: #19177C } /* Literal.String.Symbol */\n",
"body .bp { color: #008000 } /* Name.Builtin.Pseudo */\n",
"body .fm { color: #0000FF } /* Name.Function.Magic */\n",
"body .vc { color: #19177C } /* Name.Variable.Class */\n",
"body .vg { color: #19177C } /* Name.Variable.Global */\n",
"body .vi { color: #19177C } /* Name.Variable.Instance */\n",
"body .vm { color: #19177C } /* Name.Variable.Magic */\n",
"body .il { color: #666666 } /* Literal.Number.Integer.Long */\n",
"\n",
" </style>\n",
"</head>\n",
"<body>\n",
"<h2></h2>\n",
"\n",
"<div class=\"highlight\"><pre><span></span><span class=\"k\">class</span> <span class=\"nc\">Problem</span><span class=\"p\">(</span><span class=\"nb\">object</span><span class=\"p\">):</span>\n",
"\n",
" <span class=\"sd\">"""The abstract class for a formal problem. You should subclass</span>\n",
"<span class=\"sd\"> this and implement the methods actions and result, and possibly</span>\n",
"<span class=\"sd\"> __init__, goal_test, and path_cost. Then you will create instances</span>\n",
"<span class=\"sd\"> of your subclass and solve them with the various search functions."""</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"fm\">__init__</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">initial</span><span class=\"p\">,</span> <span class=\"n\">goal</span><span class=\"o\">=</span><span class=\"bp\">None</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""The constructor specifies the initial state, and possibly a goal</span>\n",
"<span class=\"sd\"> state, if there is a unique goal. Your subclass's constructor can add</span>\n",
"<span class=\"sd\"> other arguments."""</span>\n",
" <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">initial</span> <span class=\"o\">=</span> <span class=\"n\">initial</span>\n",
" <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">goal</span> <span class=\"o\">=</span> <span class=\"n\">goal</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"nf\">actions</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">state</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""Return the actions that can be executed in the given</span>\n",
"<span class=\"sd\"> state. The result would typically be a list, but if there are</span>\n",
"<span class=\"sd\"> many actions, consider yielding them one at a time in an</span>\n",
"<span class=\"sd\"> iterator, rather than building them all at once."""</span>\n",
" <span class=\"k\">raise</span> <span class=\"ne\">NotImplementedError</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"nf\">result</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">state</span><span class=\"p\">,</span> <span class=\"n\">action</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""Return the state that results from executing the given</span>\n",
"<span class=\"sd\"> action in the given state. The action must be one of</span>\n",
"<span class=\"sd\"> self.actions(state)."""</span>\n",
" <span class=\"k\">raise</span> <span class=\"ne\">NotImplementedError</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"nf\">goal_test</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">state</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""Return True if the state is a goal. The default method compares the</span>\n",
"<span class=\"sd\"> state to self.goal or checks for state in self.goal if it is a</span>\n",
"<span class=\"sd\"> list, as specified in the constructor. Override this method if</span>\n",
"<span class=\"sd\"> checking against a single self.goal is not enough."""</span>\n",
" <span class=\"k\">if</span> <span class=\"nb\">isinstance</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">goal</span><span class=\"p\">,</span> <span class=\"nb\">list</span><span class=\"p\">):</span>\n",
" <span class=\"k\">return</span> <span class=\"n\">is_in</span><span class=\"p\">(</span><span class=\"n\">state</span><span class=\"p\">,</span> <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">goal</span><span class=\"p\">)</span>\n",
" <span class=\"k\">else</span><span class=\"p\">:</span>\n",
" <span class=\"k\">return</span> <span class=\"n\">state</span> <span class=\"o\">==</span> <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">goal</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"nf\">path_cost</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">c</span><span class=\"p\">,</span> <span class=\"n\">state1</span><span class=\"p\">,</span> <span class=\"n\">action</span><span class=\"p\">,</span> <span class=\"n\">state2</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""Return the cost of a solution path that arrives at state2 from</span>\n",
"<span class=\"sd\"> state1 via action, assuming cost c to get up to state1. If the problem</span>\n",
"<span class=\"sd\"> is such that the path doesn't matter, this function will only look at</span>\n",
"<span class=\"sd\"> state2. If the path does matter, it will consider c and maybe state1</span>\n",
"<span class=\"sd\"> and action. The default method costs 1 for every step in the path."""</span>\n",
" <span class=\"k\">return</span> <span class=\"n\">c</span> <span class=\"o\">+</span> <span class=\"mi\">1</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"nf\">value</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">state</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""For optimization problems, each state has a value. Hill-climbing</span>\n",
"<span class=\"sd\"> and related algorithms try to maximize this value."""</span>\n",
" <span class=\"k\">raise</span> <span class=\"ne\">NotImplementedError</span>\n",
"</pre></div>\n",
"</body>\n",
"</html>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"The `Problem` class has six methods.\n",
"\n",
"* `__init__(self, initial, goal)` : This is what is called a `constructor`. It is the first method called when you create an instance of the class as `Problem(initial, goal)`. The variable `initial` specifies the initial state $s_0$ of the search problem. It represents the beginning state. From here, our agent begins its task of exploration to find the goal state(s) which is given in the `goal` parameter.\n",
"\n",
"\n",
"* `actions(self, state)` : This method returns all the possible actions agent can execute in the given state `state`.\n",
"\n",
"\n",
"* `result(self, state, action)` : This returns the resulting state if action `action` is taken in the state `state`. This `Problem` class only deals with deterministic outcomes. So we know for sure what every action in a state would result to.\n",
"\n",
"\n",
"* `goal_test(self, state)` : Return a boolean for a given state - `True` if it is a goal state, else `False`.\n",
"\n",
"\n",
"* `path_cost(self, c, state1, action, state2)` : Return the cost of the path that arrives at `state2` as a result of taking `action` from `state1`, assuming total cost of `c` to get up to `state1`.\n",
"\n",
"\n",
"* `value(self, state)` : This acts as a bit of extra information in problems where we try to optimise a value when we cannot do a goal test."
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## NODE\n",
"\n",
"Let's see how we define a Node. Run the next cell to see how abstract class `Node` is defined in the search module."
]
},
{
"cell_type": "code",
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
"outputs": [
{
"data": {
"text/html": [
"<!DOCTYPE html PUBLIC \"-//W3C//DTD HTML 4.01//EN\"\n",
" \"http://www.w3.org/TR/html4/strict.dtd\">\n",
"\n",
"<html>\n",
"<head>\n",
" <title></title>\n",
" <meta http-equiv=\"content-type\" content=\"text/html; charset=None\">\n",
" <style type=\"text/css\">\n",
"td.linenos { background-color: #f0f0f0; padding-right: 10px; }\n",
"span.lineno { background-color: #f0f0f0; padding: 0 5px 0 5px; }\n",
"pre { line-height: 125%; }\n",
"body .hll { background-color: #ffffcc }\n",
"body { background: #f8f8f8; }\n",
"body .c { color: #408080; font-style: italic } /* Comment */\n",
"body .err { border: 1px solid #FF0000 } /* Error */\n",
"body .k { color: #008000; font-weight: bold } /* Keyword */\n",
"body .o { color: #666666 } /* Operator */\n",
"body .ch { color: #408080; font-style: italic } /* Comment.Hashbang */\n",
"body .cm { color: #408080; font-style: italic } /* Comment.Multiline */\n",
"body .cp { color: #BC7A00 } /* Comment.Preproc */\n",
"body .cpf { color: #408080; font-style: italic } /* Comment.PreprocFile */\n",
"body .c1 { color: #408080; font-style: italic } /* Comment.Single */\n",
"body .cs { color: #408080; font-style: italic } /* Comment.Special */\n",
"body .gd { color: #A00000 } /* Generic.Deleted */\n",
"body .ge { font-style: italic } /* Generic.Emph */\n",
"body .gr { color: #FF0000 } /* Generic.Error */\n",
"body .gh { color: #000080; font-weight: bold } /* Generic.Heading */\n",
"body .gi { color: #00A000 } /* Generic.Inserted */\n",
"body .go { color: #888888 } /* Generic.Output */\n",
"body .gp { color: #000080; font-weight: bold } /* Generic.Prompt */\n",
"body .gs { font-weight: bold } /* Generic.Strong */\n",
"body .gu { color: #800080; font-weight: bold } /* Generic.Subheading */\n",
"body .gt { color: #0044DD } /* Generic.Traceback */\n",
"body .kc { color: #008000; font-weight: bold } /* Keyword.Constant */\n",
"body .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */\n",
"body .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */\n",
"body .kp { color: #008000 } /* Keyword.Pseudo */\n",
"body .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */\n",
"body .kt { color: #B00040 } /* Keyword.Type */\n",
"body .m { color: #666666 } /* Literal.Number */\n",
"body .s { color: #BA2121 } /* Literal.String */\n",
"body .na { color: #7D9029 } /* Name.Attribute */\n",
"body .nb { color: #008000 } /* Name.Builtin */\n",
"body .nc { color: #0000FF; font-weight: bold } /* Name.Class */\n",
"body .no { color: #880000 } /* Name.Constant */\n",
"body .nd { color: #AA22FF } /* Name.Decorator */\n",
"body .ni { color: #999999; font-weight: bold } /* Name.Entity */\n",
"body .ne { color: #D2413A; font-weight: bold } /* Name.Exception */\n",
"body .nf { color: #0000FF } /* Name.Function */\n",
"body .nl { color: #A0A000 } /* Name.Label */\n",
"body .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */\n",
"body .nt { color: #008000; font-weight: bold } /* Name.Tag */\n",
"body .nv { color: #19177C } /* Name.Variable */\n",
"body .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */\n",
"body .w { color: #bbbbbb } /* Text.Whitespace */\n",
"body .mb { color: #666666 } /* Literal.Number.Bin */\n",
"body .mf { color: #666666 } /* Literal.Number.Float */\n",
"body .mh { color: #666666 } /* Literal.Number.Hex */\n",
"body .mi { color: #666666 } /* Literal.Number.Integer */\n",
"body .mo { color: #666666 } /* Literal.Number.Oct */\n",
"body .sa { color: #BA2121 } /* Literal.String.Affix */\n",
"body .sb { color: #BA2121 } /* Literal.String.Backtick */\n",
"body .sc { color: #BA2121 } /* Literal.String.Char */\n",
"body .dl { color: #BA2121 } /* Literal.String.Delimiter */\n",
"body .sd { color: #BA2121; font-style: italic } /* Literal.String.Doc */\n",
"body .s2 { color: #BA2121 } /* Literal.String.Double */\n",
"body .se { color: #BB6622; font-weight: bold } /* Literal.String.Escape */\n",
"body .sh { color: #BA2121 } /* Literal.String.Heredoc */\n",
"body .si { color: #BB6688; font-weight: bold } /* Literal.String.Interpol */\n",
"body .sx { color: #008000 } /* Literal.String.Other */\n",
"body .sr { color: #BB6688 } /* Literal.String.Regex */\n",
"body .s1 { color: #BA2121 } /* Literal.String.Single */\n",
"body .ss { color: #19177C } /* Literal.String.Symbol */\n",
"body .bp { color: #008000 } /* Name.Builtin.Pseudo */\n",
"body .fm { color: #0000FF } /* Name.Function.Magic */\n",
"body .vc { color: #19177C } /* Name.Variable.Class */\n",
"body .vg { color: #19177C } /* Name.Variable.Global */\n",
"body .vi { color: #19177C } /* Name.Variable.Instance */\n",
"body .vm { color: #19177C } /* Name.Variable.Magic */\n",
"body .il { color: #666666 } /* Literal.Number.Integer.Long */\n",
"\n",
" </style>\n",
"</head>\n",
"<body>\n",
"<h2></h2>\n",
"\n",
"<div class=\"highlight\"><pre><span></span><span class=\"k\">class</span> <span class=\"nc\">Node</span><span class=\"p\">:</span>\n",
"\n",
" <span class=\"sd\">"""A node in a search tree. Contains a pointer to the parent (the node</span>\n",
"<span class=\"sd\"> that this is a successor of) and to the actual state for this node. Note</span>\n",
"<span class=\"sd\"> that if a state is arrived at by two paths, then there are two nodes with</span>\n",
"<span class=\"sd\"> the same state. Also includes the action that got us to this state, and</span>\n",
"<span class=\"sd\"> the total path_cost (also known as g) to reach the node. Other functions</span>\n",
"<span class=\"sd\"> may add an f and h value; see best_first_graph_search and astar_search for</span>\n",
"<span class=\"sd\"> an explanation of how the f and h values are handled. You will not need to</span>\n",
"<span class=\"sd\"> subclass this class."""</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"fm\">__init__</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">state</span><span class=\"p\">,</span> <span class=\"n\">parent</span><span class=\"o\">=</span><span class=\"bp\">None</span><span class=\"p\">,</span> <span class=\"n\">action</span><span class=\"o\">=</span><span class=\"bp\">None</span><span class=\"p\">,</span> <span class=\"n\">path_cost</span><span class=\"o\">=</span><span class=\"mi\">0</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""Create a search tree Node, derived from a parent by an action."""</span>\n",
" <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">state</span> <span class=\"o\">=</span> <span class=\"n\">state</span>\n",
" <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">parent</span> <span class=\"o\">=</span> <span class=\"n\">parent</span>\n",
" <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">action</span> <span class=\"o\">=</span> <span class=\"n\">action</span>\n",
" <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">path_cost</span> <span class=\"o\">=</span> <span class=\"n\">path_cost</span>\n",
" <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">depth</span> <span class=\"o\">=</span> <span class=\"mi\">0</span>\n",
" <span class=\"k\">if</span> <span class=\"n\">parent</span><span class=\"p\">:</span>\n",
" <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">depth</span> <span class=\"o\">=</span> <span class=\"n\">parent</span><span class=\"o\">.</span><span class=\"n\">depth</span> <span class=\"o\">+</span> <span class=\"mi\">1</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"fm\">__repr__</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">):</span>\n",
" <span class=\"k\">return</span> <span class=\"s2\">"<Node {}>"</span><span class=\"o\">.</span><span class=\"n\">format</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">state</span><span class=\"p\">)</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"fm\">__lt__</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">node</span><span class=\"p\">):</span>\n",
" <span class=\"k\">return</span> <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">state</span> <span class=\"o\"><</span> <span class=\"n\">node</span><span class=\"o\">.</span><span class=\"n\">state</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"nf\">expand</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">problem</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""List the nodes reachable in one step from this node."""</span>\n",
" <span class=\"k\">return</span> <span class=\"p\">[</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">child_node</span><span class=\"p\">(</span><span class=\"n\">problem</span><span class=\"p\">,</span> <span class=\"n\">action</span><span class=\"p\">)</span>\n",
" <span class=\"k\">for</span> <span class=\"n\">action</span> <span class=\"ow\">in</span> <span class=\"n\">problem</span><span class=\"o\">.</span><span class=\"n\">actions</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">state</span><span class=\"p\">)]</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"nf\">child_node</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">problem</span><span class=\"p\">,</span> <span class=\"n\">action</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""[Figure 3.10]"""</span>\n",
" <span class=\"n\">next_node</span> <span class=\"o\">=</span> <span class=\"n\">problem</span><span class=\"o\">.</span><span class=\"n\">result</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">state</span><span class=\"p\">,</span> <span class=\"n\">action</span><span class=\"p\">)</span>\n",
" <span class=\"k\">return</span> <span class=\"n\">Node</span><span class=\"p\">(</span><span class=\"n\">next_node</span><span class=\"p\">,</span> <span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">action</span><span class=\"p\">,</span>\n",
" <span class=\"n\">problem</span><span class=\"o\">.</span><span class=\"n\">path_cost</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">path_cost</span><span class=\"p\">,</span> <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">state</span><span class=\"p\">,</span>\n",
" <span class=\"n\">action</span><span class=\"p\">,</span> <span class=\"n\">next_node</span><span class=\"p\">))</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"nf\">solution</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""Return the sequence of actions to go from the root to this node."""</span>\n",
" <span class=\"k\">return</span> <span class=\"p\">[</span><span class=\"n\">node</span><span class=\"o\">.</span><span class=\"n\">action</span> <span class=\"k\">for</span> <span class=\"n\">node</span> <span class=\"ow\">in</span> <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">path</span><span class=\"p\">()[</span><span class=\"mi\">1</span><span class=\"p\">:]]</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"nf\">path</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""Return a list of nodes forming the path from the root to this node."""</span>\n",
" <span class=\"n\">node</span><span class=\"p\">,</span> <span class=\"n\">path_back</span> <span class=\"o\">=</span> <span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"p\">[]</span>\n",
" <span class=\"k\">while</span> <span class=\"n\">node</span><span class=\"p\">:</span>\n",
" <span class=\"n\">path_back</span><span class=\"o\">.</span><span class=\"n\">append</span><span class=\"p\">(</span><span class=\"n\">node</span><span class=\"p\">)</span>\n",
" <span class=\"n\">node</span> <span class=\"o\">=</span> <span class=\"n\">node</span><span class=\"o\">.</span><span class=\"n\">parent</span>\n",
" <span class=\"k\">return</span> <span class=\"nb\">list</span><span class=\"p\">(</span><span class=\"nb\">reversed</span><span class=\"p\">(</span><span class=\"n\">path_back</span><span class=\"p\">))</span>\n",
"\n",
" <span class=\"c1\"># We want for a queue of nodes in breadth_first_search or</span>\n",
" <span class=\"c1\"># astar_search to have no duplicated states, so we treat nodes</span>\n",
" <span class=\"c1\"># with the same state as equal. [Problem: this may not be what you</span>\n",
" <span class=\"c1\"># want in other contexts.]</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"fm\">__eq__</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">other</span><span class=\"p\">):</span>\n",
" <span class=\"k\">return</span> <span class=\"nb\">isinstance</span><span class=\"p\">(</span><span class=\"n\">other</span><span class=\"p\">,</span> <span class=\"n\">Node</span><span class=\"p\">)</span> <span class=\"ow\">and</span> <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">state</span> <span class=\"o\">==</span> <span class=\"n\">other</span><span class=\"o\">.</span><span class=\"n\">state</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"fm\">__hash__</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">):</span>\n",
" <span class=\"k\">return</span> <span class=\"nb\">hash</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">state</span><span class=\"p\">)</span>\n",
"</pre></div>\n",
"</body>\n",
"</html>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The `Node` class has nine methods. The first is the `__init__` method.\n",
"* `__init__(self, state, parent, action, path_cost)` : This method creates a node. `parent` represents the node that this is a successor of and `action` is the action required to get from the parent node to this node. `path_cost` is the cost to reach current node from parent node.\n",
"The next 4 methods are specific `Node`-related functions.\n",
"* `expand(self, problem)` : This method lists all the neighbouring(reachable in one step) nodes of current node. \n",
"* `child_node(self, problem, action)` : Given an `action`, this method returns the immediate neighbour that can be reached with that `action`.\n",
"\n",
"* `solution(self)` : This returns the sequence of actions required to reach this node from the root node. \n",
"\n",
"* `path(self)` : This returns a list of all the nodes that lies in the path from the root to this node.\n",
"\n",
"The remaining 4 methods override standards Python functionality for representing an object as a string, the less-than ($<$) operator, the equal-to ($=$) operator, and the `hash` function.\n",
"\n",
"* `__repr__(self)` : This returns the state of this node.\n",
"\n",
"* `__lt__(self, node)` : Given a `node`, this method returns `True` if the state of current node is less than the state of the `node`. Otherwise it returns `False`.\n",
"\n",
"* `__eq__(self, other)` : This method returns `True` if the state of current node is equal to the other node. Else it returns `False`.\n",
"\n",
"* `__hash__(self)` : This returns the hash of the state of current node."
]
},
"We will use the abstract class `Problem` to define our real **problem** named `GraphProblem`. You can see how we define `GraphProblem` by running the next cell."
{
"cell_type": "code",
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
"outputs": [
{
"data": {
"text/html": [
"<!DOCTYPE html PUBLIC \"-//W3C//DTD HTML 4.01//EN\"\n",
" \"http://www.w3.org/TR/html4/strict.dtd\">\n",
"\n",
"<html>\n",
"<head>\n",
" <title></title>\n",
" <meta http-equiv=\"content-type\" content=\"text/html; charset=None\">\n",
" <style type=\"text/css\">\n",
"td.linenos { background-color: #f0f0f0; padding-right: 10px; }\n",
"span.lineno { background-color: #f0f0f0; padding: 0 5px 0 5px; }\n",
"pre { line-height: 125%; }\n",
"body .hll { background-color: #ffffcc }\n",
"body { background: #f8f8f8; }\n",
"body .c { color: #408080; font-style: italic } /* Comment */\n",
"body .err { border: 1px solid #FF0000 } /* Error */\n",
"body .k { color: #008000; font-weight: bold } /* Keyword */\n",
"body .o { color: #666666 } /* Operator */\n",
"body .ch { color: #408080; font-style: italic } /* Comment.Hashbang */\n",
"body .cm { color: #408080; font-style: italic } /* Comment.Multiline */\n",
"body .cp { color: #BC7A00 } /* Comment.Preproc */\n",
"body .cpf { color: #408080; font-style: italic } /* Comment.PreprocFile */\n",
"body .c1 { color: #408080; font-style: italic } /* Comment.Single */\n",
"body .cs { color: #408080; font-style: italic } /* Comment.Special */\n",
"body .gd { color: #A00000 } /* Generic.Deleted */\n",
"body .ge { font-style: italic } /* Generic.Emph */\n",
"body .gr { color: #FF0000 } /* Generic.Error */\n",
"body .gh { color: #000080; font-weight: bold } /* Generic.Heading */\n",
"body .gi { color: #00A000 } /* Generic.Inserted */\n",
"body .go { color: #888888 } /* Generic.Output */\n",
"body .gp { color: #000080; font-weight: bold } /* Generic.Prompt */\n",
"body .gs { font-weight: bold } /* Generic.Strong */\n",
"body .gu { color: #800080; font-weight: bold } /* Generic.Subheading */\n",
"body .gt { color: #0044DD } /* Generic.Traceback */\n",
"body .kc { color: #008000; font-weight: bold } /* Keyword.Constant */\n",
"body .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */\n",
"body .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */\n",
"body .kp { color: #008000 } /* Keyword.Pseudo */\n",
"body .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */\n",
"body .kt { color: #B00040 } /* Keyword.Type */\n",
"body .m { color: #666666 } /* Literal.Number */\n",
"body .s { color: #BA2121 } /* Literal.String */\n",
"body .na { color: #7D9029 } /* Name.Attribute */\n",
"body .nb { color: #008000 } /* Name.Builtin */\n",
"body .nc { color: #0000FF; font-weight: bold } /* Name.Class */\n",
"body .no { color: #880000 } /* Name.Constant */\n",
"body .nd { color: #AA22FF } /* Name.Decorator */\n",
"body .ni { color: #999999; font-weight: bold } /* Name.Entity */\n",
"body .ne { color: #D2413A; font-weight: bold } /* Name.Exception */\n",
"body .nf { color: #0000FF } /* Name.Function */\n",
"body .nl { color: #A0A000 } /* Name.Label */\n",
"body .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */\n",
"body .nt { color: #008000; font-weight: bold } /* Name.Tag */\n",
"body .nv { color: #19177C } /* Name.Variable */\n",
"body .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */\n",
"body .w { color: #bbbbbb } /* Text.Whitespace */\n",
"body .mb { color: #666666 } /* Literal.Number.Bin */\n",
"body .mf { color: #666666 } /* Literal.Number.Float */\n",
"body .mh { color: #666666 } /* Literal.Number.Hex */\n",
"body .mi { color: #666666 } /* Literal.Number.Integer */\n",
"body .mo { color: #666666 } /* Literal.Number.Oct */\n",
"body .sa { color: #BA2121 } /* Literal.String.Affix */\n",
"body .sb { color: #BA2121 } /* Literal.String.Backtick */\n",
"body .sc { color: #BA2121 } /* Literal.String.Char */\n",
"body .dl { color: #BA2121 } /* Literal.String.Delimiter */\n",
"body .sd { color: #BA2121; font-style: italic } /* Literal.String.Doc */\n",
"body .s2 { color: #BA2121 } /* Literal.String.Double */\n",
"body .se { color: #BB6622; font-weight: bold } /* Literal.String.Escape */\n",
"body .sh { color: #BA2121 } /* Literal.String.Heredoc */\n",
"body .si { color: #BB6688; font-weight: bold } /* Literal.String.Interpol */\n",
"body .sx { color: #008000 } /* Literal.String.Other */\n",
"body .sr { color: #BB6688 } /* Literal.String.Regex */\n",
"body .s1 { color: #BA2121 } /* Literal.String.Single */\n",
"body .ss { color: #19177C } /* Literal.String.Symbol */\n",
"body .bp { color: #008000 } /* Name.Builtin.Pseudo */\n",
"body .fm { color: #0000FF } /* Name.Function.Magic */\n",
"body .vc { color: #19177C } /* Name.Variable.Class */\n",
"body .vg { color: #19177C } /* Name.Variable.Global */\n",
"body .vi { color: #19177C } /* Name.Variable.Instance */\n",
"body .vm { color: #19177C } /* Name.Variable.Magic */\n",
"body .il { color: #666666 } /* Literal.Number.Integer.Long */\n",
"\n",
" </style>\n",
"</head>\n",
"<body>\n",
"<h2></h2>\n",
"\n",
"<div class=\"highlight\"><pre><span></span><span class=\"k\">class</span> <span class=\"nc\">GraphProblem</span><span class=\"p\">(</span><span class=\"n\">Problem</span><span class=\"p\">):</span>\n",
"\n",
" <span class=\"sd\">"""The problem of searching a graph from one node to another."""</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"fm\">__init__</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">initial</span><span class=\"p\">,</span> <span class=\"n\">goal</span><span class=\"p\">,</span> <span class=\"n\">graph</span><span class=\"p\">):</span>\n",
" <span class=\"n\">Problem</span><span class=\"o\">.</span><span class=\"fm\">__init__</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">initial</span><span class=\"p\">,</span> <span class=\"n\">goal</span><span class=\"p\">)</span>\n",
" <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">graph</span> <span class=\"o\">=</span> <span class=\"n\">graph</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"nf\">actions</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">A</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""The actions at a graph node are just its neighbors."""</span>\n",
" <span class=\"k\">return</span> <span class=\"nb\">list</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">graph</span><span class=\"o\">.</span><span class=\"n\">get</span><span class=\"p\">(</span><span class=\"n\">A</span><span class=\"p\">)</span><span class=\"o\">.</span><span class=\"n\">keys</span><span class=\"p\">())</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"nf\">result</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">state</span><span class=\"p\">,</span> <span class=\"n\">action</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""The result of going to a neighbor is just that neighbor."""</span>\n",
" <span class=\"k\">return</span> <span class=\"n\">action</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"nf\">path_cost</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">cost_so_far</span><span class=\"p\">,</span> <span class=\"n\">A</span><span class=\"p\">,</span> <span class=\"n\">action</span><span class=\"p\">,</span> <span class=\"n\">B</span><span class=\"p\">):</span>\n",
" <span class=\"k\">return</span> <span class=\"n\">cost_so_far</span> <span class=\"o\">+</span> <span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">graph</span><span class=\"o\">.</span><span class=\"n\">get</span><span class=\"p\">(</span><span class=\"n\">A</span><span class=\"p\">,</span> <span class=\"n\">B</span><span class=\"p\">)</span> <span class=\"ow\">or</span> <span class=\"n\">infinity</span><span class=\"p\">)</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"nf\">find_min_edge</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""Find minimum value of edges."""</span>\n",
" <span class=\"n\">m</span> <span class=\"o\">=</span> <span class=\"n\">infinity</span>\n",
" <span class=\"k\">for</span> <span class=\"n\">d</span> <span class=\"ow\">in</span> <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">graph</span><span class=\"o\">.</span><span class=\"n\">graph_dict</span><span class=\"o\">.</span><span class=\"n\">values</span><span class=\"p\">():</span>\n",
" <span class=\"n\">local_min</span> <span class=\"o\">=</span> <span class=\"nb\">min</span><span class=\"p\">(</span><span class=\"n\">d</span><span class=\"o\">.</span><span class=\"n\">values</span><span class=\"p\">())</span>\n",
" <span class=\"n\">m</span> <span class=\"o\">=</span> <span class=\"nb\">min</span><span class=\"p\">(</span><span class=\"n\">m</span><span class=\"p\">,</span> <span class=\"n\">local_min</span><span class=\"p\">)</span>\n",
"\n",
" <span class=\"k\">return</span> <span class=\"n\">m</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"nf\">h</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">node</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""h function is straight-line distance from a node's state to goal."""</span>\n",
" <span class=\"n\">locs</span> <span class=\"o\">=</span> <span class=\"nb\">getattr</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">graph</span><span class=\"p\">,</span> <span class=\"s1\">'locations'</span><span class=\"p\">,</span> <span class=\"bp\">None</span><span class=\"p\">)</span>\n",
" <span class=\"k\">if</span> <span class=\"n\">locs</span><span class=\"p\">:</span>\n",
" <span class=\"k\">if</span> <span class=\"nb\">type</span><span class=\"p\">(</span><span class=\"n\">node</span><span class=\"p\">)</span> <span class=\"ow\">is</span> <span class=\"nb\">str</span><span class=\"p\">:</span>\n",
" <span class=\"k\">return</span> <span class=\"nb\">int</span><span class=\"p\">(</span><span class=\"n\">distance</span><span class=\"p\">(</span><span class=\"n\">locs</span><span class=\"p\">[</span><span class=\"n\">node</span><span class=\"p\">],</span> <span class=\"n\">locs</span><span class=\"p\">[</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">goal</span><span class=\"p\">]))</span>\n",
"\n",
" <span class=\"k\">return</span> <span class=\"nb\">int</span><span class=\"p\">(</span><span class=\"n\">distance</span><span class=\"p\">(</span><span class=\"n\">locs</span><span class=\"p\">[</span><span class=\"n\">node</span><span class=\"o\">.</span><span class=\"n\">state</span><span class=\"p\">],</span> <span class=\"n\">locs</span><span class=\"p\">[</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">goal</span><span class=\"p\">]))</span>\n",
" <span class=\"k\">else</span><span class=\"p\">:</span>\n",
" <span class=\"k\">return</span> <span class=\"n\">infinity</span>\n",
"</pre></div>\n",
"</body>\n",
"</html>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"Have a look at our romania_map, which is an Undirected Graph containing a dict of nodes as keys and neighbours as values."
