I'm using gekko to solve a MINLP problem. I'm using the APOPT solver since is the only one that can provide integer solution, which are strictly needed in my case.
The issue I have is that every time I run the solver I have a different solution, even for very small cases, so I can't be sure about the optimality of the solutions. From some solutions to others there are important differences in the objective final value.
I've noticed that only 1 iteration takes place, and I don't know if it should be like this. Also, it runs for less than 1 second when it could run longer and find better solutions.
Below the output of one of this runs:
--------- APM Model Size ------------
Each time step contains
Objects : 86
Constants : 0
Variables : 606
Intermediates: 0
Connections : 806
Equations : 1046
Residuals : 1046
Number of state variables: 606
Number of total equations: - 172
Number of slack variables: - 40
---------------------------------------
Degrees of freedom : 394
----------------------------------------------
Steady State Optimization with APOPT Solver
----------------------------------------------
Iter: 1 I: 0 Tm: 0.38 NLPi: 28 Dpth: 0 Lvs: 0 Obj: 1.27E+09 Gap: 0.00E+00
Successful solution
---------------------------------------------------
Solver : APOPT (v1.0)
Solution time : 0.38800000000628643 sec
Objective : 1271480486.0000000
Successful solution
---------------------------------------------------
I would appreciate any advice on how to tweak the solver so I can have consistent solutions. Thanks in advance
EDIT
I'm adding the code (reduced version). Basically what I'm trying to do is finding the best location for n warehouse based on the demand of m cities, which are represented by the corresponding hexagon in the h3 library.
from gekko import GEKKO
from random import randint
import pandas as pd
if __name__ == '__main__':
n_warehouses = 6
df_aggreg = pd.DataFrame.from_dict({'hex_id_basic': {32: 0, 12: 1, 2: 2, 3: 3, 22: 4, 24: 5, 38: 6, 8: 7, 19: 8, 27: 9, 21: 10, 25: 11, 28: 12, 26: 13, 29: 14, 30: 15, 31: 16, 1: 17, 20: 18, 18: 19, 17: 20, 33: 21, 35: 22, 14: 23, 13: 24, 11: 25, 10: 26, 36: 27, 6: 28, 5: 29, 4: 30, 16: 31, 34: 32, 0: 33, 23: 34, 15: 35, 9: 36, 37: 37, 7: 38, 39: 39}, 'value': {32: 1808, 12: 847, 2: 847, 3: 847, 22: 847, 24: 847, 38: 847, 8: 847, 19: 847, 27: 847, 21: 452, 25: 452, 28: 452, 26: 452, 29: 452, 30: 452, 31: 452, 1: 452, 20: 452, 18: 452, 17: 452, 33: 452, 35: 452, 14: 452, 13: 452, 11: 452, 10: 452, 36: 452, 6: 452, 5: 452, 4: 452, 16: 452, 34: 169, 0: 169, 23: 84, 15: 84, 9: 84, 37: 84, 7: 84, 39: 84}})
distance_matrix = [[0, 278320, 302712, 117682, 283287, 225645, 303065, 258900, 252165, 453768, 389125, 305694, 377415, 445329, 176671, 16098, 95378, 272352, 153948, 247011, 153063, 175620, 184734, 253592, 235204, 275271, 204377, 140151, 270207, 254950, 364642, 92383, 239928, 300635, 394936, 291140, 293377, 205417, 253778, 313127], [278320, 0, 144398, 187013, 244571, 107924, 257813, 279533, 334530, 195669, 205157, 84028, 109937, 187707, 427560, 265135, 188779, 292672, 307462, 280094, 408319, 281660, 131476, 440829, 46693, 204251, 233509, 147273, 263519, 267077, 185835, 310005, 254863, 323378, 119817, 407585, 280337, 171576, 280105, 261055], [302712, 144398, 0, 185183, 377007, 234161, 392715, 170354, 237346, 307577, 347861, 228110, 138929, 301200, 476655, 286696, 244493, 179154, 254571, 176769, 387398, 378208, 238178, 372115, 163476, 79788, 152001, 222356, 146928, 158337, 62584, 289416, 375428, 203381, 217686, 310387, 155900, 289533, 173468, 397435], [117682, 187013, 185183, 0, 291864, 179791, 311714, 170740, 192926, 379238, 347869, 240050, 272172, 370968, 293195, 101616, 87586, 185977, 129253, 162328, 222594, 233040, 150108, 262697, 153805, 162481, 109099, 101869, 173375, 162759, 246974, 123207, 265470, 218641, 306739, 255114, 197339, 195959, 167223, 320151], [283287, 244571, 377007, 291864, 0, 142846, 20212, 455483, 484791, 287216, 161617, 183085, 340463, 280631, 326676, 282534, 212575, 470828, 409823, 449527, 434084, 135211, 148574, 531347, 213849, 411617, 394742, 190552, 450777, 445332, 427673, 367985, 53066, 504293, 288485, 544788, 473256, 96874, 453151, 29897], [225645, 107924, 234161, 179791, 142846, 0, 158910, 325969, 365598, 232092, 169623, 84652, 214438, 223750, 344437, 216987, 130954, 340949, 308549, 322092, 374352, 178834, 41429, 440518, 71333, 272261, 268233, 88085, 317511, 314784, 285789, 286639, 147154, 374185, 190689, 432588, 338741, 64095, 324564, 164244], [303065, 257813, 392715, 311714, 20212, 158910, 0, 474649, 