-
Notifications
You must be signed in to change notification settings - Fork 0
/
approximation_method.py
505 lines (426 loc) · 18.6 KB
/
approximation_method.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
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
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
from abc import abstractmethod
from fractions import Fraction as Frac
from typing import Any, Tuple, List, NoReturn
import numpy as np
from sympy import Symbol, linsolve
from writer import Writer
class ApproximationMethod:
cost_table: np.ndarray
assign_table: np.ndarray
transportation_table: np.ndarray
writer: Writer
improvable: bool
entering_variable: tuple
leaving_variable: tuple
loop: List[Tuple]
rows: int
columns: int
demand_row: int
supply_column: int
most_assigned_row: int
most_assigned_column: int
v_row: int
u_column: int
deleted_rows: set
deleted_cols: set
assigned_indices: set
unassigned_indices: set
assignments_of_row: dict
assignments_of_column: dict
def __init__(self, file):
self.improvable = True
self.most_assigned_row = -1
self.most_assigned_column = -1
self.entering_variable = tuple()
self.leaving_variable = tuple()
self.loop = list()
self.unassigned_indices = set()
self.assigned_indices = set()
self.deleted_rows = set()
self.deleted_cols = set()
self.assignments_of_row = {self.most_assigned_row: -1}
self.assignments_of_column = {self.most_assigned_column: -1}
self.writer = Writer(filename=file.name)
self.__create_cost_table(file)
self.__balance_cost_table()
self.__create_assign_table()
self.__create_transportation_table()
@abstractmethod
def solve(self) -> None:
pass
@abstractmethod
def choose_cost(self) -> None:
pass
def assignment(self, pos: tuple) -> float:
return self.assign_table[pos]
def assign(self, assignment: Any, i: int, j: int, new_demand_and_supply=True) -> None:
"""
Sets a given value to the assignment table & updating the problem state
:param assignment: amount to assign in assignment table
:param i: row to assign
:param j: column to assign
:param new_demand_and_supply: false when assignment comes from loop
therefore doesn't need update
"""
self.assign_table[i][j] = assignment
self.assigned_indices.add((i, j))
self.unassigned_indices.discard((i, j))
self.increment_assignments_of(i, j)
if new_demand_and_supply:
self.assign_table[i][self.supply_column] -= assignment
self.assign_table[self.demand_row][j] -= assignment
def best_value_at(self, i: int, j: int) -> Tuple[int, int, int]:
"""
Return the minimum value between the demand an supply for a
certain cell
:param i: row to check best value
:param j: column to check best value
:return: A tuple with the best value, row & column
"""
# determine lowest value between supply & demand
demand_value = self.assign_table[self.demand_row][j]
supply_value = self.assign_table[i][self.supply_column]
best = min(demand_value, supply_value)
if demand_value < supply_value:
# mark the column as unavailable from now on
self.deleted_cols.add(j)
elif supply_value < demand_value:
# mark the row as unavailable from now on
self.deleted_rows.add(i)
else:
# mark both the row & column as unavailable from now on
self.deleted_rows.add(i)
self.deleted_cols.add(j)
return best, i, j
def increment_assignments_of(self, i: int, j: int) -> None:
"""
Updates the amount of assignments for the given row
& column increasing it by 1
:param i: row in which the assigment was made
:param j: column in which the assigment was made
"""
# rows & columns in assignments go from [1,n] & [1,m]
i, j = i + 1, j + 1
self.assignments_of_row[i] = self.assignments_of_row.get(i, 0) + 1
self.assignments_of_column[j] = self.assignments_of_column.get(j, 0) + 1
# case of new most assigned row
if self.assignments_of_row[i] > self.assignments_of_row[self.most_assigned_row]:
self.most_assigned_row = i