"metadata": {
"collapsed": true
},
"romania_map = UndirectedGraph(dict(\n",
" Arad=dict(Zerind=75, Sibiu=140, Timisoara=118),\n",
" Bucharest=dict(Urziceni=85, Pitesti=101, Giurgiu=90, Fagaras=211),\n",
" Craiova=dict(Drobeta=120, Rimnicu=146, Pitesti=138),\n",
" Drobeta=dict(Mehadia=75),\n",
" Eforie=dict(Hirsova=86),\n",
" Fagaras=dict(Sibiu=99),\n",
" Hirsova=dict(Urziceni=98),\n",
" Iasi=dict(Vaslui=92, Neamt=87),\n",
" Lugoj=dict(Timisoara=111, Mehadia=70),\n",
" Oradea=dict(Zerind=71, Sibiu=151),\n",
" Pitesti=dict(Rimnicu=97),\n",
" Rimnicu=dict(Sibiu=80),\n",
" Urziceni=dict(Vaslui=142)))\n",
"\n",
"romania_map.locations = dict(\n",
" Arad=(91, 492), Bucharest=(400, 327), Craiova=(253, 288),\n",
" Drobeta=(165, 299), Eforie=(562, 293), Fagaras=(305, 449),\n",
" Giurgiu=(375, 270), Hirsova=(534, 350), Iasi=(473, 506),\n",
" Lugoj=(165, 379), Mehadia=(168, 339), Neamt=(406, 537),\n",
" Oradea=(131, 571), Pitesti=(320, 368), Rimnicu=(233, 410),\n",
" Sibiu=(207, 457), Timisoara=(94, 410), Urziceni=(456, 350),\n",
" Vaslui=(509, 444), Zerind=(108, 531))"
]
},
{
"cell_type": "markdown",
"metadata": {
"It is pretty straightforward to understand this `romania_map`. The first node **Arad** has three neighbours named **Zerind**, **Sibiu**, **Timisoara**. Each of these nodes are 75, 140, 118 units apart from **Arad** respectively. And the same goes with other nodes.\n",
"\n",
"And `romania_map.locations` contains the positions of each of the nodes. We will use the straight line distance (which is different from the one provided in `romania_map`) between two cities in algorithms like A\\*-search and Recursive Best First Search.\n",
"\n",
"**Define a problem:**\n",
"Now it's time to define our problem. We will define it by passing `initial`, `goal`, `graph` to `GraphProblem`. So, our problem is to find the goal state starting from the given initial state on the provided graph. \n",
"\n",
"Say we want to start exploring from **Arad** and try to find **Bucharest** in our romania_map. So, this is how we do it."
"metadata": {
"collapsed": true
},
"outputs": [],
"romania_problem = GraphProblem('Arad', 'Bucharest', romania_map)"
"### Romania Map Visualisation\n",
"Let's have a visualisation of Romania map [Figure 3.2] from the book and see how different searching algorithms perform / how frontier expands in each search algorithm for a simple problem named `romania_problem`."
"Have a look at `romania_locations`. It is a dictionary defined in search module. We will use these location values to draw the romania graph using **networkx**."
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"{'Arad': (91, 492), 'Bucharest': (400, 327), 'Craiova': (253, 288), 'Drobeta': (165, 299), 'Eforie': (562, 293), 'Fagaras': (305, 449), 'Giurgiu': (375, 270), 'Hirsova': (534, 350), 'Iasi': (473, 506), 'Lugoj': (165, 379), 'Mehadia': (168, 339), 'Neamt': (406, 537), 'Oradea': (131, 571), 'Pitesti': (320, 368), 'Rimnicu': (233, 410), 'Sibiu': (207, 457), 'Timisoara': (94, 410), 'Urziceni': (456, 350), 'Vaslui': (509, 444), 'Zerind': (108, 531)}\n"
]
}
],
"source": [
"romania_locations = romania_map.locations\n",
"print(romania_locations)"
]
},
{
"cell_type": "markdown",
"source": [
"Let's get started by initializing an empty graph. We will add nodes, place the nodes in their location as shown in the book, add edges to the graph."
]
},
"metadata": {
"collapsed": true
},
"# node colors, node positions and node label positions\n",
"node_colors = {node: 'white' for node in romania_map.locations.keys()}\n",
"node_positions = romania_map.locations\n",
"node_label_pos = { k:[v[0],v[1]-10] for k,v in romania_map.locations.items() }\n",
"edge_weights = {(k, k2) : v2 for k, v in romania_map.graph_dict.items() for k2, v2 in v.items()}\n",
"romania_graph_data = { 'graph_dict' : romania_map.graph_dict,\n",
" 'node_colors': node_colors,\n",
" 'node_positions': node_positions,\n",
" 'node_label_positions': node_label_pos,\n",
" 'edge_weights': edge_weights\n",
" }"
]
},
{
"cell_type": "markdown",
"We have completed building our graph based on romania_map and its locations. It's time to display it here in the notebook. This function `show_map(node_colors)` helps us do that. We will be calling this function later on to display the map at each and every interval step while searching, using variety of algorithms from the book."
]
},
{
"cell_type": "markdown",
"source": [
"We can simply call the function with node_colors dictionary object to display it."
]
},
{
"cell_type": "code",
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAABTsAAAPKCAYAAABbVI7QAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n3TM5BbM0AAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x2871d1eda58>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"show_map(romania_graph_data)"
]
},
{
"cell_type": "markdown",
"source": [
"Voila! You see, the romania map as shown in the Figure[3.2] in the book. Now, see how different searching algorithms perform with our problem statements."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## SIMPLE PROBLEM SOLVING AGENT PROGRAM\n",
"\n",
"Let us now define a Simple Problem Solving Agent Program. Run the next cell to see how the abstract class `SimpleProblemSolvingAgentProgram` is defined in the search module."
]
},
{
"cell_type": "code",
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
"outputs": [
{
"data": {
"text/html": [
"<!DOCTYPE html PUBLIC \"-//W3C//DTD HTML 4.01//EN\"\n",
" \"http://www.w3.org/TR/html4/strict.dtd\">\n",
"\n",
"<html>\n",
"<head>\n",
" <title></title>\n",
" <meta http-equiv=\"content-type\" content=\"text/html; charset=None\">\n",
" <style type=\"text/css\">\n",
"td.linenos { background-color: #f0f0f0; padding-right: 10px; }\n",
"span.lineno { background-color: #f0f0f0; padding: 0 5px 0 5px; }\n",
"pre { line-height: 125%; }\n",
"body .hll { background-color: #ffffcc }\n",
"body { background: #f8f8f8; }\n",
"body .c { color: #408080; font-style: italic } /* Comment */\n",
"body .err { border: 1px solid #FF0000 } /* Error */\n",
"body .k { color: #008000; font-weight: bold } /* Keyword */\n",
"body .o { color: #666666 } /* Operator */\n",
"body .ch { color: #408080; font-style: italic } /* Comment.Hashbang */\n",
"body .cm { color: #408080; font-style: italic } /* Comment.Multiline */\n",
"body .cp { color: #BC7A00 } /* Comment.Preproc */\n",
"body .cpf { color: #408080; font-style: italic } /* Comment.PreprocFile */\n",
"body .c1 { color: #408080; font-style: italic } /* Comment.Single */\n",
"body .cs { color: #408080; font-style: italic } /* Comment.Special */\n",
"body .gd { color: #A00000 } /* Generic.Deleted */\n",
"body .ge { font-style: italic } /* Generic.Emph */\n",
"body .gr { color: #FF0000 } /* Generic.Error */\n",
"body .gh { color: #000080; font-weight: bold } /* Generic.Heading */\n",
"body .gi { color: #00A000 } /* Generic.Inserted */\n",
"body .go { color: #888888 } /* Generic.Output */\n",
"body .gp { color: #000080; font-weight: bold } /* Generic.Prompt */\n",
"body .gs { font-weight: bold } /* Generic.Strong */\n",
"body .gu { color: #800080; font-weight: bold } /* Generic.Subheading */\n",
"body .gt { color: #0044DD } /* Generic.Traceback */\n",
"body .kc { color: #008000; font-weight: bold } /* Keyword.Constant */\n",
"body .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */\n",
"body .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */\n",
"body .kp { color: #008000 } /* Keyword.Pseudo */\n",
"body .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */\n",
"body .kt { color: #B00040 } /* Keyword.Type */\n",
"body .m { color: #666666 } /* Literal.Number */\n",
"body .s { color: #BA2121 } /* Literal.String */\n",
"body .na { color: #7D9029 } /* Name.Attribute */\n",
"body .nb { color: #008000 } /* Name.Builtin */\n",
"body .nc { color: #0000FF; font-weight: bold } /* Name.Class */\n",
"body .no { color: #880000 } /* Name.Constant */\n",
"body .nd { color: #AA22FF } /* Name.Decorator */\n",
"body .ni { color: #999999; font-weight: bold } /* Name.Entity */\n",
"body .ne { color: #D2413A; font-weight: bold } /* Name.Exception */\n",
"body .nf { color: #0000FF } /* Name.Function */\n",
"body .nl { color: #A0A000 } /* Name.Label */\n",
"body .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */\n",
"body .nt { color: #008000; font-weight: bold } /* Name.Tag */\n",
"body .nv { color: #19177C } /* Name.Variable */\n",
"body .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */\n",
"body .w { color: #bbbbbb } /* Text.Whitespace */\n",
"body .mb { color: #666666 } /* Literal.Number.Bin */\n",
"body .mf { color: #666666 } /* Literal.Number.Float */\n",
"body .mh { color: #666666 } /* Literal.Number.Hex */\n",
"body .mi { color: #666666 } /* Literal.Number.Integer */\n",
"body .mo { color: #666666 } /* Literal.Number.Oct */\n",
"body .sa { color: #BA2121 } /* Literal.String.Affix */\n",
"body .sb { color: #BA2121 } /* Literal.String.Backtick */\n",
"body .sc { color: #BA2121 } /* Literal.String.Char */\n",
"body .dl { color: #BA2121 } /* Literal.String.Delimiter */\n",
"body .sd { color: #BA2121; font-style: italic } /* Literal.String.Doc */\n",
"body .s2 { color: #BA2121 } /* Literal.String.Double */\n",
"body .se { color: #BB6622; font-weight: bold } /* Literal.String.Escape */\n",
"body .sh { color: #BA2121 } /* Literal.String.Heredoc */\n",
"body .si { color: #BB6688; font-weight: bold } /* Literal.String.Interpol */\n",
"body .sx { color: #008000 } /* Literal.String.Other */\n",
"body .sr { color: #BB6688 } /* Literal.String.Regex */\n",
"body .s1 { color: #BA2121 } /* Literal.String.Single */\n",
"body .ss { color: #19177C } /* Literal.String.Symbol */\n",
"body .bp { color: #008000 } /* Name.Builtin.Pseudo */\n",
"body .fm { color: #0000FF } /* Name.Function.Magic */\n",
"body .vc { color: #19177C } /* Name.Variable.Class */\n",
"body .vg { color: #19177C } /* Name.Variable.Global */\n",
"body .vi { color: #19177C } /* Name.Variable.Instance */\n",
"body .vm { color: #19177C } /* Name.Variable.Magic */\n",
"body .il { color: #666666 } /* Literal.Number.Integer.Long */\n",
"\n",
" </style>\n",
"</head>\n",
"<body>\n",
"<h2></h2>\n",
"\n",
"<div class=\"highlight\"><pre><span></span><span class=\"k\">class</span> <span class=\"nc\">SimpleProblemSolvingAgentProgram</span><span class=\"p\">:</span>\n",
"\n",
" <span class=\"sd\">"""Abstract framework for a problem-solving agent. [Figure 3.1]"""</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"fm\">__init__</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">initial_state</span><span class=\"o\">=</span><span class=\"bp\">None</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""State is an abstract representation of the state</span>\n",
"<span class=\"sd\"> of the world, and seq is the list of actions required</span>\n",
"<span class=\"sd\"> to get to a particular state from the initial state(root)."""</span>\n",
" <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">state</span> <span class=\"o\">=</span> <span class=\"n\">initial_state</span>\n",
" <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">seq</span> <span class=\"o\">=</span> <span class=\"p\">[]</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"fm\">__call__</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">percept</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""[Figure 3.1] Formulate a goal and problem, then</span>\n",
"<span class=\"sd\"> search for a sequence of actions to solve it."""</span>\n",
" <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">state</span> <span class=\"o\">=</span> <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">update_state</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">state</span><span class=\"p\">,</span> <span class=\"n\">percept</span><span class=\"p\">)</span>\n",
" <span class=\"k\">if</span> <span class=\"ow\">not</span> <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">seq</span><span class=\"p\">:</span>\n",
" <span class=\"n\">goal</span> <span class=\"o\">=</span> <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">formulate_goal</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">state</span><span class=\"p\">)</span>\n",
" <span class=\"n\">problem</span> <span class=\"o\">=</span> <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">formulate_problem</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">state</span><span class=\"p\">,</span> <span class=\"n\">goal</span><span class=\"p\">)</span>\n",
" <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">seq</span> <span class=\"o\">=</span> <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">search</span><span class=\"p\">(</span><span class=\"n\">problem</span><span class=\"p\">)</span>\n",
" <span class=\"k\">if</span> <span class=\"ow\">not</span> <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">seq</span><span class=\"p\">:</span>\n",
" <span class=\"k\">return</span> <span class=\"bp\">None</span>\n",
" <span class=\"k\">return</span> <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">seq</span><span class=\"o\">.</span><span class=\"n\">pop</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">)</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"nf\">update_state</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">state</span><span class=\"p\">,</span> <span class=\"n\">percept</span><span class=\"p\">):</span>\n",
" <span class=\"k\">raise</span> <span class=\"ne\">NotImplementedError</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"nf\">formulate_goal</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">state</span><span class=\"p\">):</span>\n",
" <span class=\"k\">raise</span> <span class=\"ne\">NotImplementedError</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"nf\">formulate_problem</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">state</span><span class=\"p\">,</span> <span class=\"n\">goal</span><span class=\"p\">):</span>\n",
" <span class=\"k\">raise</span> <span class=\"ne\">NotImplementedError</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"nf\">search</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">problem</span><span class=\"p\">):</span>\n",
" <span class=\"k\">raise</span> <span class=\"ne\">NotImplementedError</span>\n",
"</pre></div>\n",
"</body>\n",
"</html>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"psource(SimpleProblemSolvingAgentProgram)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The SimpleProblemSolvingAgentProgram class has six methods: \n",
"\n",
"* `__init__(self, intial_state=None)`: This is the `contructor` of the class and is the first method to be called when the class is instantiated. It takes in a keyword argument, `initial_state` which is initially `None`. The argument `initial_state` represents the state from which the agent starts.\n",
"\n",
"* `__call__(self, percept)`: This method updates the `state` of the agent based on its `percept` using the `update_state` method. It then formulates a `goal` with the help of `formulate_goal` method and a `problem` using the `formulate_problem` method and returns a sequence of actions to solve it (using the `search` method).\n",
"\n",
"* `update_state(self, percept)`: This method updates the `state` of the agent based on its `percept`.\n",
"\n",
"* `formulate_goal(self, state)`: Given a `state` of the agent, this method formulates the `goal` for it.\n",
"\n",
"* `formulate_problem(self, state, goal)`: It is used in problem formulation given a `state` and a `goal` for the `agent`.\n",
"\n",
"* `search(self, problem)`: This method is used to search a sequence of `actions` to solve a `problem`."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us now define a Simple Problem Solving Agent Program. We will create a simple `vacuumAgent` class which will inherit from the abstract class `SimpleProblemSolvingAgentProgram` and overrides its methods. We will create a simple intelligent vacuum agent which can be in any one of the following states. It will move to any other state depending upon the current state as shown in the picture by arrows:\n",
"\n",
""
]
},
{
"cell_type": "code",
"metadata": {
"collapsed": true
},
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
"outputs": [],
"source": [
"class vacuumAgent(SimpleProblemSolvingAgentProgram):\n",
" def update_state(self, state, percept):\n",
" return percept\n",
"\n",
" def formulate_goal(self, state):\n",
" goal = [state7, state8]\n",
" return goal \n",
"\n",
" def formulate_problem(self, state, goal):\n",
" problem = state\n",
" return problem \n",
" \n",
" def search(self, problem):\n",
" if problem == state1:\n",
" seq = [\"Suck\", \"Right\", \"Suck\"]\n",
" elif problem == state2:\n",
" seq = [\"Suck\", \"Left\", \"Suck\"]\n",
" elif problem == state3:\n",
" seq = [\"Right\", \"Suck\"]\n",
" elif problem == state4:\n",
" seq = [\"Suck\"]\n",
" elif problem == state5:\n",
" seq = [\"Suck\"]\n",
" elif problem == state6:\n",
" seq = [\"Left\", \"Suck\"]\n",
" return seq"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now, we will define all the 8 states and create an object of the above class. Then, we will pass it different states and check the output:"
]
},
{
"cell_type": "code",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Left\n",
"Suck\n",
"Right\n"
]
}
],
"state1 = [(0, 0), [(0, 0), \"Dirty\"], [(1, 0), [\"Dirty\"]]]\n",
"state2 = [(1, 0), [(0, 0), \"Dirty\"], [(1, 0), [\"Dirty\"]]]\n",
"state3 = [(0, 0), [(0, 0), \"Clean\"], [(1, 0), [\"Dirty\"]]]\n",
"state4 = [(1, 0), [(0, 0), \"Clean\"], [(1, 0), [\"Dirty\"]]]\n",
"state5 = [(0, 0), [(0, 0), \"Dirty\"], [(1, 0), [\"Clean\"]]]\n",
"state6 = [(1, 0), [(0, 0), \"Dirty\"], [(1, 0), [\"Clean\"]]]\n",
"state7 = [(0, 0), [(0, 0), \"Clean\"], [(1, 0), [\"Clean\"]]]\n",
"state8 = [(1, 0), [(0, 0), \"Clean\"], [(1, 0), [\"Clean\"]]]\n",
"a = vacuumAgent(state1)\n",
"print(a(state6)) \n",
"print(a(state1))\n",
"print(a(state3))"
{
"cell_type": "markdown",
"## SEARCHING ALGORITHMS VISUALIZATION\n",
"In this section, we have visualizations of the following searching algorithms:\n",
"1. Breadth First Tree Search\n",
"2. Depth First Tree Search\n",
"3. Breadth First Search\n",
"4. Depth First Graph Search\n",
"5. Best First Graph Search\n",
"6. Uniform Cost Search\n",
"7. Depth Limited Search\n",
"8. Iterative Deepening Search\n",
"10. Recursive Best First Search\n",
"\n",
"We add the colors to the nodes to have a nice visualisation when displaying. So, these are the different colors we are using in these visuals:\n",
"* Un-explored nodes - <font color='black'>white</font>\n",
"* Frontier nodes - <font color='orange'>orange</font>\n",
"* Currently exploring node - <font color='red'>red</font>\n",
"* Already explored nodes - <font color='gray'>gray</font>"
]
},
{
"cell_type": "markdown",
"## 1. BREADTH-FIRST TREE SEARCH\n",
"We have a working implementation in search module. But as we want to interact with the graph while it is searching, we need to modify the implementation. Here's the modified breadth first tree search."
]
},
{
"cell_type": "code",
"metadata": {
"collapsed": true
},
"source": [
"def tree_search_for_vis(problem, frontier):\n",
" \"\"\"Search through the successors of a problem to find a goal.\n",
" The argument frontier should be an empty queue.\n",
" Don't worry about repeated paths to a state. [Figure 3.7]\"\"\"\n",
" \n",
" # we use these two variables at the time of visualisations\n",
" iterations = 0\n",
" all_node_colors = []\n",
" node_colors = {k : 'white' for k in problem.graph.nodes()}\n",
" \n",
" frontier.append(Node(problem.initial))\n",
" node_colors[Node(problem.initial).state] = \"orange\"\n",
" iterations += 1\n",
" all_node_colors.append(dict(node_colors))\n",
" \n",
" while frontier:\n",
" node = frontier.pop()\n",
" \n",
" # modify the currently searching node to red\n",
" node_colors[node.state] = \"red\"\n",
" iterations += 1\n",
" all_node_colors.append(dict(node_colors))\n",
" \n",
" if problem.goal_test(node.state):\n",
" # modify goal node to green after reaching the goal\n",
" node_colors[node.state] = \"green\"\n",
" iterations += 1\n",
" all_node_colors.append(dict(node_colors))\n",
" return(iterations, all_node_colors, node)\n",
" frontier.extend(node.expand(problem))\n",
" \n",
" for n in node.expand(problem):\n",
" node_colors[n.state] = \"orange\"\n",
" iterations += 1\n",
" all_node_colors.append(dict(node_colors))\n",
" # modify the color of explored nodes to gray\n",
" node_colors[node.state] = \"gray\"\n",
" iterations += 1\n",
" all_node_colors.append(dict(node_colors))\n",
" return None\n",
"\n",
"def breadth_first_tree_search_(problem):\n",
" \"Search the shallowest nodes in the search tree first.\"\n",
" iterations, all_node_colors, node = tree_search_for_vis(problem, FIFOQueue())\n",
" return(iterations, all_node_colors, node)"
]
},
{
"cell_type": "markdown",
"Now, we use `ipywidgets` to display a slider, a button and our romania map. By sliding the slider we can have a look at all the intermediate steps of a particular search algorithm. By pressing the button **Visualize**, you can see all the steps without interacting with the slider. These two helper functions are the callback functions which are called when we interact with the slider and the button."
{
"cell_type": "code",
"metadata": {},
"source": [
"all_node_colors = []\n",
"romania_problem = GraphProblem('Arad', 'Fagaras', romania_map)\n",
"a, b, c = breadth_first_tree_search_(romania_problem)\n",
"display_visual(romania_graph_data, user_input=False, \n",
" algorithm=breadth_first_tree_search_, \n",
" problem=romania_problem)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 2. Depth-First Tree Search:\n",
"Now let's discuss another searching algorithm, Depth-First Tree Search."
]
},
{
"cell_type": "code",
"metadata": {
"collapsed": true
},
"def depth_first_tree_search_graph(problem):\n",
" \"Search the deepest nodes in the search tree first.\"\n",
" # This algorithm might not work in case of repeated paths\n",
" # and may run into an infinite while loop.\n",
" iterations, all_node_colors, node = tree_search_for_vis(problem, Stack())\n",
" return(iterations, all_node_colors, node)"
]
},
{
"cell_type": "code",
"metadata": {},
"all_node_colors = []\n",
"romania_problem = GraphProblem('Arad', 'Oradea', romania_map)\n",
"display_visual(romania_graph_data, user_input=False, \n",
" algorithm=depth_first_tree_search_graph, \n",
" problem=romania_problem)"
]
},
{
"cell_type": "markdown",
"metadata": {
"## 3. BREADTH-FIRST GRAPH SEARCH\n",
"Let's change all the `node_colors` to starting position and define a different problem statement."
