-
Notifications
You must be signed in to change notification settings - Fork 1
/
branch_bound.py
338 lines (249 loc) · 11.8 KB
/
branch_bound.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
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
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
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
"""Branch and bound class.
Author : Adrien Pouyet
"""
class Counter(object):
"""Just a counter."""
def __init__(self):
"""Init total to 0."""
self.total = 0
def count(self):
"""Increment total."""
self.total += 1
class BranchAndBound(object):
"""Class to have a simple to use branch&bound algorithm.
Parameters
-----------
args : list, tuple, dir
Container of the actions to take. It is the input of next functions
evaluator : function
Exact evaluation of a solution.
nexter : function
Get the next action
optimistic : function
Optimistic evaluation of a solution. Returns an upper bounded value
feasible : function
Get a feasible solution with its value.
counter : Counter, optional
Object to call if you want to know the number of node explored
minimisation : bool, optional, default True
True if you want you minimise else False
Note
------
1 - All listed functions must have the prototype:
>>> def fun(first_actions, remaining_actions, args): pass
2 - Values returned must implements __le__ or __ge__
"""
def __init__(self, args, evaluator, nexter, optimistic, feasible, counter=None, minimisation=True):
self.args = args
self.nexter = nexter
self.optimistic = optimistic
self.feasible = feasible
self.counter = counter
self.minimisation = minimisation
def run(self, first_actions, remaining_actions, best_known):
"""Run the branch and bound.
Returns
---------
solution : list
Best feasible solution under the branch
value : float
Value of the solution, using evaluate function
"""
if self.minimisation:
if self.counter:
return self._mini_count(first_actions, remaining_actions, best_known)
else:
return self._mini(first_actions, remaining_actions, best_known)
else:
if self.counter:
return self._maxi_counter(first_actions, remaining_actions, best_known)
else:
return self._maxi(first_actions, remaining_actions, best_known)
def _mini_counter(self, first_actions, remaining_actions, best_known):
if len(remaining_actions) <= 1:
value = self.evaluate(first_actions + remaining_actions, self.args)
if value < best_known[1]:
best_known = (first_actions + remaining_actions, value)
self.counter.count()
return best_known
for nt in self.nexter(first_actions, remaining_actions, self.args):
self.counter.count()
rt = [r for r in remaining_actions if r != nt]
opt_v = self.optimistic(first_actions + [nt], rt, self.args)
if opt_v >= best_known[1]:
return best_known
feas = self.feasible(first_actions + [nt], rt, self.args)
if feas[1] < best_known[1]:
best_known = feas
if feas[1] <= opt_v:
return best_known
# We're sure to get a lower or equal solution
best_known = self._mini_counter(first_actions + [nt], rt, best_known)
return best_known
def _mini(self, first_actions, remaining_actions, best_known):
if len(remaining_actions) <= 1:
value = self.evaluate(first_actions + remaining_actions, self.args)
if value < best_known[1]:
best_known = (first_actions + remaining_actions, value)
return best_known
for nt in self.nexter(first_actions, remaining_actions, self.args):
rt = [r for r in remaining_actions if r != nt]
opt_v = self.optimistic(first_actions + [nt], rt, self.args)
if opt_v >= best_known[1]:
return best_known
feas = self.feasible(first_actions + [nt], rt, self.args)
if feas[1] < best_known[1]:
best_known = feas
if feas[1] <= opt_v:
return best_known
# We're sure to get a lower or equal solution
best_known = self._mini(first_actions + [nt], rt, best_known)
return best_known
def _maxi_counter(self, first_actions, remaining_actions, best_known):
if len(remaining_actions) <= 1:
value = self.evaluate(first_actions + remaining_actions, self.args)
if value > best_known[1]:
best_known = (first_actions + remaining_actions, value)
self.counter.count()
return best_known
for nt in self.nexter(first_actions, remaining_actions, self.args):
self.counter.count()
rt = [r for r in remaining_actions if r != nt]
opt_v = self.optimistic(first_actions + [nt], rt, self.args)
if opt_v <= best_known[1]:
return best_known
feas = self.feasible(first_actions + [nt], rt, self.args)
if feas[1] > best_known[1]:
best_known = feas
if feas[1] >= opt_v:
return best_known
# We're sure to get a lower or equal solution
best_known = self._maxi_counter(first_actions + [nt], rt, best_known)
return best_known
def _maxi(self, first_actions, remaining_actions, best_known):
if len(remaining_actions) <= 1:
value = self.evaluate(first_actions + remaining_actions, self.args)
if value > best_known[1]:
best_known = (first_actions + remaining_actions, value)
return best_known
for nt in self.nexter(first_actions, remaining_actions, self.args):
rt = [r for r in remaining_actions if r != nt]
opt_v = self.optimistic(first_actions + [nt], rt, self.args)
if opt_v <= best_known[1]:
return best_known
feas = self.feasible(first_actions + [nt], rt, self.args)
if feas[1] > best_known[1]:
best_known = feas
if feas[1] >= opt_v:
return best_known
# We're sure to get a lower or equal solution
best_known = self._maxi(first_actions + [nt], rt, best_known)
return best_known
class BranchAndBoundApprox(BranchAndBound):
"""Class to have a simple to use branch&bound algorithm.