# case of new most assigned column
if self.assignments_of_column[j] > self.assignments_of_column[self.most_assigned_column]:
self.most_assigned_column = j
def decrement_assignments_of(self, i: int, j: int) -> None:
"""
Updates the amount of assignments for the given row
& column decreasing it by 1
:param i: row in which the assigment was removed
:param j: column in which the assignment was removed
"""
i, j = i + 1, j + 1
self.assignments_of_row[i] = self.assignments_of_row.get(i, 0) - 1
# case in which the most assigned row decremented
if self.most_assigned_row == i:
self.most_assigned_row = max(self.assignments_of_row)
# case in which the most assigned column decremented
if self.most_assigned_column:
self.most_assigned_column = max(self.assignments_of_column)
def has_rows_and_columns_left(self) -> bool:
"""
Checks if they're columns & rows available for assigment
:return: false if all rows or columns were deleted/assigned
"""
return \
len(self.deleted_rows) != self.rows - 1 \
and len(self.deleted_cols) != self.columns - 1
def halt(self, message: str) -> NoReturn:
"""
Terminates the program with error code 1 with a quick log
to console/file
:param message: string to write in console/file with the error name
"""
self.writer.write_halting(message)
exit(1)
def improve(self) -> None:
"""
Applies the transportation algorithm when the problem has non basic
indicators greater than 0
"""
self.__find_dual_variables()
self.__find_non_basic_indicators()
i = 0
while self.improvable:
self.__create_loop()
self.__assign_loop()
self.writer.write_transportation_iteration(transportation_matrix=self.transportation_table,
assignment_matrix=self.assign_table,
iteration=f'[Iteration] = {i}')
self.writer.write_loop(self.loop, entering=self.entering_variable, leaving=self.leaving_variable)
self.writer.write_current_cost(self.total_cost())
self.__find_dual_variables()
self.__find_non_basic_indicators()
i += 1
self.writer.write_transportation_iteration(transportation_matrix=self.transportation_table,
assignment_matrix=self.assign_table,
iteration=f'[Final Iteration]',
final=True)
self.writer.write_optimal_cost(self.total_cost())
def total_cost(self) -> int:
"""
Multiplies each assignment for it's cost & sums them
all up
:return: integer with the total cost of the assignment table
"""
total = 0
for pos in self.assigned_indices:
total += self.assign_table[pos] * self.cost_table[pos]
return int(total)
def unassign(self, i: int, j: int) -> None:
"""
Updates the unassigned set with the given row & column
& decrementing occurrences in each of them
:param i: row to unassign from assignment table
:param j: column to unassign from assignment table
"""
self.unassigned_indices.add((i, j))
self.decrement_assignments_of(i, j)
def __assign_loop(self) -> None:
"""
Updates the assignment of each index in the loop
by decrementing or incrementing its value by the lowest
of them all
"""
# even indices are incremented, odd indices are decremented
even_indices, odd_indices = self.loop[0::2], self.loop[1::2]
# leaving variable is the lowest of the decremented indices
# in order to not have negative values
self.leaving_variable = min(odd_indices, key=self.assignment)
leaving_assignment = self.assignment(self.leaving_variable)
# unassigned indices to delete
unassigned = set()
for pos in self.assigned_indices:
if pos in even_indices:
self.assign_table[pos] += leaving_assignment
if pos in odd_indices:
self.assign_table[pos] -= leaving_assignment
# case in which the decremented value is the lowest of them all
can_be_unassigned = self.assign_table[pos] == 0
if can_be_unassigned:
unassigned.add(pos)
self.unassign(*pos)
self.assigned_indices -= unassigned
# finally assign the new variable with the lowest value (demand & supply stays the same)
self.assign(leaving_assignment, *self.entering_variable, new_demand_and_supply=False)