]
},
{
"cell_type": "code",
},
"outputs": [],
"source": [
"def breadth_first_search_graph(problem):\n",
" \"[Figure 3.11]\"\n",
" \n",
" # we use these two variables at the time of visualisations\n",
" iterations = 0\n",
" all_node_colors = []\n",
" node_colors = {k : 'white' for k in problem.graph.nodes()}\n",
" \n",
" node = Node(problem.initial)\n",
" \n",
" node_colors[node.state] = \"red\"\n",
" iterations += 1\n",
" all_node_colors.append(dict(node_colors))\n",
" \n",
" if problem.goal_test(node.state):\n",
" node_colors[node.state] = \"green\"\n",
" iterations += 1\n",
" all_node_colors.append(dict(node_colors))\n",
" return(iterations, all_node_colors, node)\n",
" \n",
" frontier = FIFOQueue()\n",
" frontier.append(node)\n",
" \n",
" # modify the color of frontier nodes to blue\n",
" node_colors[node.state] = \"orange\"\n",
" iterations += 1\n",
" all_node_colors.append(dict(node_colors))\n",
" \n",
" explored = set()\n",
" while frontier:\n",
" node = frontier.pop()\n",
" node_colors[node.state] = \"red\"\n",
" iterations += 1\n",
" all_node_colors.append(dict(node_colors))\n",
" \n",
" explored.add(node.state) \n",
" \n",
" for child in node.expand(problem):\n",
" if child.state not in explored and child not in frontier:\n",
" if problem.goal_test(child.state):\n",
" node_colors[child.state] = \"green\"\n",
" iterations += 1\n",
" all_node_colors.append(dict(node_colors))\n",
" return(iterations, all_node_colors, child)\n",
" frontier.append(child)\n",
"\n",
" node_colors[child.state] = \"orange\"\n",
" iterations += 1\n",
" all_node_colors.append(dict(node_colors))\n",
" \n",
" node_colors[node.state] = \"gray\"\n",
" iterations += 1\n",
" all_node_colors.append(dict(node_colors))\n",
" return None"
]
},
{
"cell_type": "code",
"metadata": {},
"source": [
"all_node_colors = []\n",
"romania_problem = GraphProblem('Arad', 'Bucharest', romania_map)\n",
"display_visual(romania_graph_data, user_input=False, \n",
" algorithm=breadth_first_search_graph, \n",
" problem=romania_problem)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 4. Depth-First Graph Search: \n",
"Although we have a working implementation in search module, we have to make a few changes in the algorithm to make it suitable for visualization."
]
},
{
"cell_type": "code",
"metadata": {
"collapsed": true
},
"def graph_search_for_vis(problem, frontier):\n",
" \"\"\"Search through the successors of a problem to find a goal.\n",
" The argument frontier should be an empty queue.\n",
" If two paths reach a state, only use the first one. [Figure 3.7]\"\"\"\n",
" # we use these two variables at the time of visualisations\n",
" iterations = 0\n",
" all_node_colors = []\n",
" node_colors = {k : 'white' for k in problem.graph.nodes()}\n",
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
1401
1402
1403
" \n",
" frontier.append(Node(problem.initial))\n",
" explored = set()\n",
" \n",
" # modify the color of frontier nodes to orange\n",
" node_colors[Node(problem.initial).state] = \"orange\"\n",
" iterations += 1\n",
" all_node_colors.append(dict(node_colors))\n",
" \n",
" while frontier:\n",
" # Popping first node of queue\n",
" node = frontier.pop()\n",
" \n",
" # modify the currently searching node to red\n",
" node_colors[node.state] = \"red\"\n",
" iterations += 1\n",
" all_node_colors.append(dict(node_colors))\n",
" \n",
" if problem.goal_test(node.state):\n",
" # modify goal node to green after reaching the goal\n",
" node_colors[node.state] = \"green\"\n",
" iterations += 1\n",
" all_node_colors.append(dict(node_colors))\n",
" return(iterations, all_node_colors, node)\n",
" \n",
" explored.add(node.state)\n",
" frontier.extend(child for child in node.expand(problem)\n",
" if child.state not in explored and\n",
" child not in frontier)\n",
" \n",
" for n in frontier:\n",
" # modify the color of frontier nodes to orange\n",
" node_colors[n.state] = \"orange\"\n",
" iterations += 1\n",
" all_node_colors.append(dict(node_colors))\n",
"\n",
" # modify the color of explored nodes to gray\n",
" node_colors[node.state] = \"gray\"\n",
" iterations += 1\n",
" all_node_colors.append(dict(node_colors))\n",
" \n",
" return None\n",
"\n",
"\n",
"def depth_first_graph_search(problem):\n",
" \"\"\"Search the deepest nodes in the search tree first.\"\"\"\n",
" iterations, all_node_colors, node = graph_search_for_vis(problem, Stack())\n",
" return(iterations, all_node_colors, node)"
]
},
{
"cell_type": "code",
"metadata": {},
"source": [
"all_node_colors = []\n",
"romania_problem = GraphProblem('Arad', 'Bucharest', romania_map)\n",
"display_visual(romania_graph_data, user_input=False, \n",
" algorithm=depth_first_graph_search, \n",
" problem=romania_problem)"
"cell_type": "markdown",
"## 5. BEST FIRST SEARCH\n",
"\n",
"Let's change all the `node_colors` to starting position and define a different problem statement."
]
},
{
"cell_type": "code",
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def best_first_graph_search_for_vis(problem, f):\n",
" \"\"\"Search the nodes with the lowest f scores first.\n",
" You specify the function f(node) that you want to minimize; for example,\n",
" if f is a heuristic estimate to the goal, then we have greedy best\n",
" first search; if f is node.depth then we have breadth-first search.\n",
" There is a subtlety: the line \"f = memoize(f, 'f')\" means that the f\n",
" values will be cached on the nodes as they are computed. So after doing\n",
" a best first search you can examine the f values of the path returned.\"\"\"\n",
" \n",
" # we use these two variables at the time of visualisations\n",
" iterations = 0\n",
" all_node_colors = []\n",
" node_colors = {k : 'white' for k in problem.graph.nodes()}\n",
" \n",
" f = memoize(f, 'f')\n",
" node = Node(problem.initial)\n",
" \n",
" node_colors[node.state] = \"red\"\n",
" iterations += 1\n",
" all_node_colors.append(dict(node_colors))\n",
" \n",
" if problem.goal_test(node.state):\n",
" node_colors[node.state] = \"green\"\n",
" iterations += 1\n",
" all_node_colors.append(dict(node_colors))\n",
" return(iterations, all_node_colors, node)\n",
" \n",
" frontier = PriorityQueue(min, f)\n",
" frontier.append(node)\n",
" \n",
" node_colors[node.state] = \"orange\"\n",
" iterations += 1\n",
" all_node_colors.append(dict(node_colors))\n",
" \n",
" explored = set()\n",
" while frontier:\n",
" node = frontier.pop()\n",
" \n",
" node_colors[node.state] = \"red\"\n",
" iterations += 1\n",
" all_node_colors.append(dict(node_colors))\n",
" \n",
" if problem.goal_test(node.state):\n",
" node_colors[node.state] = \"green\"\n",
" iterations += 1\n",
" all_node_colors.append(dict(node_colors))\n",
" return(iterations, all_node_colors, node)\n",
" \n",
" explored.add(node.state)\n",
" for child in node.expand(problem):\n",
" if child.state not in explored and child not in frontier:\n",
" frontier.append(child)\n",
" node_colors[child.state] = \"orange\"\n",
" iterations += 1\n",
" all_node_colors.append(dict(node_colors))\n",
" elif child in frontier:\n",
" incumbent = frontier[child]\n",
" if f(child) < f(incumbent):\n",
" del frontier[incumbent]\n",
" frontier.append(child)\n",
" node_colors[child.state] = \"orange\"\n",
" iterations += 1\n",
" all_node_colors.append(dict(node_colors))\n",
"\n",
" node_colors[node.state] = \"gray\"\n",
" iterations += 1\n",
" all_node_colors.append(dict(node_colors))\n",
" return None"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 6. UNIFORM COST SEARCH\n",
"Let's change all the `node_colors` to starting position and define a different problem statement."
"metadata": {
"collapsed": true
},
"def uniform_cost_search_graph(problem):\n",
" \"[Figure 3.14]\"\n",
" #Uniform Cost Search uses Best First Search algorithm with f(n) = g(n)\n",
" iterations, all_node_colors, node = best_first_graph_search_for_vis(problem, lambda node: node.path_cost)\n",
" return(iterations, all_node_colors, node)\n"
"cell_type": "code",
"all_node_colors = []\n",
"romania_problem = GraphProblem('Arad', 'Bucharest', romania_map)\n",
"display_visual(romania_graph_data, user_input=False, \n",
" algorithm=uniform_cost_search_graph, \n",
" problem=romania_problem)"
1545
1546
1547
1548
1549
1550
1551
1552
1553
1554
1555
1556
1557
1558
1559
1560
1561
1562
1563
1564
1565
1566
1567
1568
1569
1570
1571
1572
1573
1574
1575
1576
1577
1578
1579
1580
1581
1582
1583
1584
1585
1586
1587
1588
1589
1590
1591
1592
1593
1594
1595
1596
1597
1598
1599
1600
1601
1602
1603
1604
1605
1606
1607
1608
1609
1610
1611
1612
1613
1614
1615
1616
1617
1618
1619
1620
1621
1622
1623
1624
1625
1626
1627
1628
1629
1630
1631
1632
1633
1634
1635
1636
1637
1638
1639
1640
1641
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 7. Depth Limited Search\n",
"\n",
"Let's change all the 'node_colors' to starting position and define a different problem statement. \n",
"Although we have a working implementation, but we need to make changes."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [],
"source": [
"def depth_limited_search(problem, frontier, limit = -1):\n",
" '''\n",
" Perform depth first search of graph g.\n",
" if limit >= 0, that is the maximum depth of the search.\n",
" '''\n",
" # we use these two variables at the time of visualisations\n",
" iterations = 0\n",
" all_node_colors = []\n",
" node_colors = {k : 'white' for k in problem.graph.nodes()}\n",
" \n",
" frontier.append(Node(problem.initial))\n",
" explored = set()\n",
" \n",
" cutoff_occurred = False\n",
" node_colors[Node(problem.initial).state] = \"orange\"\n",
" iterations += 1\n",
" all_node_colors.append(dict(node_colors))\n",
" \n",
" while frontier:\n",
" # Popping first node of queue\n",
" node = frontier.pop()\n",
" \n",
" # modify the currently searching node to red\n",
" node_colors[node.state] = \"red\"\n",
" iterations += 1\n",
" all_node_colors.append(dict(node_colors))\n",
" \n",
" if problem.goal_test(node.state):\n",
" # modify goal node to green after reaching the goal\n",
" node_colors[node.state] = \"green\"\n",
" iterations += 1\n",
" all_node_colors.append(dict(node_colors))\n",
" return(iterations, all_node_colors, node)\n",
"\n",
" elif limit >= 0:\n",
" cutoff_occurred = True\n",
" limit += 1\n",
" all_node_color.pop()\n",
" iterations -= 1\n",
" node_colors[node.state] = \"gray\"\n",
"\n",
" \n",
" explored.add(node.state)\n",
" frontier.extend(child for child in node.expand(problem)\n",
" if child.state not in explored and\n",
" child not in frontier)\n",
" \n",
" for n in frontier:\n",
" limit -= 1\n",
" # modify the color of frontier nodes to orange\n",
" node_colors[n.state] = \"orange\"\n",
" iterations += 1\n",
" all_node_colors.append(dict(node_colors))\n",
"\n",
" # modify the color of explored nodes to gray\n",
" node_colors[node.state] = \"gray\"\n",
" iterations += 1\n",
" all_node_colors.append(dict(node_colors))\n",
" \n",
" return 'cutoff' if cutoff_occurred else None\n",
"\n",
"\n",
"def depth_limited_search_for_vis(problem):\n",
" \"\"\"Search the deepest nodes in the search tree first.\"\"\"\n",
" iterations, all_node_colors, node = depth_limited_search(problem, Stack())\n",
" return(iterations, all_node_colors, node) "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"all_node_colors = []\n",
"romania_problem = GraphProblem('Arad', 'Bucharest', romania_map)\n",
"display_visual(romania_graph_data, user_input=False, \n",
" algorithm=depth_limited_search_for_vis, \n",
" problem=romania_problem)"
]
},
"cell_type": "markdown",
"metadata": {},
"Let's change all the node_colors to starting position and define a different problem statement."
]
},
{
"cell_type": "code",
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def greedy_best_first_search(problem, h=None):\n",
" \"\"\"Greedy Best-first graph search is an informative searching algorithm with f(n) = h(n).\n",
" You need to specify the h function when you call best_first_search, or\n",
" else in your Problem subclass.\"\"\"\n",
" h = memoize(h or problem.h, 'h')\n",
" iterations, all_node_colors, node = best_first_graph_search_for_vis(problem, lambda n: h(n))\n",
" return(iterations, all_node_colors, node)\n"
]
},
{
"cell_type": "code",
"metadata": {},
"all_node_colors = []\n",
"romania_problem = GraphProblem('Arad', 'Bucharest', romania_map)\n",
"display_visual(romania_graph_data, user_input=False, \n",
" algorithm=greedy_best_first_search, \n",
" problem=romania_problem)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's change all the `node_colors` to starting position and define a different problem statement."
]
},
{
"cell_type": "code",
"metadata": {
"collapsed": true
},
"def astar_search_graph(problem, h=None):\n",
" \"\"\"A* search is best-first graph search with f(n) = g(n)+h(n).\n",
" You need to specify the h function when you call astar_search, or\n",
" else in your Problem subclass.\"\"\"\n",
" h = memoize(h or problem.h, 'h')\n",
" iterations, all_node_colors, node = best_first_graph_search_for_vis(problem, \n",
" lambda n: n.path_cost + h(n))\n",
" return(iterations, all_node_colors, node)\n"
"source": [
"all_node_colors = []\n",
"romania_problem = GraphProblem('Arad', 'Bucharest', romania_map)\n",
"display_visual(romania_graph_data, user_input=False, \n",
" algorithm=astar_search_graph, \n",
" problem=romania_problem)"
"source": [
"all_node_colors = []\n",
"# display_visual(romania_graph_data, user_input=True, algorithm=breadth_first_tree_search)\n",
"algorithms = { \"Breadth First Tree Search\": breadth_first_tree_search,\n",
" \"Depth First Tree Search\": depth_first_tree_search,\n",
" \"Breadth First Search\": breadth_first_search,\n",
" \"Depth First Graph Search\": depth_first_graph_search,\n",
" \"Uniform Cost Search\": uniform_cost_search,\n",
" \"A-star Search\": astar_search}\n",
"display_visual(romania_graph_data, algorithm=algorithms, user_input=True)"
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Different heuristics provide different efficiency in solving A* problems which are generally defined by the number of explored nodes as well as the branching factor. With the classic 8 puzzle we can show the efficiency of different heuristics through the number of explored nodes.\n",
"The *8 Puzzle Problem* consists of a 3x3 tray in which the goal is to get the initial configuration to the goal state by shifting the numbered tiles into the blank space.\n",
" | 7 | 2 | 4 | | 1 | 2 | 3 |\n",
" | 5 | 0 | 6 | | 4 | 5 | 6 |\n",
" | 8 | 3 | 1 | | 7 | 8 | 0 |\n",
"We have a total of 9 blank tiles giving us a total of 9! initial configuration but not all of these are solvable. The solvability of a configuration can be checked by calculating the Inversion Permutation. If the total Inversion Permutation is even then the initial configuration is solvable else the initial configuration is not solvable which means that only 9!/2 initial states lead to a solution.\n",
"<br>\n",
"Let's define our goal state."
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"goal = [1, 2, 3, 4, 5, 6, 7, 8, 0]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"1) Manhattan Distance:- For the 8 puzzle problem Manhattan distance is defined as the distance of a tile from its goal state( for the tile numbered '1' in the initial configuration Manhattan distance is 4 \"2 for left and 2 for upward displacement\").\n",
"2) No. of Misplaced Tiles:- The heuristic calculates the number of misplaced tiles between the current state and goal state.\n",
"3) Sqrt of Manhattan Distance:- It calculates the square root of Manhattan distance.\n",
"4) Max Heuristic:- It assign the score as the maximum between \"Manhattan Distance\" and \"No. of Misplaced Tiles\"."
"metadata": {
"collapsed": true
},
"def linear(node):\n",
" return sum([1 if node.state[i] != goal[i] else 0 for i in range(8)])\n",
"def manhattan(node):\n",
" state = node.state\n",
" index_goal = {0:[2,2], 1:[0,0], 2:[0,1], 3:[0,2], 4:[1,0], 5:[1,1], 6:[1,2], 7:[2,0], 8:[2,1]}\n",
" index_state = {}\n",
" index = [[0,0], [0,1], [0,2], [1,0], [1,1], [1,2], [2,0], [2,1], [2,2]]\n",
" x, y = 0, 0\n",
" \n",
" for i in range(len(state)):\n",
" index_state[state[i]] = index[i]\n",
" \n",
" mhd = 0\n",
" \n",
" for i in range(8):\n",
" for j in range(2):\n",
" mhd = abs(index_goal[i][j] - index_state[i][j]) + mhd\n",
" \n",
" return mhd\n",
"def sqrt_manhattan(node):\n",
" state = node.state\n",
" index_goal = {0:[2,2], 1:[0,0], 2:[0,1], 3:[0,2], 4:[1,0], 5:[1,1], 6:[1,2], 7:[2,0], 8:[2,1]}\n",
" index_state = {}\n",
" index = [[0,0], [0,1], [0,2], [1,0], [1,1], [1,2], [2,0], [2,1], [2,2]]\n",
" x, y = 0, 0\n",
" \n",
" for i in range(len(state)):\n",
" index_state[state[i]] = index[i]\n",
" \n",
" mhd = 0\n",
" \n",
" for i in range(8):\n",
" for j in range(2):\n",
" mhd = (index_goal[i][j] - index_state[i][j])**2 + mhd\n",
" \n",
" return math.sqrt(mhd)\n",
"def max_heuristic(node):\n",
" score1 = manhattan(node)\n",
" score2 = linear(node)\n",
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can solve the puzzle using the `astar_search` method."
]
},
"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
1868
1869
1870
1871
1872
1873
1874
1875
1876
1877
1878
1879
1880
1881
1882
1883
1884
1885
1886
1887
1888
1889
1890
1891
1892
1893
1894
1895
1896
1897
1898
1899
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909
1910
1911
1912
1913
1914
1915
1916
1917
1918
1919
1920
1921
1922
1923
1924
1925
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
2030
2031
2032
2033
2034
2035
2036
2037
2038
2039
2040
2041
2042
2043
2044
2045
2046
2047
2048
2049
2050
2051
2052
2053
2054
2055
2056
2057
2058
2059
2060
2061
2062
2063
2064
2065
2066
2067
2068
2069
2070
2071
2072
2073
2074
2075
2076
2077
2078
2079
2080
2081
2082
2083
2084
2085
2086
2087
2088
2089
2090
2091
2092
2093
2094
2095
2096
2097
2098
2099
2100
2101
2102
2103
2104
2105
2106
2107
2108
2109
2110
2111
2112
2113
2114
2115
2116
2117
2118
2119
2120
2121
2122
2123
2124
2125
2126
2127
2128
2129
2130
"puzzle = EightPuzzle((2, 4, 3, 1, 5, 6, 7, 8, 0))\n",
"puzzle.check_solvability((2, 4, 3, 1, 5, 6, 7, 8, 0)) # checks whether the initialized configuration is solvable or not"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This case is solvable, let's proceed.\n",
"<br>\n",
"The default heuristic function returns the number of misplaced tiles."
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"['UP', 'LEFT', 'UP', 'LEFT', 'DOWN', 'RIGHT', 'RIGHT', 'DOWN']"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"astar_search(puzzle).solution()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the following cells, we use different heuristic functions.\n",
"<br>"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"['UP', 'LEFT', 'UP', 'LEFT', 'DOWN', 'RIGHT', 'RIGHT', 'DOWN']"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"astar_search(puzzle, linear).solution()"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"['LEFT', 'UP', 'UP', 'LEFT', 'DOWN', 'RIGHT', 'DOWN', 'RIGHT']"
]
},
"execution_count": 35,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"astar_search(puzzle, manhattan).solution()"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"['LEFT', 'UP', 'UP', 'LEFT', 'DOWN', 'RIGHT', 'DOWN', 'RIGHT']"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"astar_search(puzzle, sqrt_manhattan).solution()"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"['LEFT', 'UP', 'UP', 'LEFT', 'DOWN', 'RIGHT', 'DOWN', 'RIGHT']"
]
},
"execution_count": 37,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"astar_search(puzzle, max_heuristic).solution()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Even though all the heuristic functions give the same solution, the difference lies in the computation time.\n",
"<br>\n",
"This might make all the difference in a scenario where high computational efficiency is required.\n",
"<br>\n",
"Let's define a few puzzle states and time `astar_search` for every heuristic function.\n",
"We will use the %%timeit magic for this."
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"puzzle_1 = EightPuzzle((2, 4, 3, 1, 5, 6, 7, 8, 0))\n",
"puzzle_2 = EightPuzzle((1, 2, 3, 4, 5, 6, 0, 7, 8))\n",
"puzzle_3 = EightPuzzle((1, 2, 3, 4, 5, 7, 8, 6, 0))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The default heuristic function is the same as the `linear` heuristic function, but we'll still check both."
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"11.3 ms ± 2.28 ms per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
]
}
],
"source": [
"%%timeit\n",
"astar_search(puzzle_1)\n",
"astar_search(puzzle_2)\n",
"astar_search(puzzle_3)"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"10.7 ms ± 591 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
]
}
],
"source": [
"%%timeit\n",
"astar_search(puzzle_1, linear)\n",
"astar_search(puzzle_2, linear)\n",
"astar_search(puzzle_3, linear)"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"8.44 ms ± 870 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
]
}
],
"source": [
"%%timeit\n",
"astar_search(puzzle_1, manhattan)\n",
"astar_search(puzzle_2, manhattan)\n",
"astar_search(puzzle_3, manhattan)"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"91.7 ms ± 1.89 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
]
}
],
"source": [
"%%timeit\n",
"astar_search(puzzle_1, sqrt_manhattan)\n",
"astar_search(puzzle_2, sqrt_manhattan)\n",
"astar_search(puzzle_3, sqrt_manhattan)"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"8.53 ms ± 601 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
]
}
],
"source": [
"%%timeit\n",
"astar_search(puzzle_1, max_heuristic)\n",
"astar_search(puzzle_2, max_heuristic)\n",
"astar_search(puzzle_3, max_heuristic)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can infer that the `manhattan` heuristic function works the fastest.\n",
"<br>\n",
"`sqrt_manhattan` has an extra `sqrt` operation which makes it quite a lot slower than the others.\n",
"<br>\n",
"`max_heuristic` should have been a bit slower as it calls two functions, but in this case, those values were already calculated which saved some time.\n",
"Feel free to play around with these functions."