Parameters
-----------
min_diff : float
Minimum improvement to explore the node. Always positive
args : list, tuple, dir
Container of the actions to take. It is the input of next functions
evaluator : function
Exact evaluation of a solution.
nexter : function
Get the next action
optimistic : function
Optimistic evaluation of a solution. Returns an upper bounded value
feasible : function
Get a feasible solution with its value.
counter : Counter, optional
Object to call if you want to know the number of node explored
minimisation : bool, optional, default True
True if you want you minimise else False
Note
------
1 - All listed functions must have the prototype:
>>> def fun(first_actions, remaining_actions, args): pass
"""
def __init__(self, min_diff, args, evaluator, nexter, optimistic, feasible, counter=None, minimisation=True):
super(BranchAndBoundApprox, self).__init__(args, evaluator, nexter, optimistic, feasible, counter=None, minimisation=True)
self.min_diff = min_diff if minimisation else -min_diff
def _mini_counter(self, first_actions, remaining_actions, best_known):
if len(remaining_actions) <= 1:
value = self.evaluate(first_actions + remaining_actions, self.args)
if value < best_known[1]:
best_known = (first_actions + remaining_actions, value)
self.counter.count()
return best_known
for nt in self.nexter(first_actions, remaining_actions, self.args):
self.counter.count()
rt = [r for r in remaining_actions if r != nt]
opt_v = self.optimistic(first_actions + [nt], rt, self.args)
if opt_v + self.min_diff >= best_known[1]:
return best_known
feas = self.feasible(first_actions + [nt], rt, self.args)
if feas[1] < best_known[1]:
best_known = feas
if feas[1] <= opt_v:
return best_known
# We're sure to get a lower or equal solution
best_known = self._mini_counter(first_actions + [nt], rt, best_known)
return best_known
def _mini(self, first_actions, remaining_actions, best_known):
if len(remaining_actions) <= 1:
value = self.evaluate(first_actions + remaining_actions, self.args)
if value < best_known[1]:
best_known = (first_actions + remaining_actions, value)
return best_known
for nt in self.nexter(first_actions, remaining_actions, self.args):
rt = [r for r in remaining_actions if r != nt]
opt_v = self.optimistic(first_actions + [nt], rt, self.args)
if opt_v + self.min_diff >= best_known[1]:
return best_known
feas = self.feasible(first_actions + [nt], rt, self.args)
if feas[1] < best_known[1]:
best_known = feas
if feas[1] <= opt_v:
return best_known
# We're sure to get a lower or equal solution
best_known = self._mini(first_actions + [nt], rt, best_known)
return best_known
def _maxi_counter(self, first_actions, remaining_actions, best_known):
if len(remaining_actions) <= 1:
value = self.evaluate(first_actions + remaining_actions, self.args)
if value > best_known[1]:
best_known = (first_actions + remaining_actions, value)
self.counter.count()
return best_known
for nt in self.nexter(first_actions, remaining_actions, self.args):
self.counter.count()
rt = [r for r in remaining_actions if r != nt]
opt_v = self.optimistic(first_actions + [nt], rt, self.args)
if opt_v + self.min_diff <= best_known[1]: # self.min_diff is negative here
return best_known
feas = self.feasible(first_actions + [nt], rt, self.args)
if feas[1] > best_known[1]:
best_known = feas
if feas[1] >= opt_v:
return best_known
# We're sure to get a lower or equal solution
best_known = self._maxi_counter(first_actions + [nt], rt, best_known)
return best_known
def _maxi(self, first_actions, remaining_actions, best_known):
if len(remaining_actions) <= 1:
value = self.evaluate(first_actions + remaining_actions, self.args)
if value > best_known[1]:
best_known = (first_actions + remaining_actions, value)
return best_known
for nt in self.nexter(first_actions, remaining_actions, self.args):
rt = [r for r in remaining_actions if r != nt]
opt_v = self.optimistic(first_actions + [nt], rt, self.args)
if opt_v + self.min_diff <= best_known[1]: # self.min_diff is negative here
return best_known
feas = self.feasible(first_actions + [nt], rt, self.args)
if feas[1] > best_known[1]:
best_known = feas
if feas[1] >= opt_v:
return best_known
# We're sure to get a lower or equal solution
best_known = self._maxi(first_actions + [nt], rt, best_known)
return best_known