def __create_cost_table(self, file) -> None:
"""
Given a file with a containing valid transportation problem
creates a cost table with demands, suppliers & cost values
:param file: file in which the problem values are located
"""
# obtain first row of txt file & make it supply column
supply = np.loadtxt(file, max_rows=1, delimiter=",", comments="\\n") + Frac()
supply = supply.reshape((-1, 1))
# obtain second row of txt file & make it demand row
demand = np.loadtxt(file, max_rows=1, delimiter=",", comments="\\n") + Frac()
demand = np.append(demand, "*").reshape((1, -1))
# finally generate the cost_table with costs + demand + supply column
costs = np.loadtxt(file, delimiter=",", comments="\\n") + Frac()
self.cost_table = np.append(costs, values=supply, axis=1)
self.cost_table = np.append(self.cost_table, values=demand, axis=0)
# update attributes
self.rows, self.columns = self.cost_table.shape
self.demand_row, self.supply_column = self.rows - 1, self.columns - 1
# file is no longer needed
file.close()
del file
def __balance_cost_table(self) -> None:
"""
Checks if the demand row sum is greater than the supply column
or viceversa & calculates the new fictional value between the
difference between them
"""
demand_sum = np.sum(self.cost_table[self.demand_row][:-1])
supply_sum = np.sum(self.cost_table[:, self.supply_column][:-1])
diff = int(abs(demand_sum - supply_sum))
# balance the problem in case of different demand sum
if demand_sum < supply_sum:
self.__insert_fictional_demand(fictional_value=diff)
# balance the problem in case of different supply sum
elif supply_sum < demand_sum:
self.__insert_fictional_supply(fictional_value=diff)
else:
pass
def __insert_fictional_demand(self, fictional_value: int) -> None:
"""
Inserts a fictional/dummy demand row with zeros
:param fictional_value: amount to balance for the demand
"""
fictional_demand = [self.demand_row * [0.0] + [fictional_value]]
self.cost_table = np.insert(self.cost_table, -1, values=fictional_demand, axis=1)
self.columns += 1
self.supply_column += 1
def __insert_fictional_supply(self, fictional_value: int) -> None:
"""
Insert a fictional/dummy supply column with zeros
:param fictional_value: amount to balance for the supply
"""
fictional_supply = self.supply_column * [0] + [fictional_value]
self.cost_table = np.insert(self.cost_table, -1, values=fictional_supply, axis=0)
self.rows += 1
self.demand_row += 1
def __create_assign_table(self) -> None:
"""
Creates a numpy nd.array with the same shape of the cost table for assigning
indices
"""
# fill table with zeros, supply cost column & demand row from cost_table
self.assign_table = np.zeros((self.rows, self.columns), dtype=object)
self.assign_table[:, self.supply_column] = self.cost_table[:, self.supply_column]
self.assign_table[self.demand_row] = self.cost_table[self.demand_row]
# assume all indices are unassigned
self.unassigned_indices = {(i, j) for i in range(self.demand_row) for j in range(self.supply_column)}
def __create_transportation_table(self) -> None:
"""
Creates a numpy nd.array with the same shape of the cost table for non
basic indicators & dual variables
"""
self.u_column = self.supply_column
self.v_row = self.demand_row
self.transportation_table = np.empty((self.rows, self.columns), dtype=object)
# bottom right corner is never used
self.transportation_table[self.v_row][self.u_column] = "*"
def __create_loop(self) -> None:
"""
Updates the loop with the neighbors indices of the entrance variable
"""
start = [self.entering_variable]
def find(loop: List[Tuple]) -> List[Tuple]:
"""
Recursively finds the smallest loop the from
a given list of visited indices
:param loop: current visited indices
:return: neighbor indices of the entrance variable (start)
"""
one_neighbor_left = len(loop) > 3
if one_neighbor_left:
not_visited = start
closable = len(self.find_neighbors(loop, not_visited)) == 1