2133
2134
2135
2136
2137
2138
2139
2140
2141
2142
2143
2144
2145
2146
2147
2148
2149
2150
2151
2152
2153
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## HILL CLIMBING\n",
"\n",
"Hill Climbing is a heuristic search used for optimization problems.\n",
"Given a large set of inputs and a good heuristic function, it tries to find a sufficiently good solution to the problem. \n",
"This solution may or may not be the global optimum.\n",
"The algorithm is a variant of generate and test algorithm. \n",
"<br>\n",
"As a whole, the algorithm works as follows:\n",
"- Evaluate the initial state.\n",
"- If it is equal to the goal state, return.\n",
"- Find a neighboring state (one which is heuristically similar to the current state)\n",
"- Evaluate this state. If it is closer to the goal state than before, replace the initial state with this state and repeat these steps.\n",
"<br>"
]
},
{
"cell_type": "code",
2154
2155
2156
2157
2158
2159
2160
2161
2162
2163
2164
2165
2166
2167
2168
2169
2170
2171
2172
2173
2174
2175
2176
2177
2178
2179
2180
2181
2182
2183
2184
2185
2186
2187
2188
2189
2190
2191
2192
2193
2194
2195
2196
2197
2198
2199
2200
2201
2202
2203
2204
2205
2206
2207
2208
2209
2210
2211
2212
2213
2214
2215
2216
2217
2218
2219
2220
2221
2222
2223
2224
2225
2226
2227
2228
2229
2230
2231
2232
2233
2234
2235
2236
2237
2238
2239
2240
2241
2242
2243
2244
2245
2246
2247
2248
2249
2250
2251
2252
2253
2254
2255
2256
2257
2258
2259
2260
2261
2262
2263
2264
2265
2266
2267
2268
2269
2270
2271
"execution_count": 44,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<!DOCTYPE html PUBLIC \"-//W3C//DTD HTML 4.01//EN\"\n",
" \"http://www.w3.org/TR/html4/strict.dtd\">\n",
"\n",
"<html>\n",
"<head>\n",
" <title></title>\n",
" <meta http-equiv=\"content-type\" content=\"text/html; charset=None\">\n",
" <style type=\"text/css\">\n",
"td.linenos { background-color: #f0f0f0; padding-right: 10px; }\n",
"span.lineno { background-color: #f0f0f0; padding: 0 5px 0 5px; }\n",
"pre { line-height: 125%; }\n",
"body .hll { background-color: #ffffcc }\n",
"body { background: #f8f8f8; }\n",
"body .c { color: #408080; font-style: italic } /* Comment */\n",
"body .err { border: 1px solid #FF0000 } /* Error */\n",
"body .k { color: #008000; font-weight: bold } /* Keyword */\n",
"body .o { color: #666666 } /* Operator */\n",
"body .ch { color: #408080; font-style: italic } /* Comment.Hashbang */\n",
"body .cm { color: #408080; font-style: italic } /* Comment.Multiline */\n",
"body .cp { color: #BC7A00 } /* Comment.Preproc */\n",
"body .cpf { color: #408080; font-style: italic } /* Comment.PreprocFile */\n",
"body .c1 { color: #408080; font-style: italic } /* Comment.Single */\n",
"body .cs { color: #408080; font-style: italic } /* Comment.Special */\n",
"body .gd { color: #A00000 } /* Generic.Deleted */\n",
"body .ge { font-style: italic } /* Generic.Emph */\n",
"body .gr { color: #FF0000 } /* Generic.Error */\n",
"body .gh { color: #000080; font-weight: bold } /* Generic.Heading */\n",
"body .gi { color: #00A000 } /* Generic.Inserted */\n",
"body .go { color: #888888 } /* Generic.Output */\n",
"body .gp { color: #000080; font-weight: bold } /* Generic.Prompt */\n",
"body .gs { font-weight: bold } /* Generic.Strong */\n",
"body .gu { color: #800080; font-weight: bold } /* Generic.Subheading */\n",
"body .gt { color: #0044DD } /* Generic.Traceback */\n",
"body .kc { color: #008000; font-weight: bold } /* Keyword.Constant */\n",
"body .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */\n",
"body .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */\n",
"body .kp { color: #008000 } /* Keyword.Pseudo */\n",
"body .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */\n",
"body .kt { color: #B00040 } /* Keyword.Type */\n",
"body .m { color: #666666 } /* Literal.Number */\n",
"body .s { color: #BA2121 } /* Literal.String */\n",
"body .na { color: #7D9029 } /* Name.Attribute */\n",
"body .nb { color: #008000 } /* Name.Builtin */\n",
"body .nc { color: #0000FF; font-weight: bold } /* Name.Class */\n",
"body .no { color: #880000 } /* Name.Constant */\n",
"body .nd { color: #AA22FF } /* Name.Decorator */\n",
"body .ni { color: #999999; font-weight: bold } /* Name.Entity */\n",
"body .ne { color: #D2413A; font-weight: bold } /* Name.Exception */\n",
"body .nf { color: #0000FF } /* Name.Function */\n",
"body .nl { color: #A0A000 } /* Name.Label */\n",
"body .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */\n",
"body .nt { color: #008000; font-weight: bold } /* Name.Tag */\n",
"body .nv { color: #19177C } /* Name.Variable */\n",
"body .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */\n",
"body .w { color: #bbbbbb } /* Text.Whitespace */\n",
"body .mb { color: #666666 } /* Literal.Number.Bin */\n",
"body .mf { color: #666666 } /* Literal.Number.Float */\n",
"body .mh { color: #666666 } /* Literal.Number.Hex */\n",
"body .mi { color: #666666 } /* Literal.Number.Integer */\n",
"body .mo { color: #666666 } /* Literal.Number.Oct */\n",
"body .sa { color: #BA2121 } /* Literal.String.Affix */\n",
"body .sb { color: #BA2121 } /* Literal.String.Backtick */\n",
"body .sc { color: #BA2121 } /* Literal.String.Char */\n",
"body .dl { color: #BA2121 } /* Literal.String.Delimiter */\n",
"body .sd { color: #BA2121; font-style: italic } /* Literal.String.Doc */\n",
"body .s2 { color: #BA2121 } /* Literal.String.Double */\n",
"body .se { color: #BB6622; font-weight: bold } /* Literal.String.Escape */\n",
"body .sh { color: #BA2121 } /* Literal.String.Heredoc */\n",
"body .si { color: #BB6688; font-weight: bold } /* Literal.String.Interpol */\n",
"body .sx { color: #008000 } /* Literal.String.Other */\n",
"body .sr { color: #BB6688 } /* Literal.String.Regex */\n",
"body .s1 { color: #BA2121 } /* Literal.String.Single */\n",
"body .ss { color: #19177C } /* Literal.String.Symbol */\n",
"body .bp { color: #008000 } /* Name.Builtin.Pseudo */\n",
"body .fm { color: #0000FF } /* Name.Function.Magic */\n",
"body .vc { color: #19177C } /* Name.Variable.Class */\n",
"body .vg { color: #19177C } /* Name.Variable.Global */\n",
"body .vi { color: #19177C } /* Name.Variable.Instance */\n",
"body .vm { color: #19177C } /* Name.Variable.Magic */\n",
"body .il { color: #666666 } /* Literal.Number.Integer.Long */\n",
"\n",
" </style>\n",
"</head>\n",
"<body>\n",
"<h2></h2>\n",
"\n",
"<div class=\"highlight\"><pre><span></span><span class=\"k\">def</span> <span class=\"nf\">hill_climbing</span><span class=\"p\">(</span><span class=\"n\">problem</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""From the initial node, keep choosing the neighbor with highest value,</span>\n",
"<span class=\"sd\"> stopping when no neighbor is better. [Figure 4.2]"""</span>\n",
" <span class=\"n\">current</span> <span class=\"o\">=</span> <span class=\"n\">Node</span><span class=\"p\">(</span><span class=\"n\">problem</span><span class=\"o\">.</span><span class=\"n\">initial</span><span class=\"p\">)</span>\n",
" <span class=\"k\">while</span> <span class=\"bp\">True</span><span class=\"p\">:</span>\n",
" <span class=\"n\">neighbors</span> <span class=\"o\">=</span> <span class=\"n\">current</span><span class=\"o\">.</span><span class=\"n\">expand</span><span class=\"p\">(</span><span class=\"n\">problem</span><span class=\"p\">)</span>\n",
" <span class=\"k\">if</span> <span class=\"ow\">not</span> <span class=\"n\">neighbors</span><span class=\"p\">:</span>\n",
" <span class=\"k\">break</span>\n",
" <span class=\"n\">neighbor</span> <span class=\"o\">=</span> <span class=\"n\">argmax_random_tie</span><span class=\"p\">(</span><span class=\"n\">neighbors</span><span class=\"p\">,</span>\n",
" <span class=\"n\">key</span><span class=\"o\">=</span><span class=\"k\">lambda</span> <span class=\"n\">node</span><span class=\"p\">:</span> <span class=\"n\">problem</span><span class=\"o\">.</span><span class=\"n\">value</span><span class=\"p\">(</span><span class=\"n\">node</span><span class=\"o\">.</span><span class=\"n\">state</span><span class=\"p\">))</span>\n",
" <span class=\"k\">if</span> <span class=\"n\">problem</span><span class=\"o\">.</span><span class=\"n\">value</span><span class=\"p\">(</span><span class=\"n\">neighbor</span><span class=\"o\">.</span><span class=\"n\">state</span><span class=\"p\">)</span> <span class=\"o\"><=</span> <span class=\"n\">problem</span><span class=\"o\">.</span><span class=\"n\">value</span><span class=\"p\">(</span><span class=\"n\">current</span><span class=\"o\">.</span><span class=\"n\">state</span><span class=\"p\">):</span>\n",
" <span class=\"k\">break</span>\n",
" <span class=\"n\">current</span> <span class=\"o\">=</span> <span class=\"n\">neighbor</span>\n",
" <span class=\"k\">return</span> <span class=\"n\">current</span><span class=\"o\">.</span><span class=\"n\">state</span>\n",
"</pre></div>\n",
"</body>\n",
"</html>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"psource(hill_climbing)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We will find an approximate solution to the traveling salespersons problem using this algorithm.\n",
"<br>\n",
"We need to define a class for this problem.\n",
"<br>\n",
"`Problem` will be used as a base class."
]
},
{
"cell_type": "code",
2290
2291
2292
2293
2294
2295
2296
2297
2298
2299
2300
2301
2302
2303
2304
2305
2306
2307
2308
2309
2310
2311
2312
2313
2314
2315
2316
2317
2318
2319
2320
2321
2322
2323
2324
2325
2326
2327
2328
2329
2330
2331
2332
2333
2334
2335
2336
2337
2338
2339
2340
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"class TSP_problem(Problem):\n",
"\n",
" \"\"\" subclass of Problem to define various functions \"\"\"\n",
"\n",
" def two_opt(self, state):\n",
" \"\"\" Neighbour generating function for Traveling Salesman Problem \"\"\"\n",
" neighbour_state = state[:]\n",
" left = random.randint(0, len(neighbour_state) - 1)\n",
" right = random.randint(0, len(neighbour_state) - 1)\n",
" if left > right:\n",
" left, right = right, left\n",
" neighbour_state[left: right + 1] = reversed(neighbour_state[left: right + 1])\n",
" return neighbour_state\n",
"\n",
" def actions(self, state):\n",
" \"\"\" action that can be excuted in given state \"\"\"\n",
" return [self.two_opt]\n",
"\n",
" def result(self, state, action):\n",
" \"\"\" result after applying the given action on the given state \"\"\"\n",
" return action(state)\n",
"\n",
" def path_cost(self, c, state1, action, state2):\n",
" \"\"\" total distance for the Traveling Salesman to be covered if in state2 \"\"\"\n",
" cost = 0\n",
" for i in range(len(state2) - 1):\n",
" cost += distances[state2[i]][state2[i + 1]]\n",
" cost += distances[state2[0]][state2[-1]]\n",
" return cost\n",
"\n",
" def value(self, state):\n",
" \"\"\" value of path cost given negative for the given state \"\"\"\n",
" return -1 * self.path_cost(None, None, None, state)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We will use cities from the Romania map as our cities for this problem.\n",
"<br>\n",
"A list of all cities and a dictionary storing distances between them will be populated."
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"['Arad', 'Bucharest', 'Craiova', 'Drobeta', 'Eforie', 'Fagaras', 'Giurgiu', 'Hirsova', 'Iasi', 'Lugoj', 'Mehadia', 'Neamt', 'Oradea', 'Pitesti', 'Rimnicu', 'Sibiu', 'Timisoara', 'Urziceni', 'Vaslui', 'Zerind']\n"
]
}
],
2352
2353
2354
2355
2356
2357
2358
2359
2360
2361
2362
2363
2364
2365
2366
2367
2368
2369
2370
2371
2372
"source": [
"distances = {}\n",
"all_cities = []\n",
"\n",
"for city in romania_map.locations.keys():\n",
" distances[city] = {}\n",
" all_cities.append(city)\n",
" \n",
"all_cities.sort()\n",
"print(all_cities)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next, we need to populate the individual lists inside the dictionary with the manhattan distance between the cities."
]
},
{
"cell_type": "code",
2374
2375
2376
2377
2378
2379
2380
2381
2382
2383
2384
2385
2386
2387
2388
2389
2390
2391
2392
2393
2394
2395
2396
2397
2398
2399
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import numpy as np\n",
"for name_1, coordinates_1 in romania_map.locations.items():\n",
" for name_2, coordinates_2 in romania_map.locations.items():\n",
" distances[name_1][name_2] = np.linalg.norm(\n",
" [coordinates_1[0] - coordinates_2[0], coordinates_1[1] - coordinates_2[1]])\n",
" distances[name_2][name_1] = np.linalg.norm(\n",
" [coordinates_1[0] - coordinates_2[0], coordinates_1[1] - coordinates_2[1]])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The way neighbours are chosen currently isn't suitable for the travelling salespersons problem.\n",
"We need a neighboring state that is similar in total path distance to the current state.\n",
"<br>\n",
"We need to change the function that finds neighbors."
]
},
{
"cell_type": "code",
2401
2402
2403
2404
2405
2406
2407
2408
2409
2410
2411
2412
2413
2414
2415
2416
2417
2418
2419
2420
2421
2422
2423
2424
2425
2426
2427
2428
2429
2430
2431
2432
2433
2434
2435
2436
2437
2438
2439
2440
2441
2442
2443
2444
2445
2446
2447
2448
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def hill_climbing(problem):\n",
" \n",
" \"\"\"From the initial node, keep choosing the neighbor with highest value,\n",
" stopping when no neighbor is better. [Figure 4.2]\"\"\"\n",
" \n",
" def find_neighbors(state, number_of_neighbors=100):\n",
" \"\"\" finds neighbors using two_opt method \"\"\"\n",
" \n",
" neighbors = []\n",
" \n",
" for i in range(number_of_neighbors):\n",
" new_state = problem.two_opt(state)\n",
" neighbors.append(Node(new_state))\n",
" state = new_state\n",
" \n",
" return neighbors\n",
"\n",
" # as this is a stochastic algorithm, we will set a cap on the number of iterations\n",
" iterations = 10000\n",
" \n",
" current = Node(problem.initial)\n",
" while iterations:\n",
" neighbors = find_neighbors(current.state)\n",
" if not neighbors:\n",
" break\n",
" neighbor = argmax_random_tie(neighbors,\n",
" key=lambda node: problem.value(node.state))\n",
" if problem.value(neighbor.state) <= problem.value(current.state):\n",
" current.state = neighbor.state\n",
" iterations -= 1\n",
" \n",
" return current.state"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"An instance of the TSP_problem class will be created."
]
},
{
"cell_type": "code",
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"tsp = TSP_problem(all_cities)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can now generate an approximate solution to the problem by calling `hill_climbing`.\n",
"The results will vary a bit each time you run it."
]
},
{
"cell_type": "code",
2468
2469
2470
2471
2472
2473
2474
2475
2476
2477
2478
2479
2480
2481
2482
2483
2484
2485
2486
2487
2488
2489
2490
2491
2492
2493
2494
2495
2496
2497
2498
2499
2500
"execution_count": 50,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"['Arad',\n",
" 'Timisoara',\n",
" 'Lugoj',\n",
" 'Mehadia',\n",
" 'Drobeta',\n",
" 'Craiova',\n",
" 'Pitesti',\n",
" 'Giurgiu',\n",
" 'Bucharest',\n",
" 'Urziceni',\n",
" 'Eforie',\n",
" 'Hirsova',\n",
" 'Vaslui',\n",
" 'Iasi',\n",
" 'Neamt',\n",
" 'Fagaras',\n",
" 'Rimnicu',\n",
" 'Sibiu',\n",
" 'Oradea',\n",
" 'Zerind']"
]
},
"execution_count": 50,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"hill_climbing(tsp)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The solution looks like this.\n",
"It is not difficult to see why this might be a good solution.\n",
"<br>\n",
""
]
2514
2515
2516
2517
2518
2519
2520
2521
2522
2523
2524
2525
2526
2527
2528
2529
2530
2531
2532
2533
2534
2535
2536
2537
2538
2539
2540
2541
2542
2543
2544
2545
2546
2547
2548
2549
2550
2551
2552
2553
2554
2555
2556
2557
2558
2559
2560
2561
2562
2563
2564
2565
2566
2567
2568
2569
2570
2571
2572
2573
2574
2575
2576
2577
2578
2579
2580
2581
2582
2583
2584
2585
2586
2587
2588
2589
2590
2591
2592
2593
2594
2595
2596
2597
2598
2599
2600
2601
2602
2603
2604
2605
2606
2607
2608
2609
2610
2611
2612
2613
2614
2615
2616
2617
2618
2619
2620
2621
2622
2623
2624
2625
2626
2627
2628
2629
2630
2631
2632
2633
2634
2635
2636
2637
2638
2639
2640
2641
2642
2643
2644
2645
2646
2647
2648
2649
2650
2651
2652
2653
2654
2655
2656
2657
2658
2659
2660
2661
2662
2663
2664
2665
2666
2667
2668
2669
2670
2671
2672
2673
2674
2675
2676
2677
2678
2679
2680
2681
2682
2683
2684
2685
2686
2687
2688
2689
2690
2691
2692
2693
2694
2695
2696
2697
2698
2699
2700
2701
2702
2703
2704
2705
2706
2707
2708
2709
2710
2711
2712
2713
2714
2715
2716
2717
2718
2719
2720
2721
2722
2723
2724
2725
2726
2727
2728
2729
2730
2731
2732
2733
2734
2735
2736
2737
2738
2739
2740
2741
2742
2743
2744
2745
2746
2747
2748
2749
2750
2751
2752
2753
2754
2755
2756
2757
2758
2759
2760
2761
2762
2763
2764
2765
2766
2767
2768
2769
2770
2771
2772
2773
2774
2775
2776
2777
2778
2779
2780
2781
2782
2783
2784
2785
2786
2787
2788
2789
2790
2791
2792
2793
2794
2795
2796
2797
2798
2799
2800
2801
2802
2803
2804
2805
2806
2807
2808
2809
2810
2811
2812
2813
2814
2815
2816
2817
2818
2819
2820
2821
2822
2823
2824
2825
2826
2827
2828
2829
2830
2831
2832
2833
2834
2835
2836
2837
2838
2839
2840
2841
2842
2843
2844
2845
2846
2847
2848
2849
2850
2851
2852
2853
2854
2855
2856
2857
2858
2859
2860
2861
2862
2863
2864
2865
2866
2867
2868
2869
2870
2871
2872
2873
2874
2875
2876
2877
2878
2879
2880
2881
2882
2883
2884
2885
2886
2887
2888
2889
2890
2891
2892
2893
2894
2895
2896
2897
2898
2899
2900
2901
2902
2903
2904
2905
2906
2907
2908
2909
2910
2911
2912
2913
2914
2915
2916
2917
2918
2919
2920
2921
2922
2923
2924
2925
2926
2927
2928
2929
2930
2931
2932
2933
2934
2935
2936
2937
2938
2939
2940
2941
2942
2943
2944
2945
2946
2947
2948
2949
2950
2951
2952
2953
2954
2955
2956
2957
2958
2959
2960
2961
2962
2963
2964
2965
2966
2967
2968
2969
2970
2971
2972
2973
2974
2975
2976
2977
2978
2979
2980
2981
2982
2983
2984
2985
2986
2987
2988
2989
2990
2991
2992
2993
2994
2995
2996
2997
2998
2999
3000
3001
3002
3003
3004
3005
3006
3007
3008
3009
3010
3011
3012
3013
3014
3015
3016
3017
3018
3019
3020
3021
3022
3023
3024
3025
3026
3027
3028
3029
3030
3031
3032
3033
3034
3035
3036
3037
3038
3039
3040
3041
3042
3043
3044
3045
3046
3047
3048
3049
3050
3051
3052
3053
3054
3055
3056
3057
3058
3059
3060
3061
3062
3063
3064
3065
3066
3067
3068
3069
3070
3071
3072
3073
3074
3075
3076
3077
3078
3079
3080
3081
3082
3083
3084
3085
3086
3087
3088
3089
3090
3091
3092
3093
3094
3095
3096
3097
3098
3099
3100
3101
3102
3103
3104
3105
3106
3107
3108
3109
3110
3111
3112
3113
3114
3115
3116
3117
3118
3119
3120
3121
3122
3123
3124
3125
3126
3127
3128
3129
3130
3131
3132
3133
3134
3135
3136
3137
3138
3139
3140
3141
3142
3143
3144
3145
3146
3147
3148
3149
3150
3151
3152
3153
3154
3155
3156
3157
3158
3159
3160
3161
3162
3163
3164
3165
3166
3167
3168
3169
3170
3171
3172
3173
3174
3175
3176
3177
3178
3179
3180
3181
3182
3183
3184
3185
3186
3187
3188
3189
3190
3191
3192
3193
3194
3195
3196
3197
3198
3199
3200
3201
3202
3203
3204
3205
3206
3207
3208
3209
3210
3211
3212
3213
3214
3215
3216
3217
3218
3219
3220
3221
3222
3223
3224
3225
3226
3227
3228
3229
3230
3231
3232
3233
3234
3235
3236
3237
3238
3239
3240
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## SIMULATED ANNEALING\n",
"\n",
"The intuition behind Hill Climbing was developed from the metaphor of climbing up the graph of a function to find its peak. \n",
"There is a fundamental problem in the implementation of the algorithm however.\n",
"To find the highest hill, we take one step at a time, always uphill, hoping to find the highest point, \n",
"but if we are unlucky to start from the shoulder of the second-highest hill, there is no way we can find the highest one. \n",
"The algorithm will always converge to the local optimum.\n",
"Hill Climbing is also bad at dealing with functions that flatline in certain regions.\n",
"If all neighboring states have the same value, we cannot find the global optimum using this algorithm.\n",
"<br>\n",
"<br>\n",
"Let's now look at an algorithm that can deal with these situations.\n",
"<br>\n",
"Simulated Annealing is quite similar to Hill Climbing, \n",
"but instead of picking the _best_ move every iteration, it picks a _random_ move. \n",
"If this random move brings us closer to the global optimum, it will be accepted, \n",
"but if it doesn't, the algorithm may accept or reject the move based on a probability dictated by the _temperature_. \n",
"When the `temperature` is high, the algorithm is more likely to accept a random move even if it is bad.\n",
"At low temperatures, only good moves are accepted, with the occasional exception.\n",
"This allows exploration of the state space and prevents the algorithm from getting stuck at the local optimum.\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<!DOCTYPE html PUBLIC \"-//W3C//DTD HTML 4.01//EN\"\n",
" \"http://www.w3.org/TR/html4/strict.dtd\">\n",
"\n",
"<html>\n",
"<head>\n",
" <title></title>\n",
" <meta http-equiv=\"content-type\" content=\"text/html; charset=None\">\n",
" <style type=\"text/css\">\n",
"td.linenos { background-color: #f0f0f0; padding-right: 10px; }\n",
"span.lineno { background-color: #f0f0f0; padding: 0 5px 0 5px; }\n",
"pre { line-height: 125%; }\n",
"body .hll { background-color: #ffffcc }\n",
"body { background: #f8f8f8; }\n",
"body .c { color: #408080; font-style: italic } /* Comment */\n",
"body .err { border: 1px solid #FF0000 } /* Error */\n",
"body .k { color: #008000; font-weight: bold } /* Keyword */\n",
"body .o { color: #666666 } /* Operator */\n",
"body .ch { color: #408080; font-style: italic } /* Comment.Hashbang */\n",
"body .cm { color: #408080; font-style: italic } /* Comment.Multiline */\n",
"body .cp { color: #BC7A00 } /* Comment.Preproc */\n",
"body .cpf { color: #408080; font-style: italic } /* Comment.PreprocFile */\n",
"body .c1 { color: #408080; font-style: italic } /* Comment.Single */\n",
"body .cs { color: #408080; font-style: italic } /* Comment.Special */\n",
"body .gd { color: #A00000 } /* Generic.Deleted */\n",
"body .ge { font-style: italic } /* Generic.Emph */\n",
"body .gr { color: #FF0000 } /* Generic.Error */\n",
"body .gh { color: #000080; font-weight: bold } /* Generic.Heading */\n",
"body .gi { color: #00A000 } /* Generic.Inserted */\n",
"body .go { color: #888888 } /* Generic.Output */\n",
"body .gp { color: #000080; font-weight: bold } /* Generic.Prompt */\n",
"body .gs { font-weight: bold } /* Generic.Strong */\n",
"body .gu { color: #800080; font-weight: bold } /* Generic.Subheading */\n",
"body .gt { color: #0044DD } /* Generic.Traceback */\n",
"body .kc { color: #008000; font-weight: bold } /* Keyword.Constant */\n",
"body .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */\n",
"body .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */\n",
"body .kp { color: #008000 } /* Keyword.Pseudo */\n",
"body .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */\n",
"body .kt { color: #B00040 } /* Keyword.Type */\n",
"body .m { color: #666666 } /* Literal.Number */\n",
"body .s { color: #BA2121 } /* Literal.String */\n",
"body .na { color: #7D9029 } /* Name.Attribute */\n",
"body .nb { color: #008000 } /* Name.Builtin */\n",
"body .nc { color: #0000FF; font-weight: bold } /* Name.Class */\n",
"body .no { color: #880000 } /* Name.Constant */\n",
"body .nd { color: #AA22FF } /* Name.Decorator */\n",
"body .ni { color: #999999; font-weight: bold } /* Name.Entity */\n",
"body .ne { color: #D2413A; font-weight: bold } /* Name.Exception */\n",
"body .nf { color: #0000FF } /* Name.Function */\n",
"body .nl { color: #A0A000 } /* Name.Label */\n",
"body .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */\n",
"body .nt { color: #008000; font-weight: bold } /* Name.Tag */\n",
"body .nv { color: #19177C } /* Name.Variable */\n",
"body .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */\n",
"body .w { color: #bbbbbb } /* Text.Whitespace */\n",
"body .mb { color: #666666 } /* Literal.Number.Bin */\n",
"body .mf { color: #666666 } /* Literal.Number.Float */\n",
"body .mh { color: #666666 } /* Literal.Number.Hex */\n",
"body .mi { color: #666666 } /* Literal.Number.Integer */\n",
"body .mo { color: #666666 } /* Literal.Number.Oct */\n",
"body .sa { color: #BA2121 } /* Literal.String.Affix */\n",
"body .sb { color: #BA2121 } /* Literal.String.Backtick */\n",
"body .sc { color: #BA2121 } /* Literal.String.Char */\n",
"body .dl { color: #BA2121 } /* Literal.String.Delimiter */\n",
"body .sd { color: #BA2121; font-style: italic } /* Literal.String.Doc */\n",
"body .s2 { color: #BA2121 } /* Literal.String.Double */\n",
"body .se { color: #BB6622; font-weight: bold } /* Literal.String.Escape */\n",
"body .sh { color: #BA2121 } /* Literal.String.Heredoc */\n",
"body .si { color: #BB6688; font-weight: bold } /* Literal.String.Interpol */\n",
"body .sx { color: #008000 } /* Literal.String.Other */\n",
"body .sr { color: #BB6688 } /* Literal.String.Regex */\n",
"body .s1 { color: #BA2121 } /* Literal.String.Single */\n",
"body .ss { color: #19177C } /* Literal.String.Symbol */\n",
"body .bp { color: #008000 } /* Name.Builtin.Pseudo */\n",
"body .fm { color: #0000FF } /* Name.Function.Magic */\n",
"body .vc { color: #19177C } /* Name.Variable.Class */\n",
"body .vg { color: #19177C } /* Name.Variable.Global */\n",
"body .vi { color: #19177C } /* Name.Variable.Instance */\n",
"body .vm { color: #19177C } /* Name.Variable.Magic */\n",
"body .il { color: #666666 } /* Literal.Number.Integer.Long */\n",
"\n",
" </style>\n",
"</head>\n",
"<body>\n",
"<h2></h2>\n",
"\n",
"<div class=\"highlight\"><pre><span></span><span class=\"k\">def</span> <span class=\"nf\">simulated_annealing</span><span class=\"p\">(</span><span class=\"n\">problem</span><span class=\"p\">,</span> <span class=\"n\">schedule</span><span class=\"o\">=</span><span class=\"n\">exp_schedule</span><span class=\"p\">()):</span>\n",
" <span class=\"sd\">"""[Figure 4.5] CAUTION: This differs from the pseudocode as it</span>\n",
"<span class=\"sd\"> returns a state instead of a Node."""</span>\n",
" <span class=\"n\">current</span> <span class=\"o\">=</span> <span class=\"n\">Node</span><span class=\"p\">(</span><span class=\"n\">problem</span><span class=\"o\">.</span><span class=\"n\">initial</span><span class=\"p\">)</span>\n",
" <span class=\"k\">for</span> <span class=\"n\">t</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">sys</span><span class=\"o\">.</span><span class=\"n\">maxsize</span><span class=\"p\">):</span>\n",
" <span class=\"n\">T</span> <span class=\"o\">=</span> <span class=\"n\">schedule</span><span class=\"p\">(</span><span class=\"n\">t</span><span class=\"p\">)</span>\n",
" <span class=\"k\">if</span> <span class=\"n\">T</span> <span class=\"o\">==</span> <span class=\"mi\">0</span><span class=\"p\">:</span>\n",
" <span class=\"k\">return</span> <span class=\"n\">current</span><span class=\"o\">.</span><span class=\"n\">state</span>\n",
" <span class=\"n\">neighbors</span> <span class=\"o\">=</span> <span class=\"n\">current</span><span class=\"o\">.</span><span class=\"n\">expand</span><span class=\"p\">(</span><span class=\"n\">problem</span><span class=\"p\">)</span>\n",
" <span class=\"k\">if</span> <span class=\"ow\">not</span> <span class=\"n\">neighbors</span><span class=\"p\">:</span>\n",
" <span class=\"k\">return</span> <span class=\"n\">current</span><span class=\"o\">.</span><span class=\"n\">state</span>\n",
" <span class=\"n\">next_choice</span> <span class=\"o\">=</span> <span class=\"n\">random</span><span class=\"o\">.</span><span class=\"n\">choice</span><span class=\"p\">(</span><span class=\"n\">neighbors</span><span class=\"p\">)</span>\n",
" <span class=\"n\">delta_e</span> <span class=\"o\">=</span> <span class=\"n\">problem</span><span class=\"o\">.</span><span class=\"n\">value</span><span class=\"p\">(</span><span class=\"n\">next_choice</span><span class=\"o\">.</span><span class=\"n\">state</span><span class=\"p\">)</span> <span class=\"o\">-</span> <span class=\"n\">problem</span><span class=\"o\">.</span><span class=\"n\">value</span><span class=\"p\">(</span><span class=\"n\">current</span><span class=\"o\">.</span><span class=\"n\">state</span><span class=\"p\">)</span>\n",
" <span class=\"k\">if</span> <span class=\"n\">delta_e</span> <span class=\"o\">></span> <span class=\"mi\">0</span> <span class=\"ow\">or</span> <span class=\"n\">probability</span><span class=\"p\">(</span><span class=\"n\">math</span><span class=\"o\">.</span><span class=\"n\">exp</span><span class=\"p\">(</span><span class=\"n\">delta_e</span> <span class=\"o\">/</span> <span class=\"n\">T</span><span class=\"p\">)):</span>\n",
" <span class=\"n\">current</span> <span class=\"o\">=</span> <span class=\"n\">next_choice</span>\n",
"</pre></div>\n",
"</body>\n",
"</html>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"psource(simulated_annealing)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The temperature is gradually decreased over the course of the iteration.\n",
"This is done by a scheduling routine.\n",
"The current implementation uses exponential decay of temperature, but we can use a different scheduling routine instead.\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<!DOCTYPE html PUBLIC \"-//W3C//DTD HTML 4.01//EN\"\n",
" \"http://www.w3.org/TR/html4/strict.dtd\">\n",
"\n",
"<html>\n",
"<head>\n",
" <title></title>\n",
" <meta http-equiv=\"content-type\" content=\"text/html; charset=None\">\n",
" <style type=\"text/css\">\n",
"td.linenos { background-color: #f0f0f0; padding-right: 10px; }\n",
"span.lineno { background-color: #f0f0f0; padding: 0 5px 0 5px; }\n",
"pre { line-height: 125%; }\n",
"body .hll { background-color: #ffffcc }\n",
"body { background: #f8f8f8; }\n",
"body .c { color: #408080; font-style: italic } /* Comment */\n",
"body .err { border: 1px solid #FF0000 } /* Error */\n",
"body .k { color: #008000; font-weight: bold } /* Keyword */\n",
"body .o { color: #666666 } /* Operator */\n",
"body .ch { color: #408080; font-style: italic } /* Comment.Hashbang */\n",
"body .cm { color: #408080; font-style: italic } /* Comment.Multiline */\n",
"body .cp { color: #BC7A00 } /* Comment.Preproc */\n",
"body .cpf { color: #408080; font-style: italic } /* Comment.PreprocFile */\n",
"body .c1 { color: #408080; font-style: italic } /* Comment.Single */\n",
"body .cs { color: #408080; font-style: italic } /* Comment.Special */\n",
"body .gd { color: #A00000 } /* Generic.Deleted */\n",
"body .ge { font-style: italic } /* Generic.Emph */\n",
"body .gr { color: #FF0000 } /* Generic.Error */\n",
"body .gh { color: #000080; font-weight: bold } /* Generic.Heading */\n",
"body .gi { color: #00A000 } /* Generic.Inserted */\n",
"body .go { color: #888888 } /* Generic.Output */\n",
"body .gp { color: #000080; font-weight: bold } /* Generic.Prompt */\n",
"body .gs { font-weight: bold } /* Generic.Strong */\n",
"body .gu { color: #800080; font-weight: bold } /* Generic.Subheading */\n",
"body .gt { color: #0044DD } /* Generic.Traceback */\n",
"body .kc { color: #008000; font-weight: bold } /* Keyword.Constant */\n",
"body .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */\n",
"body .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */\n",
"body .kp { color: #008000 } /* Keyword.Pseudo */\n",
"body .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */\n",
"body .kt { color: #B00040 } /* Keyword.Type */\n",
"body .m { color: #666666 } /* Literal.Number */\n",
"body .s { color: #BA2121 } /* Literal.String */\n",
"body .na { color: #7D9029 } /* Name.Attribute */\n",
"body .nb { color: #008000 } /* Name.Builtin */\n",
"body .nc { color: #0000FF; font-weight: bold } /* Name.Class */\n",
"body .no { color: #880000 } /* Name.Constant */\n",
"body .nd { color: #AA22FF } /* Name.Decorator */\n",
"body .ni { color: #999999; font-weight: bold } /* Name.Entity */\n",
"body .ne { color: #D2413A; font-weight: bold } /* Name.Exception */\n",
"body .nf { color: #0000FF } /* Name.Function */\n",
"body .nl { color: #A0A000 } /* Name.Label */\n",
"body .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */\n",
"body .nt { color: #008000; font-weight: bold } /* Name.Tag */\n",
"body .nv { color: #19177C } /* Name.Variable */\n",
"body .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */\n",
"body .w { color: #bbbbbb } /* Text.Whitespace */\n",
"body .mb { color: #666666 } /* Literal.Number.Bin */\n",
"body .mf { color: #666666 } /* Literal.Number.Float */\n",
"body .mh { color: #666666 } /* Literal.Number.Hex */\n",
"body .mi { color: #666666 } /* Literal.Number.Integer */\n",
"body .mo { color: #666666 } /* Literal.Number.Oct */\n",
"body .sa { color: #BA2121 } /* Literal.String.Affix */\n",
"body .sb { color: #BA2121 } /* Literal.String.Backtick */\n",
"body .sc { color: #BA2121 } /* Literal.String.Char */\n",
"body .dl { color: #BA2121 } /* Literal.String.Delimiter */\n",
"body .sd { color: #BA2121; font-style: italic } /* Literal.String.Doc */\n",
"body .s2 { color: #BA2121 } /* Literal.String.Double */\n",
"body .se { color: #BB6622; font-weight: bold } /* Literal.String.Escape */\n",
"body .sh { color: #BA2121 } /* Literal.String.Heredoc */\n",
"body .si { color: #BB6688; font-weight: bold } /* Literal.String.Interpol */\n",
"body .sx { color: #008000 } /* Literal.String.Other */\n",
"body .sr { color: #BB6688 } /* Literal.String.Regex */\n",
"body .s1 { color: #BA2121 } /* Literal.String.Single */\n",
"body .ss { color: #19177C } /* Literal.String.Symbol */\n",
"body .bp { color: #008000 } /* Name.Builtin.Pseudo */\n",
"body .fm { color: #0000FF } /* Name.Function.Magic */\n",
"body .vc { color: #19177C } /* Name.Variable.Class */\n",
"body .vg { color: #19177C } /* Name.Variable.Global */\n",
"body .vi { color: #19177C } /* Name.Variable.Instance */\n",
"body .vm { color: #19177C } /* Name.Variable.Magic */\n",
"body .il { color: #666666 } /* Literal.Number.Integer.Long */\n",
"\n",
" </style>\n",
"</head>\n",
"<body>\n",
"<h2></h2>\n",
"\n",
"<div class=\"highlight\"><pre><span></span><span class=\"k\">def</span> <span class=\"nf\">exp_schedule</span><span class=\"p\">(</span><span class=\"n\">k</span><span class=\"o\">=</span><span class=\"mi\">20</span><span class=\"p\">,</span> <span class=\"n\">lam</span><span class=\"o\">=</span><span class=\"mf\">0.005</span><span class=\"p\">,</span> <span class=\"n\">limit</span><span class=\"o\">=</span><span class=\"mi\">100</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""One possible schedule function for simulated annealing"""</span>\n",
" <span class=\"k\">return</span> <span class=\"k\">lambda</span> <span class=\"n\">t</span><span class=\"p\">:</span> <span class=\"p\">(</span><span class=\"n\">k</span> <span class=\"o\">*</span> <span class=\"n\">math</span><span class=\"o\">.</span><span class=\"n\">exp</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"n\">lam</span> <span class=\"o\">*</span> <span class=\"n\">t</span><span class=\"p\">)</span> <span class=\"k\">if</span> <span class=\"n\">t</span> <span class=\"o\"><</span> <span class=\"n\">limit</span> <span class=\"k\">else</span> <span class=\"mi\">0</span><span class=\"p\">)</span>\n",
"</pre></div>\n",
"</body>\n",
"</html>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"psource(exp_schedule)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next, we'll define a peak-finding problem and try to solve it using Simulated Annealing.\n",
"Let's define the grid and the initial state first.\n"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"initial = (0, 0)\n",
"grid = [[3, 7, 2, 8], [5, 2, 9, 1], [5, 3, 3, 1]]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We want to allow only four directions, namely `N`, `S`, `E` and `W`.\n",
"Let's use the predefined `directions4` dictionary."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"{'E': (1, 0), 'N': (0, 1), 'S': (0, -1), 'W': (-1, 0)}"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"directions4"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Define a problem with these parameters."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"problem = PeakFindingProblem(initial, grid, directions4)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We'll run `simulated_annealing` a few times and store the solutions in a set."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"solutions = {problem.value(simulated_annealing(problem)) for i in range(100)}"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"9"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"max(solutions)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Hence, the maximum value is 9."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's find the peak of a two-dimensional gaussian distribution.\n",
"We'll use the `gaussian_kernel` function from notebook.py to get the distribution."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"grid = gaussian_kernel()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's use the `heatmap` function from notebook.py to plot this."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAeAAAAHwCAYAAAB+ArwOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nCeBTp06dOnVqB50APnXq1KlTp3bQ/we5egeI3ld27AAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x25f94953c50>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"heatmap(grid, cmap='jet', interpolation='spline16')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's define the problem.\n",
"This time, we will allow movement in eight directions as defined in `directions8`."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"{'E': (1, 0),\n",
" 'N': (0, 1),\n",
" 'NE': (1, 1),\n",
" 'NW': (-1, 1),\n",
" 'S': (0, -1),\n",
" 'SE': (1, -1),\n",
" 'SW': (-1, -1),\n",
" 'W': (-1, 0)}"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"directions8"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We'll solve the problem just like we did last time.\n",
"<br>\n",
"Let's also time it."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"problem = PeakFindingProblem(initial, grid, directions8)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"533 ms ± 51 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
]
}
],
"source": [
"%%timeit\n",
"solutions = {problem.value(simulated_annealing(problem)) for i in range(100)}"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"9"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"max(solutions)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The peak is at 1.0 which is how gaussian distributions are defined.\n",
"<br>\n",
"This could also be solved by Hill Climbing as follows."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"206 µs ± 21.6 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n"
]
}
],
"source": [
"%%timeit\n",
"solution = problem.value(hill_climbing(problem))"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.0"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"solution = problem.value(hill_climbing(problem))\n",
"solution"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As you can see, Hill-Climbing is about 24 times faster than Simulated Annealing.\n",
"(Notice that we ran Simulated Annealing for 100 iterations whereas we ran Hill Climbing only once.)\n",
"<br>\n",
"Simulated Annealing makes up for its tardiness by its ability to be applicable in a larger number of scenarios than Hill Climbing as illustrated by the example below.\n",
"<br>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's define a 2D surface as a matrix."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"grid = [[0, 0, 0, 1, 4], \n",
" [0, 0, 2, 8, 10], \n",
" [0, 0, 2, 4, 12], \n",
" [0, 2, 4, 8, 16], \n",
" [1, 4, 8, 16, 32]]"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAeAAAAHwCAYAAAB+ArwOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nUqkd9P8DnGSSkMm/7/MAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x25f96a19c18>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"heatmap(grid, cmap='jet', interpolation='spline16')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The peak value is 32 at the lower right corner.\n",
"<br>\n",
"The region at the upper left corner is planar."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's instantiate `PeakFindingProblem` one last time."
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"problem = PeakFindingProblem(initial, grid, directions8)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Solution by Hill Climbing"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"solution = problem.value(hill_climbing(problem))"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"solution"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Solution by Simulated Annealing"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"32"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"solutions = {problem.value(simulated_annealing(problem)) for i in range(100)}\n",
"max(solutions)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Notice that even though both algorithms started at the same initial state, \n",
"Hill Climbing could never escape from the planar region and gave a locally optimum solution of **0**,\n",
"whereas Simulated Annealing could reach the peak at **32**.\n",
"<br>\n",
"A very similar situation arises when there are two peaks of different heights.\n",
"One should carefully consider the possible search space before choosing the algorithm for the task."
]
{
"cell_type": "markdown",
"\n",
"Genetic algorithms (or GA) are inspired by natural evolution and are particularly useful in optimization and search problems with large state spaces.\n",
"\n",
"Given a problem, algorithms in the domain make use of a *population* of solutions (also called *states*), where each solution/state represents a feasible solution. At each iteration (often called *generation*), the population gets updated using methods inspired by biology and evolution, like *crossover*, *mutation* and *natural selection*."
]
},
{
"cell_type": "markdown",
"source": [
"### Overview\n",
"\n",
"A genetic algorithm works in the following way:\n",
"\n",
"1) Initialize random population.\n",
"\n",
"2) Calculate population fitness.\n",
"\n",
"3) Select individuals for mating.\n",
"\n",
"4) Mate selected individuals to produce new population.\n",
"\n",
" * Random chance to mutate individuals.\n",
"\n",
"5) Repeat from step 2) until an individual is fit enough or the maximum number of iterations was reached."
]
},
{
"cell_type": "markdown",
"### Glossary\n",
"\n",
"Before we continue, we will lay the basic terminology of the algorithm.\n",
"\n",
"* Individual/State: A list of elements (called *genes*) that represent possible solutions.\n",
"* Population: The list of all the individuals/states.\n",
"\n",
"* Gene pool: The alphabet of possible values for an individual's genes.\n",
"\n",
"* Generation/Iteration: The number of times the population will be updated.\n",
"\n",
"* Fitness: An individual's score, calculated by a function specific to the problem."
]
},
{
"cell_type": "markdown",
"### Crossover\n",
"\n",
"Two individuals/states can \"mate\" and produce one child. This offspring bears characteristics from both of its parents. There are many ways we can implement this crossover. Here we will take a look at the most common ones. Most other methods are variations of those below.\n",
"\n",
"* Point Crossover: The crossover occurs around one (or more) point. The parents get \"split\" at the chosen point or points and then get merged. In the example below we see two parents get split and merged at the 3rd digit, producing the following offspring after the crossover.\n",
"\n",
"\n",
"\n",
"* Uniform Crossover: This type of crossover chooses randomly the genes to get merged. Here the genes 1, 2 and 5 were chosen from the first parent, so the genes 3, 4 were added by the second parent.\n",
"\n",
""
]
},
{
"cell_type": "markdown",
"### Mutation\n",
"\n",
"When an offspring is produced, there is a chance it will mutate, having one (or more, depending on the implementation) of its genes altered.\n",
"\n",
"For example, let's say the new individual to undergo mutation is \"abcde\". Randomly we pick to change its third gene to 'z'. The individual now becomes \"abzde\" and is added to the population."
]
},
{
"cell_type": "markdown",
"At each iteration, the fittest individuals are picked randomly to mate and produce offsprings. We measure an individual's fitness with a *fitness function*. That function depends on the given problem and it is used to score an individual. Usually the higher the better.\n",
"The selection process is this:\n",
"1) Individuals are scored by the fitness function.\n",
"\n",
"2) Individuals are picked randomly, according to their score (higher score means higher chance to get picked). Usually the formula to calculate the chance to pick an individual is the following (for population *P* and individual *i*):\n",
"\n",
"$$ chance(i) = \\dfrac{fitness(i)}{\\sum_{k \\, in \\, P}{fitness(k)}} $$"
]
},
{
"cell_type": "markdown",
"### Implementation\n",
"\n",
"Below we look over the implementation of the algorithm in the `search` module.\n",
"\n",
"First the implementation of the main core of the algorithm:"
]
},
{
"cell_type": "code",
3351
3352
3353
3354
3355
3356
3357
3358
3359
3360
3361
3362
3363
3364
3365
3366
3367
3368
3369
3370
3371
3372
3373
3374
3375
3376
3377
3378
3379
3380
3381
3382
3383
3384
3385
3386
3387
3388
3389
3390
3391
3392
3393
3394
3395
3396
3397
3398
3399
3400
3401
3402
3403
3404
3405
3406
3407
3408
3409
3410
3411
3412
3413
3414
3415
3416
3417
3418
3419
3420
3421
3422
3423
3424
3425
3426
3427
3428
3429
3430
3431
3432
3433
3434
3435
3436
3437
3438
3439
3440
3441
3442
3443
3444
3445
3446
3447
3448
3449
3450
3451
3452
3453
3454
3455
3456
3457
3458
3459
3460
3461
3462
3463
3464
3465
3466
"execution_count": 51,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<!DOCTYPE html PUBLIC \"-//W3C//DTD HTML 4.01//EN\"\n",
" \"http://www.w3.org/TR/html4/strict.dtd\">\n",
"\n",
"<html>\n",
"<head>\n",
" <title></title>\n",
" <meta http-equiv=\"content-type\" content=\"text/html; charset=None\">\n",
" <style type=\"text/css\">\n",
"td.linenos { background-color: #f0f0f0; padding-right: 10px; }\n",
"span.lineno { background-color: #f0f0f0; padding: 0 5px 0 5px; }\n",
"pre { line-height: 125%; }\n",
"body .hll { background-color: #ffffcc }\n",
"body { background: #f8f8f8; }\n",
"body .c { color: #408080; font-style: italic } /* Comment */\n",
"body .err { border: 1px solid #FF0000 } /* Error */\n",
"body .k { color: #008000; font-weight: bold } /* Keyword */\n",
"body .o { color: #666666 } /* Operator */\n",
"body .ch { color: #408080; font-style: italic } /* Comment.Hashbang */\n",
"body .cm { color: #408080; font-style: italic } /* Comment.Multiline */\n",
"body .cp { color: #BC7A00 } /* Comment.Preproc */\n",
"body .cpf { color: #408080; font-style: italic } /* Comment.PreprocFile */\n",
"body .c1 { color: #408080; font-style: italic } /* Comment.Single */\n",
"body .cs { color: #408080; font-style: italic } /* Comment.Special */\n",
"body .gd { color: #A00000 } /* Generic.Deleted */\n",
"body .ge { font-style: italic } /* Generic.Emph */\n",
"body .gr { color: #FF0000 } /* Generic.Error */\n",
"body .gh { color: #000080; font-weight: bold } /* Generic.Heading */\n",
"body .gi { color: #00A000 } /* Generic.Inserted */\n",
"body .go { color: #888888 } /* Generic.Output */\n",
"body .gp { color: #000080; font-weight: bold } /* Generic.Prompt */\n",
"body .gs { font-weight: bold } /* Generic.Strong */\n",
"body .gu { color: #800080; font-weight: bold } /* Generic.Subheading */\n",
"body .gt { color: #0044DD } /* Generic.Traceback */\n",
"body .kc { color: #008000; font-weight: bold } /* Keyword.Constant */\n",
"body .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */\n",
"body .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */\n",
"body .kp { color: #008000 } /* Keyword.Pseudo */\n",
"body .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */\n",
"body .kt { color: #B00040 } /* Keyword.Type */\n",
"body .m { color: #666666 } /* Literal.Number */\n",
"body .s { color: #BA2121 } /* Literal.String */\n",
"body .na { color: #7D9029 } /* Name.Attribute */\n",
"body .nb { color: #008000 } /* Name.Builtin */\n",
"body .nc { color: #0000FF; font-weight: bold } /* Name.Class */\n",
"body .no { color: #880000 } /* Name.Constant */\n",
"body .nd { color: #AA22FF } /* Name.Decorator */\n",
"body .ni { color: #999999; font-weight: bold } /* Name.Entity */\n",
"body .ne { color: #D2413A; font-weight: bold } /* Name.Exception */\n",
"body .nf { color: #0000FF } /* Name.Function */\n",
"body .nl { color: #A0A000 } /* Name.Label */\n",
"body .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */\n",
"body .nt { color: #008000; font-weight: bold } /* Name.Tag */\n",
"body .nv { color: #19177C } /* Name.Variable */\n",
"body .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */\n",
"body .w { color: #bbbbbb } /* Text.Whitespace */\n",
"body .mb { color: #666666 } /* Literal.Number.Bin */\n",
"body .mf { color: #666666 } /* Literal.Number.Float */\n",
"body .mh { color: #666666 } /* Literal.Number.Hex */\n",
"body .mi { color: #666666 } /* Literal.Number.Integer */\n",
"body .mo { color: #666666 } /* Literal.Number.Oct */\n",
"body .sa { color: #BA2121 } /* Literal.String.Affix */\n",
"body .sb { color: #BA2121 } /* Literal.String.Backtick */\n",
"body .sc { color: #BA2121 } /* Literal.String.Char */\n",
"body .dl { color: #BA2121 } /* Literal.String.Delimiter */\n",
"body .sd { color: #BA2121; font-style: italic } /* Literal.String.Doc */\n",
"body .s2 { color: #BA2121 } /* Literal.String.Double */\n",
"body .se { color: #BB6622; font-weight: bold } /* Literal.String.Escape */\n",
"body .sh { color: #BA2121 } /* Literal.String.Heredoc */\n",
"body .si { color: #BB6688; font-weight: bold } /* Literal.String.Interpol */\n",
"body .sx { color: #008000 } /* Literal.String.Other */\n",
"body .sr { color: #BB6688 } /* Literal.String.Regex */\n",
"body .s1 { color: #BA2121 } /* Literal.String.Single */\n",
"body .ss { color: #19177C } /* Literal.String.Symbol */\n",
"body .bp { color: #008000 } /* Name.Builtin.Pseudo */\n",
"body .fm { color: #0000FF } /* Name.Function.Magic */\n",
"body .vc { color: #19177C } /* Name.Variable.Class */\n",
"body .vg { color: #19177C } /* Name.Variable.Global */\n",
"body .vi { color: #19177C } /* Name.Variable.Instance */\n",
"body .vm { color: #19177C } /* Name.Variable.Magic */\n",
"body .il { color: #666666 } /* Literal.Number.Integer.Long */\n",
"\n",
" </style>\n",
"</head>\n",
"<body>\n",
"<h2></h2>\n",
"\n",
"<div class=\"highlight\"><pre><span></span><span class=\"k\">def</span> <span class=\"nf\">genetic_algorithm</span><span class=\"p\">(</span><span class=\"n\">population</span><span class=\"p\">,</span> <span class=\"n\">fitness_fn</span><span class=\"p\">,</span> <span class=\"n\">gene_pool</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">],</span> <span class=\"n\">f_thres</span><span class=\"o\">=</span><span class=\"bp\">None</span><span class=\"p\">,</span> <span class=\"n\">ngen</span><span class=\"o\">=</span><span class=\"mi\">1000</span><span class=\"p\">,</span> <span class=\"n\">pmut</span><span class=\"o\">=</span><span class=\"mf\">0.1</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""[Figure 4.8]"""</span>\n",
" <span class=\"k\">for</span> <span class=\"n\">i</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">ngen</span><span class=\"p\">):</span>\n",
" <span class=\"n\">population</span> <span class=\"o\">=</span> <span class=\"p\">[</span><span class=\"n\">mutate</span><span class=\"p\">(</span><span class=\"n\">recombine</span><span class=\"p\">(</span><span class=\"o\">*</span><span class=\"n\">select</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span> <span class=\"n\">population</span><span class=\"p\">,</span> <span class=\"n\">fitness_fn</span><span class=\"p\">)),</span> <span class=\"n\">gene_pool</span><span class=\"p\">,</span> <span class=\"n\">pmut</span><span class=\"p\">)</span>\n",
" <span class=\"k\">for</span> <span class=\"n\">i</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"nb\">len</span><span class=\"p\">(</span><span class=\"n\">population</span><span class=\"p\">))]</span>\n",
"\n",
" <span class=\"n\">fittest_individual</span> <span class=\"o\">=</span> <span class=\"n\">fitness_threshold</span><span class=\"p\">(</span><span class=\"n\">fitness_fn</span><span class=\"p\">,</span> <span class=\"n\">f_thres</span><span class=\"p\">,</span> <span class=\"n\">population</span><span class=\"p\">)</span>\n",
" <span class=\"k\">if</span> <span class=\"n\">fittest_individual</span><span class=\"p\">:</span>\n",
" <span class=\"k\">return</span> <span class=\"n\">fittest_individual</span>\n",
"\n",
"\n",
" <span class=\"k\">return</span> <span class=\"n\">argmax</span><span class=\"p\">(</span><span class=\"n\">population</span><span class=\"p\">,</span> <span class=\"n\">key</span><span class=\"o\">=</span><span class=\"n\">fitness_fn</span><span class=\"p\">)</span>\n",
"</pre></div>\n",
"</body>\n",
"</html>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
Aman Deep Singh
a validé
"psource(genetic_algorithm)"
]
},
{
"cell_type": "markdown",
"source": [
"The algorithm takes the following input:\n",
"\n",
"* `population`: The initial population.\n",
"\n",
"* `fitness_fn`: The problem's fitness function.\n",
"\n",
"* `gene_pool`: The gene pool of the states/individuals. By default 0 and 1.\n",
"* `f_thres`: The fitness threshold. If an individual reaches that score, iteration stops. By default 'None', which means the algorithm will not halt until the generations are ran.\n",
"\n",
"* `ngen`: The number of iterations/generations.\n",
"\n",
"* `pmut`: The probability of mutation.\n",
"\n",
"The algorithm gives as output the state with the largest score."