if closable:
return loop
not_visited = list(self.assigned_indices - set(loop))
possible_neighbors = self.find_neighbors(loop, not_visited)
for neighbor in possible_neighbors:
new_loop = find(loop + [neighbor])
if new_loop:
return new_loop
self.loop = find(loop=start)
@staticmethod
def find_neighbors(loop: List[Tuple], not_visited: List[Tuple]) -> List[Tuple]:
"""
Finds a list of possible indices to visited based on the last index
of the list
:param loop: visited indices
:param not_visited: pending indices that don't have an assignment value
:return: possible indices that can be assigned some value
"""
last_row, last_column = loop[-1]
row_neighbors, column_neighbors = list(), list()
for i, j in not_visited:
if i == last_row:
row_neighbors.append((i, j))
if j == last_column:
column_neighbors.append((i, j))
loop_incomplete = len(loop) < 2
if loop_incomplete:
return row_neighbors + column_neighbors
else:
previous_row, _ = loop[-2]
is_row_move = previous_row == last_row
if is_row_move:
return column_neighbors
return row_neighbors
def __find_non_basic_indicators(self) -> None:
"""
Iterates over the unassigned indices & calculates
each indicator by the form U variable + V variable - C cost
"""
# assume that it isn't improvable from the start
self.improvable = False
best_indicator = -np.inf
for i, j in self.unassigned_indices:
u = self.transportation_table[i][self.u_column]
v = self.transportation_table[self.v_row][j]
c = self.cost_table[i][j]
nb_indicator = int(u + v - c)
if nb_indicator > 0:
self.improvable = True
if nb_indicator > best_indicator:
best_indicator = nb_indicator
self.entering_variable = (i, j)
self.transportation_table[i][j] = nb_indicator
def __find_dual_variables(self) -> None:
"""
Iterates over the assigned indices & calculates
each variable by the form U variable + V variable - C cost
"""
u_vars, v_vars = self.__find_equation_vars()
equations = list()
for i, j in self.assigned_indices:
u = u_vars[i]
v = v_vars[j]
c = self.cost_table[i][j]
eq = u + v - c
equations.append(eq)
solved_v, solved_u = self.__solve_variables(equations, u_vars, v_vars)
self.transportation_table[-1, :-1] = solved_v
self.transportation_table[:-1, -1] = solved_u
def __solve_variables(self, equations: List[Symbol],
u_vars: Tuple[Symbol],
v_vars: Tuple[Symbol]):
"""
Finds a value for each U var & V var by having a
list of equations
:param equations: list of unsolved equations
:param u_vars: list of needed u variables to solve
:param v_vars: list of needed v variables to solve
:return: tuple with the solved v vars & solved u vars
"""
try:
solved = linsolve(equations, (u_vars + v_vars)).args[0]
amount_of_u = self.rows - 1
solved_u = list(map(int, solved[:amount_of_u]))
solved_v = list(map(int, solved[amount_of_u:]))
return solved_v, solved_u
# TypeError occurs when a dual variable is not solvable hence
# it's a degenerated solution
except TypeError as te:
self.writer.write_optimal_cost(self.total_cost())
self.halt(f'Caught exception "{te}"\nDegenerated solutions found, exiting...')
def __find_equation_vars(self) -> Tuple[Tuple, Tuple]:
"""
Creates a list of U vars & V vars with the exception
of the most assigned row or column which takes the value of
zero
:return: tuple with the v vars & u vars
"""
if self.assignments_of_column[self.most_assigned_column] >= \
self.assignments_of_row[self.most_assigned_row]:
zero_candidate = Symbol(f'V{self.most_assigned_column}')
else:
zero_candidate = Symbol(f'U{self.most_assigned_row}')
# V1, V2, V3 ... Vm
v_vars = list()
for i in range(1, self.columns):
v = Symbol(f'V{i}')
if v == zero_candidate:
v_vars.append(0)
else:
v_vars.append(v)
# U1, U2, U3 ... Un
u_vars = list()
for j in range(1, self.rows):
u = Symbol(f'U{j}')
if u == zero_candidate:
u_vars.append(0)
else:
u_vars.append(u)
return tuple(u_vars), tuple(v_vars)