]
},
{
"cell_type": "markdown",
"For each generation, the algorithm updates the population. First it calculates the fitnesses of the individuals, then it selects the most fit ones and finally crosses them over to produce offsprings. There is a chance that the offspring will be mutated, given by `pmut`. If at the end of the generation an individual meets the fitness threshold, the algorithm halts and returns that individual.\n",
"\n",
Aman Deep Singh
a validé
"The function of mating is accomplished by the method `recombine`:"
]
},
{
"cell_type": "code",
3503
3504
3505
3506
3507
3508
3509
3510
3511
3512
3513
3514
3515
3516
3517
3518
3519
3520
3521
3522
3523
3524
3525
3526
3527
3528
3529
3530
3531
3532
3533
3534
3535
3536
3537
3538
3539
3540
3541
3542
3543
3544
3545
3546
3547
3548
3549
3550
3551
3552
3553
3554
3555
3556
3557
3558
3559
3560
3561
3562
3563
3564
3565
3566
3567
3568
3569
3570
3571
3572
3573
3574
3575
3576
3577
3578
3579
3580
3581
3582
3583
3584
3585
3586
3587
3588
3589
3590
3591
3592
3593
3594
3595
3596
3597
3598
3599
3600
3601
3602
3603
3604
3605
3606
3607
3608
3609
3610
"execution_count": 52,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<!DOCTYPE html PUBLIC \"-//W3C//DTD HTML 4.01//EN\"\n",
" \"http://www.w3.org/TR/html4/strict.dtd\">\n",
"\n",
"<html>\n",
"<head>\n",
" <title></title>\n",
" <meta http-equiv=\"content-type\" content=\"text/html; charset=None\">\n",
" <style type=\"text/css\">\n",
"td.linenos { background-color: #f0f0f0; padding-right: 10px; }\n",
"span.lineno { background-color: #f0f0f0; padding: 0 5px 0 5px; }\n",
"pre { line-height: 125%; }\n",
"body .hll { background-color: #ffffcc }\n",
"body { background: #f8f8f8; }\n",
"body .c { color: #408080; font-style: italic } /* Comment */\n",
"body .err { border: 1px solid #FF0000 } /* Error */\n",
"body .k { color: #008000; font-weight: bold } /* Keyword */\n",
"body .o { color: #666666 } /* Operator */\n",
"body .ch { color: #408080; font-style: italic } /* Comment.Hashbang */\n",
"body .cm { color: #408080; font-style: italic } /* Comment.Multiline */\n",
"body .cp { color: #BC7A00 } /* Comment.Preproc */\n",
"body .cpf { color: #408080; font-style: italic } /* Comment.PreprocFile */\n",
"body .c1 { color: #408080; font-style: italic } /* Comment.Single */\n",
"body .cs { color: #408080; font-style: italic } /* Comment.Special */\n",
"body .gd { color: #A00000 } /* Generic.Deleted */\n",
"body .ge { font-style: italic } /* Generic.Emph */\n",
"body .gr { color: #FF0000 } /* Generic.Error */\n",
"body .gh { color: #000080; font-weight: bold } /* Generic.Heading */\n",
"body .gi { color: #00A000 } /* Generic.Inserted */\n",
"body .go { color: #888888 } /* Generic.Output */\n",
"body .gp { color: #000080; font-weight: bold } /* Generic.Prompt */\n",
"body .gs { font-weight: bold } /* Generic.Strong */\n",
"body .gu { color: #800080; font-weight: bold } /* Generic.Subheading */\n",
"body .gt { color: #0044DD } /* Generic.Traceback */\n",
"body .kc { color: #008000; font-weight: bold } /* Keyword.Constant */\n",
"body .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */\n",
"body .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */\n",
"body .kp { color: #008000 } /* Keyword.Pseudo */\n",
"body .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */\n",
"body .kt { color: #B00040 } /* Keyword.Type */\n",
"body .m { color: #666666 } /* Literal.Number */\n",
"body .s { color: #BA2121 } /* Literal.String */\n",
"body .na { color: #7D9029 } /* Name.Attribute */\n",
"body .nb { color: #008000 } /* Name.Builtin */\n",
"body .nc { color: #0000FF; font-weight: bold } /* Name.Class */\n",
"body .no { color: #880000 } /* Name.Constant */\n",
"body .nd { color: #AA22FF } /* Name.Decorator */\n",
"body .ni { color: #999999; font-weight: bold } /* Name.Entity */\n",
"body .ne { color: #D2413A; font-weight: bold } /* Name.Exception */\n",
"body .nf { color: #0000FF } /* Name.Function */\n",
"body .nl { color: #A0A000 } /* Name.Label */\n",
"body .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */\n",
"body .nt { color: #008000; font-weight: bold } /* Name.Tag */\n",
"body .nv { color: #19177C } /* Name.Variable */\n",
"body .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */\n",
"body .w { color: #bbbbbb } /* Text.Whitespace */\n",
"body .mb { color: #666666 } /* Literal.Number.Bin */\n",
"body .mf { color: #666666 } /* Literal.Number.Float */\n",
"body .mh { color: #666666 } /* Literal.Number.Hex */\n",
"body .mi { color: #666666 } /* Literal.Number.Integer */\n",
"body .mo { color: #666666 } /* Literal.Number.Oct */\n",
"body .sa { color: #BA2121 } /* Literal.String.Affix */\n",
"body .sb { color: #BA2121 } /* Literal.String.Backtick */\n",
"body .sc { color: #BA2121 } /* Literal.String.Char */\n",
"body .dl { color: #BA2121 } /* Literal.String.Delimiter */\n",
"body .sd { color: #BA2121; font-style: italic } /* Literal.String.Doc */\n",
"body .s2 { color: #BA2121 } /* Literal.String.Double */\n",
"body .se { color: #BB6622; font-weight: bold } /* Literal.String.Escape */\n",
"body .sh { color: #BA2121 } /* Literal.String.Heredoc */\n",
"body .si { color: #BB6688; font-weight: bold } /* Literal.String.Interpol */\n",
"body .sx { color: #008000 } /* Literal.String.Other */\n",
"body .sr { color: #BB6688 } /* Literal.String.Regex */\n",
"body .s1 { color: #BA2121 } /* Literal.String.Single */\n",
"body .ss { color: #19177C } /* Literal.String.Symbol */\n",
"body .bp { color: #008000 } /* Name.Builtin.Pseudo */\n",
"body .fm { color: #0000FF } /* Name.Function.Magic */\n",
"body .vc { color: #19177C } /* Name.Variable.Class */\n",
"body .vg { color: #19177C } /* Name.Variable.Global */\n",
"body .vi { color: #19177C } /* Name.Variable.Instance */\n",
"body .vm { color: #19177C } /* Name.Variable.Magic */\n",
"body .il { color: #666666 } /* Literal.Number.Integer.Long */\n",
"\n",
" </style>\n",
"</head>\n",
"<body>\n",
"<h2></h2>\n",
"\n",
"<div class=\"highlight\"><pre><span></span><span class=\"k\">def</span> <span class=\"nf\">recombine</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">y</span><span class=\"p\">):</span>\n",
" <span class=\"n\">n</span> <span class=\"o\">=</span> <span class=\"nb\">len</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n",
" <span class=\"n\">c</span> <span class=\"o\">=</span> <span class=\"n\">random</span><span class=\"o\">.</span><span class=\"n\">randrange</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"n\">n</span><span class=\"p\">)</span>\n",
" <span class=\"k\">return</span> <span class=\"n\">x</span><span class=\"p\">[:</span><span class=\"n\">c</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"n\">y</span><span class=\"p\">[</span><span class=\"n\">c</span><span class=\"p\">:]</span>\n",
"</pre></div>\n",
"</body>\n",
"</html>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
Aman Deep Singh
a validé
"source": [
"psource(recombine)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The method picks at random a point and merges the parents (`x` and `y`) around it.\n",
"\n",
"The mutation is done in the method `mutate`:"
]
},
{
"cell_type": "code",
3626
3627
3628
3629
3630
3631
3632
3633
3634
3635
3636
3637
3638
3639
3640
3641
3642
3643
3644
3645
3646
3647
3648
3649
3650
3651
3652
3653
3654
3655
3656
3657
3658
3659
3660
3661
3662
3663
3664
3665
3666
3667
3668
3669
3670
3671
3672
3673
3674
3675
3676
3677
3678
3679
3680
3681
3682
3683
3684
3685
3686
3687
3688
3689
3690
3691
3692
3693
3694
3695
3696
3697
3698
3699
3700
3701
3702
3703
3704
3705
3706
3707
3708
3709
3710
3711
3712
3713
3714
3715
3716
3717
3718
3719
3720
3721
3722
3723
3724
3725
3726
3727
3728
3729
3730
3731
3732
3733
3734
3735
3736
3737
3738
3739
3740
"execution_count": 53,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<!DOCTYPE html PUBLIC \"-//W3C//DTD HTML 4.01//EN\"\n",
" \"http://www.w3.org/TR/html4/strict.dtd\">\n",
"\n",
"<html>\n",
"<head>\n",
" <title></title>\n",
" <meta http-equiv=\"content-type\" content=\"text/html; charset=None\">\n",
" <style type=\"text/css\">\n",
"td.linenos { background-color: #f0f0f0; padding-right: 10px; }\n",
"span.lineno { background-color: #f0f0f0; padding: 0 5px 0 5px; }\n",
"pre { line-height: 125%; }\n",
"body .hll { background-color: #ffffcc }\n",
"body { background: #f8f8f8; }\n",
"body .c { color: #408080; font-style: italic } /* Comment */\n",
"body .err { border: 1px solid #FF0000 } /* Error */\n",
"body .k { color: #008000; font-weight: bold } /* Keyword */\n",
"body .o { color: #666666 } /* Operator */\n",
"body .ch { color: #408080; font-style: italic } /* Comment.Hashbang */\n",
"body .cm { color: #408080; font-style: italic } /* Comment.Multiline */\n",
"body .cp { color: #BC7A00 } /* Comment.Preproc */\n",
"body .cpf { color: #408080; font-style: italic } /* Comment.PreprocFile */\n",
"body .c1 { color: #408080; font-style: italic } /* Comment.Single */\n",
"body .cs { color: #408080; font-style: italic } /* Comment.Special */\n",
"body .gd { color: #A00000 } /* Generic.Deleted */\n",
"body .ge { font-style: italic } /* Generic.Emph */\n",
"body .gr { color: #FF0000 } /* Generic.Error */\n",
"body .gh { color: #000080; font-weight: bold } /* Generic.Heading */\n",
"body .gi { color: #00A000 } /* Generic.Inserted */\n",
"body .go { color: #888888 } /* Generic.Output */\n",
"body .gp { color: #000080; font-weight: bold } /* Generic.Prompt */\n",
"body .gs { font-weight: bold } /* Generic.Strong */\n",
"body .gu { color: #800080; font-weight: bold } /* Generic.Subheading */\n",
"body .gt { color: #0044DD } /* Generic.Traceback */\n",
"body .kc { color: #008000; font-weight: bold } /* Keyword.Constant */\n",
"body .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */\n",
"body .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */\n",
"body .kp { color: #008000 } /* Keyword.Pseudo */\n",
"body .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */\n",
"body .kt { color: #B00040 } /* Keyword.Type */\n",
"body .m { color: #666666 } /* Literal.Number */\n",
"body .s { color: #BA2121 } /* Literal.String */\n",
"body .na { color: #7D9029 } /* Name.Attribute */\n",
"body .nb { color: #008000 } /* Name.Builtin */\n",
"body .nc { color: #0000FF; font-weight: bold } /* Name.Class */\n",
"body .no { color: #880000 } /* Name.Constant */\n",
"body .nd { color: #AA22FF } /* Name.Decorator */\n",
"body .ni { color: #999999; font-weight: bold } /* Name.Entity */\n",
"body .ne { color: #D2413A; font-weight: bold } /* Name.Exception */\n",
"body .nf { color: #0000FF } /* Name.Function */\n",
"body .nl { color: #A0A000 } /* Name.Label */\n",
"body .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */\n",
"body .nt { color: #008000; font-weight: bold } /* Name.Tag */\n",
"body .nv { color: #19177C } /* Name.Variable */\n",
"body .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */\n",
"body .w { color: #bbbbbb } /* Text.Whitespace */\n",
"body .mb { color: #666666 } /* Literal.Number.Bin */\n",
"body .mf { color: #666666 } /* Literal.Number.Float */\n",
"body .mh { color: #666666 } /* Literal.Number.Hex */\n",
"body .mi { color: #666666 } /* Literal.Number.Integer */\n",
"body .mo { color: #666666 } /* Literal.Number.Oct */\n",
"body .sa { color: #BA2121 } /* Literal.String.Affix */\n",
"body .sb { color: #BA2121 } /* Literal.String.Backtick */\n",
"body .sc { color: #BA2121 } /* Literal.String.Char */\n",
"body .dl { color: #BA2121 } /* Literal.String.Delimiter */\n",
"body .sd { color: #BA2121; font-style: italic } /* Literal.String.Doc */\n",
"body .s2 { color: #BA2121 } /* Literal.String.Double */\n",
"body .se { color: #BB6622; font-weight: bold } /* Literal.String.Escape */\n",
"body .sh { color: #BA2121 } /* Literal.String.Heredoc */\n",
"body .si { color: #BB6688; font-weight: bold } /* Literal.String.Interpol */\n",
"body .sx { color: #008000 } /* Literal.String.Other */\n",
"body .sr { color: #BB6688 } /* Literal.String.Regex */\n",
"body .s1 { color: #BA2121 } /* Literal.String.Single */\n",
"body .ss { color: #19177C } /* Literal.String.Symbol */\n",
"body .bp { color: #008000 } /* Name.Builtin.Pseudo */\n",
"body .fm { color: #0000FF } /* Name.Function.Magic */\n",
"body .vc { color: #19177C } /* Name.Variable.Class */\n",
"body .vg { color: #19177C } /* Name.Variable.Global */\n",
"body .vi { color: #19177C } /* Name.Variable.Instance */\n",
"body .vm { color: #19177C } /* Name.Variable.Magic */\n",
"body .il { color: #666666 } /* Literal.Number.Integer.Long */\n",
"\n",
" </style>\n",
"</head>\n",
"<body>\n",
"<h2></h2>\n",
"\n",
"<div class=\"highlight\"><pre><span></span><span class=\"k\">def</span> <span class=\"nf\">mutate</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">gene_pool</span><span class=\"p\">,</span> <span class=\"n\">pmut</span><span class=\"p\">):</span>\n",
" <span class=\"k\">if</span> <span class=\"n\">random</span><span class=\"o\">.</span><span class=\"n\">uniform</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"o\">>=</span> <span class=\"n\">pmut</span><span class=\"p\">:</span>\n",
" <span class=\"k\">return</span> <span class=\"n\">x</span>\n",
"\n",
" <span class=\"n\">n</span> <span class=\"o\">=</span> <span class=\"nb\">len</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n",
" <span class=\"n\">g</span> <span class=\"o\">=</span> <span class=\"nb\">len</span><span class=\"p\">(</span><span class=\"n\">gene_pool</span><span class=\"p\">)</span>\n",
" <span class=\"n\">c</span> <span class=\"o\">=</span> <span class=\"n\">random</span><span class=\"o\">.</span><span class=\"n\">randrange</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"n\">n</span><span class=\"p\">)</span>\n",
" <span class=\"n\">r</span> <span class=\"o\">=</span> <span class=\"n\">random</span><span class=\"o\">.</span><span class=\"n\">randrange</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"n\">g</span><span class=\"p\">)</span>\n",
"\n",
" <span class=\"n\">new_gene</span> <span class=\"o\">=</span> <span class=\"n\">gene_pool</span><span class=\"p\">[</span><span class=\"n\">r</span><span class=\"p\">]</span>\n",
" <span class=\"k\">return</span> <span class=\"n\">x</span><span class=\"p\">[:</span><span class=\"n\">c</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"p\">[</span><span class=\"n\">new_gene</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"n\">x</span><span class=\"p\">[</span><span class=\"n\">c</span><span class=\"o\">+</span><span class=\"mi\">1</span><span class=\"p\">:]</span>\n",
"</pre></div>\n",
"</body>\n",
"</html>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
Aman Deep Singh
a validé
"source": [
"psource(mutate)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We pick a gene in `x` to mutate and a gene from the gene pool to replace it with.\n",
"\n",
"To help initializing the population we have the helper function `init_population`\":"
]
},
{
"cell_type": "code",
3756
3757
3758
3759
3760
3761
3762
3763
3764
3765
3766
3767
3768
3769
3770
3771
3772
3773
3774
3775
3776
3777
3778
3779
3780
3781
3782
3783
3784
3785
3786
3787
3788
3789
3790
3791
3792
3793
3794
3795
3796
3797
3798
3799
3800
3801
3802
3803
3804
3805
3806
3807
3808
3809
3810
3811
3812
3813
3814
3815
3816
3817
3818
3819
3820
3821
3822
3823
3824
3825
3826
3827
3828
3829
3830
3831
3832
3833
3834
3835
3836
3837
3838
3839
3840
3841
3842
3843
3844
3845
3846
3847
3848
3849
3850
3851
3852
3853
3854
3855
3856
3857
3858
3859
3860
3861
3862
3863
3864
3865
3866
3867
3868
3869
3870
3871
"execution_count": 54,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<!DOCTYPE html PUBLIC \"-//W3C//DTD HTML 4.01//EN\"\n",
" \"http://www.w3.org/TR/html4/strict.dtd\">\n",
"\n",
"<html>\n",
"<head>\n",
" <title></title>\n",
" <meta http-equiv=\"content-type\" content=\"text/html; charset=None\">\n",
" <style type=\"text/css\">\n",
"td.linenos { background-color: #f0f0f0; padding-right: 10px; }\n",
"span.lineno { background-color: #f0f0f0; padding: 0 5px 0 5px; }\n",
"pre { line-height: 125%; }\n",
"body .hll { background-color: #ffffcc }\n",
"body { background: #f8f8f8; }\n",
"body .c { color: #408080; font-style: italic } /* Comment */\n",
"body .err { border: 1px solid #FF0000 } /* Error */\n",
"body .k { color: #008000; font-weight: bold } /* Keyword */\n",
"body .o { color: #666666 } /* Operator */\n",
"body .ch { color: #408080; font-style: italic } /* Comment.Hashbang */\n",
"body .cm { color: #408080; font-style: italic } /* Comment.Multiline */\n",
"body .cp { color: #BC7A00 } /* Comment.Preproc */\n",
"body .cpf { color: #408080; font-style: italic } /* Comment.PreprocFile */\n",
"body .c1 { color: #408080; font-style: italic } /* Comment.Single */\n",
"body .cs { color: #408080; font-style: italic } /* Comment.Special */\n",
"body .gd { color: #A00000 } /* Generic.Deleted */\n",
"body .ge { font-style: italic } /* Generic.Emph */\n",
"body .gr { color: #FF0000 } /* Generic.Error */\n",
"body .gh { color: #000080; font-weight: bold } /* Generic.Heading */\n",
"body .gi { color: #00A000 } /* Generic.Inserted */\n",
"body .go { color: #888888 } /* Generic.Output */\n",
"body .gp { color: #000080; font-weight: bold } /* Generic.Prompt */\n",
"body .gs { font-weight: bold } /* Generic.Strong */\n",
"body .gu { color: #800080; font-weight: bold } /* Generic.Subheading */\n",
"body .gt { color: #0044DD } /* Generic.Traceback */\n",
"body .kc { color: #008000; font-weight: bold } /* Keyword.Constant */\n",
"body .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */\n",
"body .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */\n",
"body .kp { color: #008000 } /* Keyword.Pseudo */\n",
"body .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */\n",
"body .kt { color: #B00040 } /* Keyword.Type */\n",
"body .m { color: #666666 } /* Literal.Number */\n",
"body .s { color: #BA2121 } /* Literal.String */\n",
"body .na { color: #7D9029 } /* Name.Attribute */\n",
"body .nb { color: #008000 } /* Name.Builtin */\n",
"body .nc { color: #0000FF; font-weight: bold } /* Name.Class */\n",
"body .no { color: #880000 } /* Name.Constant */\n",
"body .nd { color: #AA22FF } /* Name.Decorator */\n",
"body .ni { color: #999999; font-weight: bold } /* Name.Entity */\n",
"body .ne { color: #D2413A; font-weight: bold } /* Name.Exception */\n",
"body .nf { color: #0000FF } /* Name.Function */\n",
"body .nl { color: #A0A000 } /* Name.Label */\n",
"body .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */\n",
"body .nt { color: #008000; font-weight: bold } /* Name.Tag */\n",
"body .nv { color: #19177C } /* Name.Variable */\n",
"body .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */\n",
"body .w { color: #bbbbbb } /* Text.Whitespace */\n",
"body .mb { color: #666666 } /* Literal.Number.Bin */\n",
"body .mf { color: #666666 } /* Literal.Number.Float */\n",
"body .mh { color: #666666 } /* Literal.Number.Hex */\n",
"body .mi { color: #666666 } /* Literal.Number.Integer */\n",
"body .mo { color: #666666 } /* Literal.Number.Oct */\n",
"body .sa { color: #BA2121 } /* Literal.String.Affix */\n",
"body .sb { color: #BA2121 } /* Literal.String.Backtick */\n",
"body .sc { color: #BA2121 } /* Literal.String.Char */\n",
"body .dl { color: #BA2121 } /* Literal.String.Delimiter */\n",
"body .sd { color: #BA2121; font-style: italic } /* Literal.String.Doc */\n",
"body .s2 { color: #BA2121 } /* Literal.String.Double */\n",
"body .se { color: #BB6622; font-weight: bold } /* Literal.String.Escape */\n",
"body .sh { color: #BA2121 } /* Literal.String.Heredoc */\n",
"body .si { color: #BB6688; font-weight: bold } /* Literal.String.Interpol */\n",
"body .sx { color: #008000 } /* Literal.String.Other */\n",
"body .sr { color: #BB6688 } /* Literal.String.Regex */\n",
"body .s1 { color: #BA2121 } /* Literal.String.Single */\n",
"body .ss { color: #19177C } /* Literal.String.Symbol */\n",
"body .bp { color: #008000 } /* Name.Builtin.Pseudo */\n",
"body .fm { color: #0000FF } /* Name.Function.Magic */\n",
"body .vc { color: #19177C } /* Name.Variable.Class */\n",
"body .vg { color: #19177C } /* Name.Variable.Global */\n",
"body .vi { color: #19177C } /* Name.Variable.Instance */\n",
"body .vm { color: #19177C } /* Name.Variable.Magic */\n",
"body .il { color: #666666 } /* Literal.Number.Integer.Long */\n",
"\n",
" </style>\n",
"</head>\n",
"<body>\n",
"<h2></h2>\n",
"\n",
"<div class=\"highlight\"><pre><span></span><span class=\"k\">def</span> <span class=\"nf\">init_population</span><span class=\"p\">(</span><span class=\"n\">pop_number</span><span class=\"p\">,</span> <span class=\"n\">gene_pool</span><span class=\"p\">,</span> <span class=\"n\">state_length</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""Initializes population for genetic algorithm</span>\n",
"<span class=\"sd\"> pop_number : Number of individuals in population</span>\n",
"<span class=\"sd\"> gene_pool : List of possible values for individuals</span>\n",
"<span class=\"sd\"> state_length: The length of each individual"""</span>\n",
" <span class=\"n\">g</span> <span class=\"o\">=</span> <span class=\"nb\">len</span><span class=\"p\">(</span><span class=\"n\">gene_pool</span><span class=\"p\">)</span>\n",
" <span class=\"n\">population</span> <span class=\"o\">=</span> <span class=\"p\">[]</span>\n",
" <span class=\"k\">for</span> <span class=\"n\">i</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">pop_number</span><span class=\"p\">):</span>\n",
" <span class=\"n\">new_individual</span> <span class=\"o\">=</span> <span class=\"p\">[</span><span class=\"n\">gene_pool</span><span class=\"p\">[</span><span class=\"n\">random</span><span class=\"o\">.</span><span class=\"n\">randrange</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"n\">g</span><span class=\"p\">)]</span> <span class=\"k\">for</span> <span class=\"n\">j</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">state_length</span><span class=\"p\">)]</span>\n",
" <span class=\"n\">population</span><span class=\"o\">.</span><span class=\"n\">append</span><span class=\"p\">(</span><span class=\"n\">new_individual</span><span class=\"p\">)</span>\n",
"\n",
" <span class=\"k\">return</span> <span class=\"n\">population</span>\n",
"</pre></div>\n",
"</body>\n",
"</html>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
Aman Deep Singh
a validé
"source": [
"psource(init_population)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The function takes as input the number of individuals in the population, the gene pool and the length of each individual/state. It creates individuals with random genes and returns the population when done."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Explanation\n",
"\n",
"Before we solve problems using the genetic algorithm, we will explain how to intuitively understand the algorithm using a trivial example.\n",
Aman Deep Singh
a validé
"\n",
"#### Generating Phrases\n",
"\n",
"In this problem, we use a genetic algorithm to generate a particular target phrase from a population of random strings. This is a classic example that helps build intuition about how to use this algorithm in other problems as well. Before we break the problem down, let us try to brute force the solution. Let us say that we want to generate the phrase \"genetic algorithm\". The phrase is 17 characters long. We can use any character from the 26 lowercase characters and the space character. To generate a random phrase of length 17, each space can be filled in 27 ways. So the total number of possible phrases is\n",
"\n",
"$$ 27^{17} = 2153693963075557766310747 $$\n",
"\n",
"which is a massive number. If we wanted to generate the phrase \"Genetic Algorithm\", we would also have to include all the 26 uppercase characters into consideration thereby increasing the sample space from 27 characters to 53 characters and the total number of possible phrases then would be\n",
"\n",
"$$ 53^{17} = 205442259656281392806087233013 $$\n",
"\n",
"If we wanted to include punctuations and numerals into the sample space, we would have further complicated an already impossible problem. Hence, brute forcing is not an option. Now we'll apply the genetic algorithm and see how it significantly reduces the search space. We essentially want to *evolve* our population of random strings so that they better approximate the target phrase as the number of generations increase. Genetic algorithms work on the principle of Darwinian Natural Selection according to which, there are three key concepts that need to be in place for evolution to happen. They are:\n",
"\n",
"* **Heredity**: There must be a process in place by which children receive the properties of their parents. <br> \n",
Aman Deep Singh
a validé
"For this particular problem, two strings from the population will be chosen as parents and will be split at a random index and recombined as described in the `recombine` function to create a child. This child string will then be added to the new generation.\n",
"\n",
"\n",
"* **Variation**: There must be a variety of traits present in the population or a means with which to introduce variation. <br>If there is no variation in the sample space, we might never reach the global optimum. To ensure that there is enough variation, we can initialize a large population, but this gets computationally expensive as the population gets larger. Hence, we often use another method called mutation. In this method, we randomly change one or more characters of some strings in the population based on a predefined probability value called the mutation rate or mutation probability as described in the `mutate` function. The mutation rate is usually kept quite low. A mutation rate of zero fails to introduce variation in the population and a high mutation rate (say 50%) is as good as a coin flip and the population fails to benefit from the previous recombinations. An optimum balance has to be maintained between population size and mutation rate so as to reduce the computational cost as well as have sufficient variation in the population.\n",
"\n",
"\n",
"* **Selection**: There must be some mechanism by which some members of the population have the opportunity to be parents and pass down their genetic information and some do not. This is typically referred to as \"survival of the fittest\". <br>\n",
Aman Deep Singh
a validé
"There has to be some way of determining which phrases in our population have a better chance of eventually evolving into the target phrase. This is done by introducing a fitness function that calculates how close the generated phrase is to the target phrase. The function will simply return a scalar value corresponding to the number of matching characters between the generated phrase and the target phrase."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Before solving the problem, we first need to define our target phrase."
]
},
{
"cell_type": "code",
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
Aman Deep Singh
a validé
"target = 'Genetic Algorithm'"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"We then need to define our gene pool, i.e the elements which an individual from the population might comprise of. Here, the gene pool contains all uppercase and lowercase letters of the English alphabet and the space character."
]
},
{
"cell_type": "code",
Aman Deep Singh
a validé
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# The ASCII values of uppercase characters ranges from 65 to 91\n",
"u_case = [chr(x) for x in range(65, 91)]\n",
"# The ASCII values of lowercase characters ranges from 97 to 123\n",
"l_case = [chr(x) for x in range(97, 123)]\n",
"\n",
"gene_pool = []\n",
"gene_pool.extend(u_case) # adds the uppercase list to the gene pool\n",
"gene_pool.extend(l_case) # adds the lowercase list to the gene pool\n",
"gene_pool.append(' ') # adds the space character to the gene pool"
]
},
{
"cell_type": "markdown",
Aman Deep Singh
a validé
"We now need to define the maximum size of each population. Larger populations have more variation but are computationally more expensive to run algorithms on."
]
},
{
"cell_type": "code",
Aman Deep Singh
a validé
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"max_population = 100"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As our population is not very large, we can afford to keep a relatively large mutation rate."
]
},
{
"cell_type": "code",
Aman Deep Singh
a validé
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"mutation_rate = 0.07 # 7%"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Great! Now, we need to define the most important metric for the genetic algorithm, i.e the fitness function. This will simply return the number of matching characters between the generated sample and the target phrase."
]
},
{
"cell_type": "code",
Aman Deep Singh
a validé
4006
4007
4008
4009
4010
4011
4012
4013
4014
4015
4016
4017
4018
4019
4020
4021
4022
4023
4024
4025
4026
4027
4028
4029
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def fitness_fn(sample):\n",
" # initialize fitness to 0\n",
" fitness = 0\n",
" for i in range(len(sample)):\n",
" # increment fitness by 1 for every matching character\n",
" if sample[i] == target[i]:\n",
" fitness += 1\n",
" return fitness"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Before we run our genetic algorithm, we need to initialize a random population. We will use the `init_population` function to do this. We need to pass in the maximum population size, the gene pool and the length of each individual, which in this case will be the same as the length of the target phrase."
]
},
{
"cell_type": "code",
Aman Deep Singh
a validé
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"population = init_population(max_population, gene_pool, len(target))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We will now define how the individuals in the population should change as the number of generations increases. First, the `select` function will be run on the population to select *two* individuals with high fitness values. These will be the parents which will then be recombined using the `recombine` function to generate the child."
]
},
{
"cell_type": "code",
Aman Deep Singh
a validé
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"parents = select(2, population, fitness_fn) "
]
},
{
"cell_type": "code",
Aman Deep Singh
a validé
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# The recombine function takes two parents as arguments, so we need to unpack the previous variable\n",
"child = recombine(*parents)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next, we need to apply a mutation according to the mutation rate. We call the `mutate` function on the child with the gene pool and mutation rate as the additional arguments."
]
},
{
"cell_type": "code",
Aman Deep Singh
a validé
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"child = mutate(child, gene_pool, mutation_rate)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The above lines can be condensed into\n",
Aman Deep Singh
a validé
"`child = mutate(recombine(*select(2, population, fitness_fn)), gene_pool, mutation_rate)`\n",
"\n",
"And, we need to do this `for` every individual in the current population to generate the new population."
]
},
{
"cell_type": "code",
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
Aman Deep Singh
a validé
"population = [mutate(recombine(*select(2, population, fitness_fn)), gene_pool, mutation_rate) for i in range(len(population))]"
]
},
{
"cell_type": "markdown",
Aman Deep Singh
a validé
"The individual with the highest fitness can then be found using the `max` function."
]
},
{
"cell_type": "code",
Aman Deep Singh
a validé
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"current_best = max(population, key=fitness_fn)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's print this out"
]
},
{
"cell_type": "code",
"execution_count": 66,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"['J', 'y', 'O', 'e', ' ', 'h', 'c', 'r', 'C', 'W', 'H', 'o', 'r', 'R', 'y', 'P', 'U']\n"
]
}
],
Aman Deep Singh
a validé
"source": [
"print(current_best)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We see that this is a list of characters. This can be converted to a string using the join function"
]
},
{
"cell_type": "code",
"execution_count": 67,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"JyOe hcrCWHorRyPU\n"
]
}
],
Aman Deep Singh
a validé
"source": [
"current_best_string = ''.join(current_best)\n",
"print(current_best_string)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now need to define the conditions to terminate the algorithm. This can happen in two ways\n",
"1. Termination after a predefined number of generations\n",
"2. Termination when the fitness of the best individual of the current generation reaches a predefined threshold value.\n",
Aman Deep Singh
a validé
"We define these variables below"
]
},
{
"cell_type": "code",
Aman Deep Singh
a validé
4190
4191
4192
4193
4194
4195
4196
4197
4198
4199
4200
4201
4202
4203
4204
4205
4206
4207
4208
4209
4210
4211
4212
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"ngen = 1200 # maximum number of generations\n",
"# we set the threshold fitness equal to the length of the target phrase\n",
"# i.e the algorithm only terminates whne it has got all the characters correct \n",
"# or it has completed 'ngen' number of generations\n",
"f_thres = len(target)"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"To generate `ngen` number of generations, we run a `for` loop `ngen` number of times. After each generation, we calculate the fitness of the best individual of the generation and compare it to the value of `f_thres` using the `fitness_threshold` function. After every generation, we print out the best individual of the generation and the corresponding fitness value. Lets now write a function to do this."
]
},
{
"cell_type": "code",
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
Aman Deep Singh
a validé
"def genetic_algorithm_stepwise(population, fitness_fn, gene_pool=[0, 1], f_thres=None, ngen=1200, pmut=0.1):\n",
" for generation in range(ngen):\n",
" population = [mutate(recombine(*select(2, population, fitness_fn)), gene_pool, pmut) for i in range(len(population))]\n",
" # stores the individual genome with the highest fitness in the current population\n",
" current_best = ''.join(max(population, key=fitness_fn))\n",
" print(f'Current best: {current_best}\\t\\tGeneration: {str(generation)}\\t\\tFitness: {fitness_fn(current_best)}\\r', end='')\n",
" \n",
" # compare the fitness of the current best individual to f_thres\n",
" fittest_individual = fitness_threshold(fitness_fn, f_thres, population)\n",
" \n",
" # if fitness is greater than or equal to f_thres, we terminate the algorithm\n",
" if fittest_individual:\n",
" return fittest_individual, generation\n",
" return max(population, key=fitness_fn) , generation "
]
},
{
"cell_type": "markdown",
Aman Deep Singh
a validé
"The function defined above is essentially the same as the one defined in `search.py` with the added functionality of printing out the data of each generation."
]
},
{
"cell_type": "code",
4244
4245
4246
4247
4248
4249
4250
4251
4252
4253
4254
4255
4256
4257
4258
4259
4260
4261
4262
4263
4264
4265
4266
4267
4268
4269
4270
4271
4272
4273
4274
4275
4276
4277
4278
4279
4280
4281
4282
4283
4284
4285
4286
4287
4288
4289
4290
4291
4292
4293
4294
4295
4296
4297
4298
4299
4300
4301
4302
4303
4304
4305
4306
4307
4308
4309
4310
4311
4312
4313
4314
4315
4316
4317
4318
4319
4320
4321
4322
4323
4324
4325
4326
4327
4328
4329
4330
4331
4332
4333
4334
4335
4336
4337
4338
4339
4340
4341
4342
4343
4344
4345
4346
4347
4348
4349
4350
4351
4352
4353
4354
4355
4356
4357
4358
4359
"execution_count": 70,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<!DOCTYPE html PUBLIC \"-//W3C//DTD HTML 4.01//EN\"\n",
" \"http://www.w3.org/TR/html4/strict.dtd\">\n",
"\n",
"<html>\n",
"<head>\n",
" <title></title>\n",
" <meta http-equiv=\"content-type\" content=\"text/html; charset=None\">\n",
" <style type=\"text/css\">\n",
"td.linenos { background-color: #f0f0f0; padding-right: 10px; }\n",
"span.lineno { background-color: #f0f0f0; padding: 0 5px 0 5px; }\n",
"pre { line-height: 125%; }\n",
"body .hll { background-color: #ffffcc }\n",
"body { background: #f8f8f8; }\n",
"body .c { color: #408080; font-style: italic } /* Comment */\n",
"body .err { border: 1px solid #FF0000 } /* Error */\n",
"body .k { color: #008000; font-weight: bold } /* Keyword */\n",
"body .o { color: #666666 } /* Operator */\n",
"body .ch { color: #408080; font-style: italic } /* Comment.Hashbang */\n",
"body .cm { color: #408080; font-style: italic } /* Comment.Multiline */\n",
"body .cp { color: #BC7A00 } /* Comment.Preproc */\n",
"body .cpf { color: #408080; font-style: italic } /* Comment.PreprocFile */\n",
"body .c1 { color: #408080; font-style: italic } /* Comment.Single */\n",
"body .cs { color: #408080; font-style: italic } /* Comment.Special */\n",
"body .gd { color: #A00000 } /* Generic.Deleted */\n",
"body .ge { font-style: italic } /* Generic.Emph */\n",
"body .gr { color: #FF0000 } /* Generic.Error */\n",
"body .gh { color: #000080; font-weight: bold } /* Generic.Heading */\n",
"body .gi { color: #00A000 } /* Generic.Inserted */\n",
"body .go { color: #888888 } /* Generic.Output */\n",
"body .gp { color: #000080; font-weight: bold } /* Generic.Prompt */\n",
"body .gs { font-weight: bold } /* Generic.Strong */\n",
"body .gu { color: #800080; font-weight: bold } /* Generic.Subheading */\n",
"body .gt { color: #0044DD } /* Generic.Traceback */\n",
"body .kc { color: #008000; font-weight: bold } /* Keyword.Constant */\n",
"body .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */\n",
"body .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */\n",
"body .kp { color: #008000 } /* Keyword.Pseudo */\n",
"body .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */\n",
"body .kt { color: #B00040 } /* Keyword.Type */\n",
"body .m { color: #666666 } /* Literal.Number */\n",
"body .s { color: #BA2121 } /* Literal.String */\n",
"body .na { color: #7D9029 } /* Name.Attribute */\n",
"body .nb { color: #008000 } /* Name.Builtin */\n",
"body .nc { color: #0000FF; font-weight: bold } /* Name.Class */\n",
"body .no { color: #880000 } /* Name.Constant */\n",
"body .nd { color: #AA22FF } /* Name.Decorator */\n",
"body .ni { color: #999999; font-weight: bold } /* Name.Entity */\n",
"body .ne { color: #D2413A; font-weight: bold } /* Name.Exception */\n",
"body .nf { color: #0000FF } /* Name.Function */\n",
"body .nl { color: #A0A000 } /* Name.Label */\n",
"body .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */\n",
"body .nt { color: #008000; font-weight: bold } /* Name.Tag */\n",
"body .nv { color: #19177C } /* Name.Variable */\n",
"body .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */\n",
"body .w { color: #bbbbbb } /* Text.Whitespace */\n",
"body .mb { color: #666666 } /* Literal.Number.Bin */\n",
"body .mf { color: #666666 } /* Literal.Number.Float */\n",
"body .mh { color: #666666 } /* Literal.Number.Hex */\n",
"body .mi { color: #666666 } /* Literal.Number.Integer */\n",
"body .mo { color: #666666 } /* Literal.Number.Oct */\n",
"body .sa { color: #BA2121 } /* Literal.String.Affix */\n",
"body .sb { color: #BA2121 } /* Literal.String.Backtick */\n",
"body .sc { color: #BA2121 } /* Literal.String.Char */\n",
"body .dl { color: #BA2121 } /* Literal.String.Delimiter */\n",
"body .sd { color: #BA2121; font-style: italic } /* Literal.String.Doc */\n",
"body .s2 { color: #BA2121 } /* Literal.String.Double */\n",
"body .se { color: #BB6622; font-weight: bold } /* Literal.String.Escape */\n",
"body .sh { color: #BA2121 } /* Literal.String.Heredoc */\n",
"body .si { color: #BB6688; font-weight: bold } /* Literal.String.Interpol */\n",
"body .sx { color: #008000 } /* Literal.String.Other */\n",
"body .sr { color: #BB6688 } /* Literal.String.Regex */\n",
"body .s1 { color: #BA2121 } /* Literal.String.Single */\n",
"body .ss { color: #19177C } /* Literal.String.Symbol */\n",
"body .bp { color: #008000 } /* Name.Builtin.Pseudo */\n",
"body .fm { color: #0000FF } /* Name.Function.Magic */\n",
"body .vc { color: #19177C } /* Name.Variable.Class */\n",
"body .vg { color: #19177C } /* Name.Variable.Global */\n",
"body .vi { color: #19177C } /* Name.Variable.Instance */\n",
"body .vm { color: #19177C } /* Name.Variable.Magic */\n",
"body .il { color: #666666 } /* Literal.Number.Integer.Long */\n",
"\n",
" </style>\n",
"</head>\n",
"<body>\n",
"<h2></h2>\n",
"\n",
"<div class=\"highlight\"><pre><span></span><span class=\"k\">def</span> <span class=\"nf\">genetic_algorithm</span><span class=\"p\">(</span><span class=\"n\">population</span><span class=\"p\">,</span> <span class=\"n\">fitness_fn</span><span class=\"p\">,</span> <span class=\"n\">gene_pool</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">],</span> <span class=\"n\">f_thres</span><span class=\"o\">=</span><span class=\"bp\">None</span><span class=\"p\">,</span> <span class=\"n\">ngen</span><span class=\"o\">=</span><span class=\"mi\">1000</span><span class=\"p\">,</span> <span class=\"n\">pmut</span><span class=\"o\">=</span><span class=\"mf\">0.1</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""[Figure 4.8]"""</span>\n",
" <span class=\"k\">for</span> <span class=\"n\">i</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">ngen</span><span class=\"p\">):</span>\n",
" <span class=\"n\">population</span> <span class=\"o\">=</span> <span class=\"p\">[</span><span class=\"n\">mutate</span><span class=\"p\">(</span><span class=\"n\">recombine</span><span class=\"p\">(</span><span class=\"o\">*</span><span class=\"n\">select</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span> <span class=\"n\">population</span><span class=\"p\">,</span> <span class=\"n\">fitness_fn</span><span class=\"p\">)),</span> <span class=\"n\">gene_pool</span><span class=\"p\">,</span> <span class=\"n\">pmut</span><span class=\"p\">)</span>\n",
" <span class=\"k\">for</span> <span class=\"n\">i</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"nb\">len</span><span class=\"p\">(</span><span class=\"n\">population</span><span class=\"p\">))]</span>\n",
"\n",
" <span class=\"n\">fittest_individual</span> <span class=\"o\">=</span> <span class=\"n\">fitness_threshold</span><span class=\"p\">(</span><span class=\"n\">fitness_fn</span><span class=\"p\">,</span> <span class=\"n\">f_thres</span><span class=\"p\">,</span> <span class=\"n\">population</span><span class=\"p\">)</span>\n",
" <span class=\"k\">if</span> <span class=\"n\">fittest_individual</span><span class=\"p\">:</span>\n",
" <span class=\"k\">return</span> <span class=\"n\">fittest_individual</span>\n",
"\n",
"\n",
" <span class=\"k\">return</span> <span class=\"n\">argmax</span><span class=\"p\">(</span><span class=\"n\">population</span><span class=\"p\">,</span> <span class=\"n\">key</span><span class=\"o\">=</span><span class=\"n\">fitness_fn</span><span class=\"p\">)</span>\n",
"</pre></div>\n",
"</body>\n",
"</html>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
Aman Deep Singh
a validé
"source": [
"psource(genetic_algorithm)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We have defined all the required functions and variables. Let's now create a new population and test the function we wrote above."
]
},
{
"cell_type": "code",
"execution_count": 71,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Current best: Genetic Algorithm\t\tGeneration: 985\t\tFitness: 17\r"
]
}
],
Aman Deep Singh
a validé
"source": [
"population = init_population(max_population, gene_pool, len(target))\n",
"solution, generations = genetic_algorithm_stepwise(population, fitness_fn, gene_pool, f_thres, ngen, mutation_rate)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The genetic algorithm was able to converge!\n",
"We implore you to rerun the above cell and play around with `target, max_population, f_thres, ngen` etc parameters to get a better intuition of how the algorithm works. To summarize, if we can define the problem states in simple array format and if we can create a fitness function to gauge how good or bad our approximate solutions are, there is a high chance that we can get a satisfactory solution using a genetic algorithm. \n",
"- There is also a better GUI version of this program `genetic_algorithm_example.py` in the GUI folder for you to play around with."
]
},
{
"cell_type": "markdown",
"source": [
"### Usage\n",
"Below we give two example usages for the genetic algorithm, for a graph coloring problem and the 8 queens problem.\n",
"First we will take on the simpler problem of coloring a small graph with two colors. Before we do anything, let's imagine how a solution might look. First, we have to represent our colors. Say, 'R' for red and 'G' for green. These make up our gene pool. What of the individual solutions though? For that, we will look at our problem. We stated we have a graph. A graph has nodes and edges, and we want to color the nodes. Naturally, we want to store each node's color. If we have four nodes, we can store their colors in a list of genes, one for each node. A possible solution will then look like this: ['R', 'R', 'G', 'R']. In the general case, we will represent each solution with a list of chars ('R' and 'G'), with length the number of nodes.\n",
"Next we need to come up with a fitness function that appropriately scores individuals. Again, we will look at the problem definition at hand. We want to color a graph. For a solution to be optimal, no edge should connect two nodes of the same color. How can we use this information to score a solution? A naive (and ineffective) approach would be to count the different colors in the string. So ['R', 'R', 'R', 'R'] has a score of 1 and ['R', 'R', 'G', 'G'] has a score of 2. Why that fitness function is not ideal though? Why, we forgot the information about the edges! The edges are pivotal to the problem and the above function only deals with node colors. We didn't use all the information at hand and ended up with an ineffective answer. How, then, can we use that information to our advantage?\n",
"We said that the optimal solution will have all the edges connecting nodes of different color. So, to score a solution we can count how many edges are valid (aka connecting nodes of different color). That is a great fitness function!\n",
"Let's jump into solving this problem using the `genetic_algorithm` function."
]
},
{
"cell_type": "markdown",
"source": [
"First we need to represent the graph. Since we mostly need information about edges, we will just store the edges. We will denote edges with capital letters and nodes with integers:"
]
},
{
"cell_type": "code",
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"edges = {\n",
" 'A': [0, 1],\n",
" 'B': [0, 3],\n",
" 'C': [1, 2],\n",
" 'D': [2, 3]\n",
"}"
]
},
{
"cell_type": "markdown",
"Edge 'A' connects nodes 0 and 1, edge 'B' connects nodes 0 and 3 etc.\n",
"\n",
"We already said our gene pool is 'R' and 'G', so we can jump right into initializing our population. Since we have only four nodes, `state_length` should be 4. For the number of individuals, we will try 8. We can increase this number if we need higher accuracy, but be careful! Larger populations need more computating power and take longer. You need to strike that sweet balance between accuracy and cost (the ultimate dilemma of the programmer!)."
]
},
{
"cell_type": "code",
"execution_count": 73,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[['R', 'G', 'G', 'G'], ['G', 'R', 'R', 'G'], ['G', 'G', 'G', 'G'], ['G', 'R', 'G', 'G'], ['G', 'G', 'G', 'R'], ['G', 'R', 'R', 'G'], ['G', 'R', 'G', 'G'], ['G', 'G', 'R', 'G']]\n"
]
}
],
"population = init_population(8, ['R', 'G'], 4)\n",
]
},
{
"cell_type": "markdown",
"We created and printed the population. You can see that the genes in the individuals are random and there are 8 individuals each with 4 genes.\n",
"Next we need to write our fitness function. We previously said we want the function to count how many edges are valid. So, given a coloring/individual `c`, we will do just that:"
]
},
{
"cell_type": "code",
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def fitness(c):\n",
" return sum(c[n1] != c[n2] for (n1, n2) in edges.values())"
]
},
{
"cell_type": "markdown",
"Great! Now we will run the genetic algorithm and see what solution it gives."
]
},
{
"cell_type": "code",
"execution_count": 75,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"['R', 'G', 'R', 'G']\n"
]
}
],
"solution = genetic_algorithm(population, fitness, gene_pool=['R', 'G'])\n",
"print(solution)"
]
},
{
"cell_type": "markdown",
"source": [
"The algorithm converged to a solution. Let's check its score:"
]
},
{
"cell_type": "code",
"execution_count": 76,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"4\n"
]
}
],
"source": [
"print(fitness(solution))"
]
},
{
"cell_type": "markdown",
"source": [
"The solution has a score of 4. Which means it is optimal, since we have exactly 4 edges in our graph, meaning all are valid!\n",
"*NOTE: Because the algorithm is non-deterministic, there is a chance a different solution is given. It might even be wrong, if we are very unlucky!*"
]
},
{
"cell_type": "markdown",
"#### Eight Queens\n",
"\n",
"Let's take a look at a more complicated problem.\n",
"\n",
"In the *Eight Queens* problem, we are tasked with placing eight queens on an 8x8 chessboard without any queen threatening the others (aka queens should not be in the same row, column or diagonal). In its general form the problem is defined as placing *N* queens in an NxN chessboard without any conflicts.\n",
"\n",
"First we need to think about the representation of each solution. We can go the naive route of representing the whole chessboard with the queens' placements on it. That is definitely one way to go about it, but for the purpose of this tutorial we will do something different. We have eight queens, so we will have a gene for each of them. The gene pool will be numbers from 0 to 7, for the different columns. The *position* of the gene in the state will denote the row the particular queen is placed in.\n",
"\n",
"For example, we can have the state \"03304577\". Here the first gene with a value of 0 means \"the queen at row 0 is placed at column 0\", for the second gene \"the queen at row 1 is placed at column 3\" and so forth.\n",
"\n",
"We now need to think about the fitness function. On the graph coloring problem we counted the valid edges. The same thought process can be applied here. Instead of edges though, we have positioning between queens. If two queens are not threatening each other, we say they are at a \"non-attacking\" positioning. We can, therefore, count how many such positionings are there.\n",
"\n",
"Let's dive right in and initialize our population:"
]
},
{
"cell_type": "code",
"execution_count": 77,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[[2, 6, 2, 0, 2, 3, 4, 7], [7, 2, 0, 6, 3, 3, 0, 6], [2, 3, 0, 6, 6, 2, 5, 5], [2, 6, 4, 2, 3, 5, 5, 5], [3, 1, 5, 1, 5, 1, 0, 3]]\n"
]
}
],
"population = init_population(100, range(8), 8)\n",
]
},
{
"cell_type": "markdown",
"We have a population of 100 and each individual has 8 genes. The gene pool is the integers from 0 to 7, in string form. Above you can see the first five individuals.\n",
"\n",
"Next we need to write our fitness function. Remember, queens threaten each other if they are at the same row, column or diagonal.\n",
"Since positionings are mutual, we must take care not to count them twice. Therefore for each queen, we will only check for conflicts for the queens after her.\n",
"\n",
"A gene's value in an individual `q` denotes the queen's column, and the position of the gene denotes its row. We can check if the aforementioned values between two genes are the same. We also need to check for diagonals. A queen *a* is in the diagonal of another queen, *b*, if the difference of the rows between them is equal to either their difference in columns (for the diagonal on the right of *a*) or equal to the negative difference of their columns (for the left diagonal of *a*). Below is given the fitness function."
]
},
{
"cell_type": "code",
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def fitness(q):\n",
" non_attacking = 0\n",
" for row1 in range(len(q)):\n",
" for row2 in range(row1+1, len(q)):\n",
" col1 = int(q[row1])\n",
" col2 = int(q[row2])\n",
" row_diff = row1 - row2\n",
" col_diff = col1 - col2\n",
" if col1 != col2 and row_diff != col_diff and row_diff != -col_diff:\n",
" non_attacking += 1\n",
]
},
{
"cell_type": "markdown",
"Note that the best score achievable is 28. That is because for each queen we only check for the queens after her. For the first queen we check 7 other queens, for the second queen 6 others and so on. In short, the number of checks we make is the sum 7+6+5+...+1. Which is equal to 7\\*(7+1)/2 = 28.\n",
"\n",
"Because it is very hard and will take long to find a perfect solution, we will set the fitness threshold at 25. If we find an individual with a score greater or equal to that, we will halt. Let's see how the genetic algorithm will fare."
"execution_count": 79,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[2, 5, 7, 1, 3, 6, 4, 6]\n",
"25\n"
]
}
],
"solution = genetic_algorithm(population, fitness, f_thres=25, gene_pool=range(8))\n",
"print(solution)\n",
"print(fitness(solution))"
]
},
{
"cell_type": "markdown",
"Above you can see the solution and its fitness score, which should be no less than 25."
]
},
{
"cell_type": "markdown",
4659
4660
4661
4662
4663
4664
4665
4666
4667
4668
4669
4670
4671
4672
4673
4674
4675
4676
4677
4678
4679
4680
4681
4682
4683
4684
4685
4686
4687
4688
4689
4690
4691
4692
4693
4694
4695
4696
4697
4698
4699
4700
4701
4702
4703
4704
4705
4706
4707
4708
4709
4710
4711
4712
4713
4714
4715
4716
4717
4718
4719
4720
4721
4722
4723
4724
4725
4726
4727
4728
4729
4730
4731
4732
4733
4734
4735
4736
4737
4738
4739
4740
4741
4742
4743
4744
4745
4746
4747
4748
4749
4750
4751
4752
4753
4754
4755
4756
4757
4758
4759
4760
4761
4762
4763
4764
4765
4766
4767
4768
4769
4770
4771
4772
4773
4774
4775
4776
4777
4778
4779
4780
4781
4782
4783
4784
4785
4786
4787
4788
4789
4790
4791
4792
4793
4794
4795
4796
4797
4798
4799
4800
4801
4802
4803
4804
4805
4806
4807
4808
4809
4810
4811
4812
4813
4814
4815
4816
4817
4818
4819
4820
4821
4822
4823
4824
4825
4826
4827
4828
4829
4830
4831
4832
4833
4834
4835
4836
4837
4838
4839
4840
4841
4842
4843
4844
4845
4846
4847
4848
4849
4850
4851
4852
4853
4854
4855
4856
4857
4858
4859
4860
4861
4862
4863
4864
4865
4866
4867
4868
4869
4870
4871
4872
4873
4874
4875
4876
4877
4878
4879
4880
4881
4882
4883
4884
4885
4886
4887
4888
4889
4890
4891
4892
4893
4894
4895
4896
4897
4898
4899
4900
4901
4902
4903
4904
4905
4906
4907
4908
4909
4910
4911
4912
4913
4914
4915
4916
4917
4918
4919
4920
4921
4922
4923
4924
4925
4926
4927
4928
4929
4930
4931
4932
4933
4934
4935
4936
4937
4938
4939
4940
4941
4942
4943
4944
4945
4946
4947
4948
4949
4950
4951
4952
4953
4954
4955
4956
4957
4958
4959
4960
4961
4962
4963
4964
4965
4966
4967
4968
4969
4970
4971
4972
4973
4974
4975
4976
4977
4978
4979
4980
4981
4982
4983
4984
4985
4986
4987
4988
4989
4990
4991
4992
4993
4994
4995
4996
4997
4998
4999
5000
5001
5002
5003
5004
5005
5006
5007
5008
5009
5010
5011
5012
5013
5014
5015
5016
5017
5018
5019
5020
5021
5022
5023
5024
5025
5026
5027
5028
5029
5030
5031
5032
5033
5034
5035
5036
5037
5038
5039
5040
5041
5042
5043
5044
5045
5046
5047
5048
5049
5050
5051
5052
5053
5054
5055
5056
5057
5058
5059
5060
5061
5062
5063
5064
5065
5066
5067
5068
5069
5070
5071
5072
5073
5074
5075
5076
5077
5078
5079
5080
5081
5082
5083
5084
5085
5086
5087
5088
5089
5090
5091
5092
5093
5094
5095
5096
5097
5098
5099
5100
5101
5102
5103
5104
5105
5106
5107
5108
5109
5110
5111
5112
5113
5114
5115
5116
5117
5118
5119
5120
5121
5122
5123
5124
5125
5126
5127
5128
5129
5130
5131
5132
5133
5134
5135
5136
5137
5138
5139
5140
5141
5142
5143
5144
5145
5146
5147
5148
5149
5150
5151
5152
5153
5154
5155
5156
5157
5158
5159
5160
5161
5162
5163
5164
5165
5166
5167
5168
5169
5170
5171
5172
5173
5174
5175
5176
5177
5178
5179
5180
5181
5182
5183
5184
5185
5186
5187
5188
5189
5190
5191
5192
5193
5194
5195
5196
5197
5198
5199
5200
5201
5202
5203
5204
5205
5206
5207
5208
5209
5210
5211
5212
5213
5214
5215
5216
5217
5218
5219
5220
5221
5222
5223
5224
5225
5226
5227
5228
5229
5230
5231
5232
5233
5234
5235
"This is where we conclude Genetic Algorithms."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### N-Queens Problem\n",
"Here, we will look at the generalized cae of the Eight Queens problem.\n",
"<br>\n",
"We are given a `N` x `N` chessboard, with `N` queens, and we need to place them in such a way that no two queens can attack each other.\n",
"<br>\n",
"We will solve this problem using search algorithms.\n",
"To do this, we already have a `NQueensProblem` class in `search.py`."
]
},
{
"cell_type": "code",
"execution_count": 80,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<!DOCTYPE html PUBLIC \"-//W3C//DTD HTML 4.01//EN\"\n",
" \"http://www.w3.org/TR/html4/strict.dtd\">\n",
"\n",
"<html>\n",
"<head>\n",
" <title></title>\n",
" <meta http-equiv=\"content-type\" content=\"text/html; charset=None\">\n",
" <style type=\"text/css\">\n",
"td.linenos { background-color: #f0f0f0; padding-right: 10px; }\n",
"span.lineno { background-color: #f0f0f0; padding: 0 5px 0 5px; }\n",
"pre { line-height: 125%; }\n",
"body .hll { background-color: #ffffcc }\n",
"body { background: #f8f8f8; }\n",
"body .c { color: #408080; font-style: italic } /* Comment */\n",
"body .err { border: 1px solid #FF0000 } /* Error */\n",
"body .k { color: #008000; font-weight: bold } /* Keyword */\n",
"body .o { color: #666666 } /* Operator */\n",
"body .ch { color: #408080; font-style: italic } /* Comment.Hashbang */\n",
"body .cm { color: #408080; font-style: italic } /* Comment.Multiline */\n",
"body .cp { color: #BC7A00 } /* Comment.Preproc */\n",
"body .cpf { color: #408080; font-style: italic } /* Comment.PreprocFile */\n",
"body .c1 { color: #408080; font-style: italic } /* Comment.Single */\n",
"body .cs { color: #408080; font-style: italic } /* Comment.Special */\n",
"body .gd { color: #A00000 } /* Generic.Deleted */\n",
"body .ge { font-style: italic } /* Generic.Emph */\n",
"body .gr { color: #FF0000 } /* Generic.Error */\n",
"body .gh { color: #000080; font-weight: bold } /* Generic.Heading */\n",
"body .gi { color: #00A000 } /* Generic.Inserted */\n",
"body .go { color: #888888 } /* Generic.Output */\n",
"body .gp { color: #000080; font-weight: bold } /* Generic.Prompt */\n",
"body .gs { font-weight: bold } /* Generic.Strong */\n",
"body .gu { color: #800080; font-weight: bold } /* Generic.Subheading */\n",
"body .gt { color: #0044DD } /* Generic.Traceback */\n",
"body .kc { color: #008000; font-weight: bold } /* Keyword.Constant */\n",
"body .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */\n",
"body .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */\n",
"body .kp { color: #008000 } /* Keyword.Pseudo */\n",
"body .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */\n",
"body .kt { color: #B00040 } /* Keyword.Type */\n",
"body .m { color: #666666 } /* Literal.Number */\n",
"body .s { color: #BA2121 } /* Literal.String */\n",
"body .na { color: #7D9029 } /* Name.Attribute */\n",
"body .nb { color: #008000 } /* Name.Builtin */\n",
"body .nc { color: #0000FF; font-weight: bold } /* Name.Class */\n",
"body .no { color: #880000 } /* Name.Constant */\n",
"body .nd { color: #AA22FF } /* Name.Decorator */\n",
"body .ni { color: #999999; font-weight: bold } /* Name.Entity */\n",
"body .ne { color: #D2413A; font-weight: bold } /* Name.Exception */\n",
"body .nf { color: #0000FF } /* Name.Function */\n",
"body .nl { color: #A0A000 } /* Name.Label */\n",
"body .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */\n",
"body .nt { color: #008000; font-weight: bold } /* Name.Tag */\n",
"body .nv { color: #19177C } /* Name.Variable */\n",
"body .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */\n",
"body .w { color: #bbbbbb } /* Text.Whitespace */\n",
"body .mb { color: #666666 } /* Literal.Number.Bin */\n",
"body .mf { color: #666666 } /* Literal.Number.Float */\n",
"body .mh { color: #666666 } /* Literal.Number.Hex */\n",
"body .mi { color: #666666 } /* Literal.Number.Integer */\n",
"body .mo { color: #666666 } /* Literal.Number.Oct */\n",
"body .sa { color: #BA2121 } /* Literal.String.Affix */\n",
"body .sb { color: #BA2121 } /* Literal.String.Backtick */\n",
"body .sc { color: #BA2121 } /* Literal.String.Char */\n",
"body .dl { color: #BA2121 } /* Literal.String.Delimiter */\n",
"body .sd { color: #BA2121; font-style: italic } /* Literal.String.Doc */\n",
"body .s2 { color: #BA2121 } /* Literal.String.Double */\n",
"body .se { color: #BB6622; font-weight: bold } /* Literal.String.Escape */\n",
"body .sh { color: #BA2121 } /* Literal.String.Heredoc */\n",
"body .si { color: #BB6688; font-weight: bold } /* Literal.String.Interpol */\n",
"body .sx { color: #008000 } /* Literal.String.Other */\n",
"body .sr { color: #BB6688 } /* Literal.String.Regex */\n",
"body .s1 { color: #BA2121 } /* Literal.String.Single */\n",
"body .ss { color: #19177C } /* Literal.String.Symbol */\n",
"body .bp { color: #008000 } /* Name.Builtin.Pseudo */\n",
"body .fm { color: #0000FF } /* Name.Function.Magic */\n",
"body .vc { color: #19177C } /* Name.Variable.Class */\n",
"body .vg { color: #19177C } /* Name.Variable.Global */\n",
"body .vi { color: #19177C } /* Name.Variable.Instance */\n",
"body .vm { color: #19177C } /* Name.Variable.Magic */\n",
"body .il { color: #666666 } /* Literal.Number.Integer.Long */\n",
"\n",
" </style>\n",
"</head>\n",
"<body>\n",
"<h2></h2>\n",
"\n",
"<div class=\"highlight\"><pre><span></span><span class=\"k\">class</span> <span class=\"nc\">NQueensProblem</span><span class=\"p\">(</span><span class=\"n\">Problem</span><span class=\"p\">):</span>\n",
"\n",
" <span class=\"sd\">"""The problem of placing N queens on an NxN board with none attacking</span>\n",
"<span class=\"sd\"> each other. A state is represented as an N-element array, where</span>\n",
"<span class=\"sd\"> a value of r in the c-th entry means there is a queen at column c,</span>\n",
"<span class=\"sd\"> row r, and a value of -1 means that the c-th column has not been</span>\n",
"<span class=\"sd\"> filled in yet. We fill in columns left to right.</span>\n",
"<span class=\"sd\"> >>> depth_first_tree_search(NQueensProblem(8))</span>\n",
"<span class=\"sd\"> <Node (7, 3, 0, 2, 5, 1, 6, 4)></span>\n",
"<span class=\"sd\"> """</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"fm\">__init__</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">N</span><span class=\"p\">):</span>\n",
" <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">N</span> <span class=\"o\">=</span> <span class=\"n\">N</span>\n",
" <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">initial</span> <span class=\"o\">=</span> <span class=\"nb\">tuple</span><span class=\"p\">([</span><span class=\"o\">-</span><span class=\"mi\">1</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">N</span><span class=\"p\">)</span>\n",
" <span class=\"n\">Problem</span><span class=\"o\">.</span><span class=\"fm\">__init__</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">initial</span><span class=\"p\">)</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"nf\">actions</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">state</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""In the leftmost empty column, try all non-conflicting rows."""</span>\n",
" <span class=\"k\">if</span> <span class=\"n\">state</span><span class=\"p\">[</span><span class=\"o\">-</span><span class=\"mi\">1</span><span class=\"p\">]</span> <span class=\"ow\">is</span> <span class=\"ow\">not</span> <span class=\"o\">-</span><span class=\"mi\">1</span><span class=\"p\">:</span>\n",
" <span class=\"k\">return</span> <span class=\"p\">[]</span> <span class=\"c1\"># All columns filled; no successors</span>\n",
" <span class=\"k\">else</span><span class=\"p\">:</span>\n",
" <span class=\"n\">col</span> <span class=\"o\">=</span> <span class=\"n\">state</span><span class=\"o\">.</span><span class=\"n\">index</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mi\">1</span><span class=\"p\">)</span>\n",
" <span class=\"k\">return</span> <span class=\"p\">[</span><span class=\"n\">row</span> <span class=\"k\">for</span> <span class=\"n\">row</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">N</span><span class=\"p\">)</span>\n",
" <span class=\"k\">if</span> <span class=\"ow\">not</span> <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">conflicted</span><span class=\"p\">(</span><span class=\"n\">state</span><span class=\"p\">,</span> <span class=\"n\">row</span><span class=\"p\">,</span> <span class=\"n\">col</span><span class=\"p\">)]</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"nf\">result</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">state</span><span class=\"p\">,</span> <span class=\"n\">row</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""Place the next queen at the given row."""</span>\n",
" <span class=\"n\">col</span> <span class=\"o\">=</span> <span class=\"n\">state</span><span class=\"o\">.</span><span class=\"n\">index</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mi\">1</span><span class=\"p\">)</span>\n",
" <span class=\"n\">new</span> <span class=\"o\">=</span> <span class=\"nb\">list</span><span class=\"p\">(</span><span class=\"n\">state</span><span class=\"p\">[:])</span>\n",
" <span class=\"n\">new</span><span class=\"p\">[</span><span class=\"n\">col</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"n\">row</span>\n",
" <span class=\"k\">return</span> <span class=\"nb\">tuple</span><span class=\"p\">(</span><span class=\"n\">new</span><span class=\"p\">)</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"nf\">conflicted</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">state</span><span class=\"p\">,</span> <span class=\"n\">row</span><span class=\"p\">,</span> <span class=\"n\">col</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""Would placing a queen at (row, col) conflict with anything?"""</span>\n",
" <span class=\"k\">return</span> <span class=\"nb\">any</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">conflict</span><span class=\"p\">(</span><span class=\"n\">row</span><span class=\"p\">,</span> <span class=\"n\">col</span><span class=\"p\">,</span> <span class=\"n\">state</span><span class=\"p\">[</span><span class=\"n\">c</span><span class=\"p\">],</span> <span class=\"n\">c</span><span class=\"p\">)</span>\n",
" <span class=\"k\">for</span> <span class=\"n\">c</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">col</span><span class=\"p\">))</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"nf\">conflict</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">row1</span><span class=\"p\">,</span> <span class=\"n\">col1</span><span class=\"p\">,</span> <span class=\"n\">row2</span><span class=\"p\">,</span> <span class=\"n\">col2</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""Would putting two queens in (row1, col1) and (row2, col2) conflict?"""</span>\n",
" <span class=\"k\">return</span> <span class=\"p\">(</span><span class=\"n\">row1</span> <span class=\"o\">==</span> <span class=\"n\">row2</span> <span class=\"ow\">or</span> <span class=\"c1\"># same row</span>\n",
" <span class=\"n\">col1</span> <span class=\"o\">==</span> <span class=\"n\">col2</span> <span class=\"ow\">or</span> <span class=\"c1\"># same column</span>\n",
" <span class=\"n\">row1</span> <span class=\"o\">-</span> <span class=\"n\">col1</span> <span class=\"o\">==</span> <span class=\"n\">row2</span> <span class=\"o\">-</span> <span class=\"n\">col2</span> <span class=\"ow\">or</span> <span class=\"c1\"># same \\ diagonal</span>\n",
" <span class=\"n\">row1</span> <span class=\"o\">+</span> <span class=\"n\">col1</span> <span class=\"o\">==</span> <span class=\"n\">row2</span> <span class=\"o\">+</span> <span class=\"n\">col2</span><span class=\"p\">)</span> <span class=\"c1\"># same / diagonal</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"nf\">goal_test</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">state</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""Check if all columns filled, no conflicts."""</span>\n",
" <span class=\"k\">if</span> <span class=\"n\">state</span><span class=\"p\">[</span><span class=\"o\">-</span><span class=\"mi\">1</span><span class=\"p\">]</span> <span class=\"ow\">is</span> <span class=\"o\">-</span><span class=\"mi\">1</span><span class=\"p\">:</span>\n",
" <span class=\"k\">return</span> <span class=\"bp\">False</span>\n",
" <span class=\"k\">return</span> <span class=\"ow\">not</span> <span class=\"nb\">any</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">conflicted</span><span class=\"p\">(</span><span class=\"n\">state</span><span class=\"p\">,</span> <span class=\"n\">state</span><span class=\"p\">[</span><span class=\"n\">col</span><span class=\"p\">],</span> <span class=\"n\">col</span><span class=\"p\">)</span>\n",
" <span class=\"k\">for</span> <span class=\"n\">col</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"nb\">len</span><span class=\"p\">(</span><span class=\"n\">state</span><span class=\"p\">)))</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"nf\">h</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">node</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""Return number of conflicting queens for a given node"""</span>\n",
" <span class=\"n\">num_conflicts</span> <span class=\"o\">=</span> <span class=\"mi\">0</span>\n",
" <span class=\"k\">for</span> <span class=\"p\">(</span><span class=\"n\">r1</span><span class=\"p\">,</span> <span class=\"n\">c1</span><span class=\"p\">)</span> <span class=\"ow\">in</span> <span class=\"nb\">enumerate</span><span class=\"p\">(</span><span class=\"n\">node</span><span class=\"o\">.</span><span class=\"n\">state</span><span class=\"p\">):</span>\n",
" <span class=\"k\">for</span> <span class=\"p\">(</span><span class=\"n\">r2</span><span class=\"p\">,</span> <span class=\"n\">c2</span><span class=\"p\">)</span> <span class=\"ow\">in</span> <span class=\"nb\">enumerate</span><span class=\"p\">(</span><span class=\"n\">node</span><span class=\"o\">.</span><span class=\"n\">state</span><span class=\"p\">):</span>\n",
" <span class=\"k\">if</span> <span class=\"p\">(</span><span class=\"n\">r1</span><span class=\"p\">,</span> <span class=\"n\">c1</span><span class=\"p\">)</span> <span class=\"o\">!=</span> <span class=\"p\">(</span><span class=\"n\">r2</span><span class=\"p\">,</span> <span class=\"n\">c2</span><span class=\"p\">):</span>\n",
" <span class=\"n\">num_conflicts</span> <span class=\"o\">+=</span> <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">conflict</span><span class=\"p\">(</span><span class=\"n\">r1</span><span class=\"p\">,</span> <span class=\"n\">c1</span><span class=\"p\">,</span> <span class=\"n\">r2</span><span class=\"p\">,</span> <span class=\"n\">c2</span><span class=\"p\">)</span>\n",
"\n",
" <span class=\"k\">return</span> <span class=\"n\">num_conflicts</span>\n",
"</pre></div>\n",
"</body>\n",
"</html>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"psource(NQueensProblem)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In [`csp.ipynb`](https://github.com/aimacode/aima-python/blob/master/csp.ipynb) we have seen that the N-Queens problem can be formulated as a CSP and can be solved by \n",
"the `min_conflicts` algorithm in a way similar to Hill-Climbing. \n",
"Here, we want to solve it using heuristic search algorithms and even some classical search algorithms.\n",
"The `NQueensProblem` class derives from the `Problem` class and is implemented in such a way that the search algorithms we already have, can solve it.\n",
"<br>\n",
"Let's instantiate the class."
]
},
{
"cell_type": "code",
"execution_count": 81,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"nqp = NQueensProblem(8)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's use `depth_first_tree_search` first.\n",
"<br>\n",
"We will also use the %%timeit magic with each algorithm to see how much time they take."
]
},
{
"cell_type": "code",
"execution_count": 82,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"4.82 ms ± 498 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
]
}
],
"source": [
"%%timeit\n",
"depth_first_tree_search(nqp)"
]
},
{
"cell_type": "code",
"execution_count": 83,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"dfts = depth_first_tree_search(nqp).solution()"
]
},
{
"cell_type": "code",
"execution_count": 84,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAewAAAHwCAYAAABkPlyAAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x2871fddf550>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_NQueens(dfts)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`breadth_first_tree_search`"
]
},
{
"cell_type": "code",
"execution_count": 85,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"88.6 ms ± 2.01 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
]
}
],
"source": [
"%%timeit\n",
"breadth_first_tree_search(nqp)"
]
},
{
"cell_type": "code",
"execution_count": 86,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"bfts = breadth_first_tree_search(nqp).solution()"
]
},
{
"cell_type": "code",
"execution_count": 87,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAewAAAHwCAYAAABkPlyAAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n/P+uMuaa/akHvAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x2871fde6898>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_NQueens(bfts)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`uniform_cost_search`"
]
},
{
"cell_type": "code",
"execution_count": 88,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1.08 s ± 154 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
]
}
],
"source": [
"%%timeit\n",
"uniform_cost_search(nqp)"
]
},
{
"cell_type": "code",
"execution_count": 89,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"ucs = uniform_cost_search(nqp).solution()"
]
},
{
"cell_type": "code",
"execution_count": 90,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAewAAAHwCAYAAABkPlyAAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n/P+uMuaa/akHvAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x2871f6c04e0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_NQueens(ucs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`depth_first_tree_search` is almost 20 times faster than `breadth_first_tree_search` and more than 200 times faster than `uniform_cost_search`."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can also solve this problem using `astar_search` with a suitable heuristic function. \n",
"<br>\n",
"The best heuristic function for this scenario will be one that returns the number of conflicts in the current state."
]
},
{
"cell_type": "code",
"execution_count": 91,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<!DOCTYPE html PUBLIC \"-//W3C//DTD HTML 4.01//EN\"\n",
" \"http://www.w3.org/TR/html4/strict.dtd\">\n",
"\n",
"<html>\n",
"<head>\n",
" <title></title>\n",
" <meta http-equiv=\"content-type\" content=\"text/html; charset=None\">\n",
" <style type=\"text/css\">\n",
"td.linenos { background-color: #f0f0f0; padding-right: 10px; }\n",
"span.lineno { background-color: #f0f0f0; padding: 0 5px 0 5px; }\n",
"pre { line-height: 125%; }\n",
"body .hll { background-color: #ffffcc }\n",
"body { background: #f8f8f8; }\n",
"body .c { color: #408080; font-style: italic } /* Comment */\n",
"body .err { border: 1px solid #FF0000 } /* Error */\n",
"body .k { color: #008000; font-weight: bold } /* Keyword */\n",
"body .o { color: #666666 } /* Operator */\n",
"body .ch { color: #408080; font-style: italic } /* Comment.Hashbang */\n",
"body .cm { color: #408080; font-style: italic } /* Comment.Multiline */\n",
"body .cp { color: #BC7A00 } /* Comment.Preproc */\n",
"body .cpf { color: #408080; font-style: italic } /* Comment.PreprocFile */\n",
"body .c1 { color: #408080; font-style: italic } /* Comment.Single */\n",
"body .cs { color: #408080; font-style: italic } /* Comment.Special */\n",
"body .gd { color: #A00000 } /* Generic.Deleted */\n",
"body .ge { font-style: italic } /* Generic.Emph */\n",
"body .gr { color: #FF0000 } /* Generic.Error */\n",
"body .gh { color: #000080; font-weight: bold } /* Generic.Heading */\n",
"body .gi { color: #00A000 } /* Generic.Inserted */\n",
"body .go { color: #888888 } /* Generic.Output */\n",
"body .gp { color: #000080; font-weight: bold } /* Generic.Prompt */\n",
"body .gs { font-weight: bold } /* Generic.Strong */\n",
"body .gu { color: #800080; font-weight: bold } /* Generic.Subheading */\n",
"body .gt { color: #0044DD } /* Generic.Traceback */\n",
"body .kc { color: #008000; font-weight: bold } /* Keyword.Constant */\n",
"body .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */\n",
"body .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */\n",
"body .kp { color: #008000 } /* Keyword.Pseudo */\n",
"body .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */\n",
"body .kt { color: #B00040 } /* Keyword.Type */\n",
"body .m { color: #666666 } /* Literal.Number */\n",
"body .s { color: #BA2121 } /* Literal.String */\n",
"body .na { color: #7D9029 } /* Name.Attribute */\n",
"body .nb { color: #008000 } /* Name.Builtin */\n",
"body .nc { color: #0000FF; font-weight: bold } /* Name.Class */\n",
"body .no { color: #880000 } /* Name.Constant */\n",
"body .nd { color: #AA22FF } /* Name.Decorator */\n",
"body .ni { color: #999999; font-weight: bold } /* Name.Entity */\n",
"body .ne { color: #D2413A; font-weight: bold } /* Name.Exception */\n",
"body .nf { color: #0000FF } /* Name.Function */\n",
"body .nl { color: #A0A000 } /* Name.Label */\n",
"body .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */\n",
"body .nt { color: #008000; font-weight: bold } /* Name.Tag */\n",
"body .nv { color: #19177C } /* Name.Variable */\n",
"body .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */\n",
"body .w { color: #bbbbbb } /* Text.Whitespace */\n",
"body .mb { color: #666666 } /* Literal.Number.Bin */\n",
"body .mf { color: #666666 } /* Literal.Number.Float */\n",
"body .mh { color: #666666 } /* Literal.Number.Hex */\n",
"body .mi { color: #666666 } /* Literal.Number.Integer */\n",
"body .mo { color: #666666 } /* Literal.Number.Oct */\n",
"body .sa { color: #BA2121 } /* Literal.String.Affix */\n",
"body .sb { color: #BA2121 } /* Literal.String.Backtick */\n",
"body .sc { color: #BA2121 } /* Literal.String.Char */\n",
"body .dl { color: #BA2121 } /* Literal.String.Delimiter */\n",
"body .sd { color: #BA2121; font-style: italic } /* Literal.String.Doc */\n",
"body .s2 { color: #BA2121 } /* Literal.String.Double */\n",
"body .se { color: #BB6622; font-weight: bold } /* Literal.String.Escape */\n",
"body .sh { color: #BA2121 } /* Literal.String.Heredoc */\n",
"body .si { color: #BB6688; font-weight: bold } /* Literal.String.Interpol */\n",
"body .sx { color: #008000 } /* Literal.String.Other */\n",
"body .sr { color: #BB6688 } /* Literal.String.Regex */\n",
"body .s1 { color: #BA2121 } /* Literal.String.Single */\n",
"body .ss { color: #19177C } /* Literal.String.Symbol */\n",
"body .bp { color: #008000 } /* Name.Builtin.Pseudo */\n",
"body .fm { color: #0000FF } /* Name.Function.Magic */\n",
"body .vc { color: #19177C } /* Name.Variable.Class */\n",
"body .vg { color: #19177C } /* Name.Variable.Global */\n",
"body .vi { color: #19177C } /* Name.Variable.Instance */\n",
"body .vm { color: #19177C } /* Name.Variable.Magic */\n",
"body .il { color: #666666 } /* Literal.Number.Integer.Long */\n",
"\n",
" </style>\n",
"</head>\n",
"<body>\n",
"<h2></h2>\n",
"\n",
"<div class=\"highlight\"><pre><span></span> <span class=\"k\">def</span> <span class=\"nf\">h</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">node</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""Return number of conflicting queens for a given node"""</span>\n",
" <span class=\"n\">num_conflicts</span> <span class=\"o\">=</span> <span class=\"mi\">0</span>\n",
" <span class=\"k\">for</span> <span class=\"p\">(</span><span class=\"n\">r1</span><span class=\"p\">,</span> <span class=\"n\">c1</span><span class=\"p\">)</span> <span class=\"ow\">in</span> <span class=\"nb\">enumerate</span><span class=\"p\">(</span><span class=\"n\">node</span><span class=\"o\">.</span><span class=\"n\">state</span><span class=\"p\">):</span>\n",
" <span class=\"k\">for</span> <span class=\"p\">(</span><span class=\"n\">r2</span><span class=\"p\">,</span> <span class=\"n\">c2</span><span class=\"p\">)</span> <span class=\"ow\">in</span> <span class=\"nb\">enumerate</span><span class=\"p\">(</span><span class=\"n\">node</span><span class=\"o\">.</span><span class=\"n\">state</span><span class=\"p\">):</span>\n",
" <span class=\"k\">if</span> <span class=\"p\">(</span><span class=\"n\">r1</span><span class=\"p\">,</span> <span class=\"n\">c1</span><span class=\"p\">)</span> <span class=\"o\">!=</span> <span class=\"p\">(</span><span class=\"n\">r2</span><span class=\"p\">,</span> <span class=\"n\">c2</span><span class=\"p\">):</span>\n",
" <span class=\"n\">num_conflicts</span> <span class=\"o\">+=</span> <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">conflict</span><span class=\"p\">(</span><span class=\"n\">r1</span><span class=\"p\">,</span> <span class=\"n\">c1</span><span class=\"p\">,</span> <span class=\"n\">r2</span><span class=\"p\">,</span> <span class=\"n\">c2</span><span class=\"p\">)</span>\n",
"\n",
" <span class=\"k\">return</span> <span class=\"n\">num_conflicts</span>\n",
"</pre></div>\n",
"</body>\n",
"</html>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"psource(NQueensProblem.h)"
]
},
{
"cell_type": "code",
"execution_count": 92,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"8.85 ms ± 424 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
]
}
],
"source": [
"%%timeit\n",
"astar_search(nqp)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`astar_search` is faster than both `uniform_cost_search` and `breadth_first_tree_search`."
]
},
{
"cell_type": "code",
"execution_count": 93,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"astar = astar_search(nqp).solution()"
]
},
{
"cell_type": "code",
"execution_count": 94,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAewAAAHwCAYAAABkPlyAAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nELABAMgAAjYAABnw/wPRIOc/pYUmbAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x2871ff9f518>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_NQueens(astar)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<br>\n",
"This concludes the notebook.\n",
"Hope you learned something new!"
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
5255
5256
5257
5258
5259
5260
5261
5262
5263
5264
5265
5266
5267
5268
5269
5270
5271
5272
5273
5274
5275
5276
5277
5278
5279
5280
5281
5282
5283
5284
5285
5286
5287
5288
"version": "3.6.1"
},
"widgets": {
"state": {
"1516e2501ddd4a2e8e3250bffc0164db": {
"views": [
{
"cell_index": 59
}
]
},
"17be64c89a9a4a43b3272cb018df0970": {
"views": [
{
"cell_index": 59
}
]
},
"ac05040009a340b0af81b0ee69161fbc": {
"views": [
{
"cell_index": 59
}
]
},
"d9735ffe77c24f13ae4ad3620ce84334": {
"views": [
{
"cell_index": 59
}
]
}
},
"version": "1.2.0"
}
},
"nbformat": 4,