504627, 286841, 156847, 192075, 350549, 280649, 341260, 302511, 232768, 489976, 430017, 468858, 453490, 151205, 167295, 551499, 229266, 429328, 414077, 210234, 469552, 464393, 442147, 388101, 68990, 523448, 294341, 564878, 491892, 116277, 472394, 10359], [258900, 279533, 170354, 170740, 455483, 325969, 474649, 0, 68930, 467349, 478557, 358082, 308273, 460170, 428178, 244879, 258325, 15394, 131661, 13671, 271974, 403214, 307634, 213649, 272011, 90917, 61801, 266220, 26455, 12593, 202481, 195575, 434164, 48812, 379747, 140257, 39308, 358628, 6107, 482200], [252165, 334530, 237346, 192926, 484791, 365598, 504627, 68930, 0, 526826, 526392, 408559, 373685, 519349, 407413, 240840, 276462, 66186, 101574, 60620, 226811, 414422, 341075, 147167, 320118, 158889, 101274, 294543, 95127, 79800, 271409, 171262, 456912, 68984, 441013, 74111, 100302, 388712, 64684, 513007], [453768, 195669, 307577, 379238, 287216, 232092, 286841, 467349, 526826, 0, 136244, 148461, 178102, 8441, 573471, 443171, 358499, 479086, 502816, 469837, 595669, 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254733, 285601, 295994, 139047, 393079, 358593, 342270, 90310, 447455, 294687, 278510, 310960, 351759], [445329, 187707, 301200, 370968, 280631, 223750, 280649, 460170, 519349, 8441, 131581, 140049, 173125, 0, 565355, 434730, 350062, 472002, 494725, 462533, 587263, 384786, 264901, 628392, 217517, 376220, 419266, 305200, 440993, 447576, 311937, 491975, 321105, 500318, 84177, 593082, 454296, 270683, 461573, 276700], [176671, 427560, 476655, 293195, 326676, 344437, 341260, 428178, 407413, 573471, 475633, 428839, 534732, 565355, 0, 192659, 241685, 440309, 306114, 415366, 213722, 192267, 305547, 353506, 381057, 451860, 378110, 280381, 442537, 425977, 539074, 236503, 273614, 465255, 533298, 426186, 464854, 295413, 422602, 351173], [16098, 265135, 286696, 101616, 282534, 216987, 302511, 244879, 240840, 443171, 382466, 295540, 362967, 434730, 192659, 0, 86037, 258560, 144482, 233219, 158401, 180937, 176621, 250690, 222751, 259395, 189468, 130132, 255508, 240568, 348587, 87437, 241145, 287389, 382525, 282778, 278823, 201018, 239867, 312431], [95378, 188779, 244493, 87586, 212575, 130954, 232768, 258325, 276462, 358499, 297470, 210329, 293628, 350062, 241685, 86037, 0, 273554, 197249, 249773, 243741, 146171, 90840, 321549, 143532, 241689, 196668, 44890, 260330, 250266, 306721, 160762, 180583, 306135, 302150, 332965, 284225, 121772, 254773, 241969], [272352, 292672, 179154, 185977, 470828, 340949, 489976, 15394, 66186, 479086, 492617, 371886, 317765, 472002, 440309, 258560, 273554, 0, 140627, 25344, 279225, 418280, 322922, 213131, 286282, 99366, 77144, 281612, 32238, 26277, 207287, 206362, 449552, 33473, 391005, 133626, 34477, 373979, 19000, 497504], [153948, 307462, 254571, 129253, 409823, 308549, 430017, 131661, 101574, 502816, 477097, 368057, 374520, 494725, 306114, 144482, 197249, 140627, 0, 117996, 141824, 323726, 276426, 134201, 280163, 191685, 105340, 226127, 152834, 133897, 305377, 69716, 375475, 161033, 424673, 138867, 170911, 317471, 125583, 439203], [247011, 280094, 176769, 162328, 449527, 322092, 468858, 13671, 60620, 469837, 477118, 357279, 313604, 462533, 415366, 233219, 249773, 25344, 117996, 0, 258348, 393955, 302253, 202640, 270296, 98356, 54784, 259602, 38118, 20016, 211973, 182205, 426898, 56395, 382945, 133870, 52974, 352657, 7588, 476592], [153063, 408319, 387398, 222594, 434084, 374352, 453490, 271974, 226811, 595669, 540843, 450043, 493385, 587263, 213722, 158401, 243741, 279225, 141824, 258348, 0, 314904, 334581, 140210, 370743, 331489, 244983, 286515, 294300, 275249, 442428, 100328, 387881, 294243, 528076, 223497, 311245, 358451, 265867, 463708], [175620, 281660, 378208, 233040, 135211, 178834, 151205, 403214, 414422, 392502, 284992, 256851, 391108, 384786, 192267, 180937, 146171, 418280, 323726, 393955, 314904, 0, 150414, 428871, 237099, 386147, 341933, 156045, 406310, 395685, 438153, 267684, 82364, 450314, 367218, 462586, 430241, 117601, 399353, 161423], [184734, 131476, 238178, 150108, 148574, 41429, 167295, 307634, 341075, 273266, 206940, 125251, 241276, 264901, 305547, 176621, 90840, 322922, 276426, 302253, 334581, 150414, 0, 406344, 86738, 264273, 247556, 50786, 302265, 297224, 294689, 249321, 137664, 356394, 227861, 405170, 324686, 53055, 305544, 174613], [253592, 440829, 372115, 262697, 531347, 440518, 551499, 213649, 147167, 636429, 609805, 502181, 501197, 628392, 353506, 250690, 321549, 213131, 134201, 202640, 140210, 428871, 406344, 0, 414364, 298374, 221122, 355576, 240067, 222654, 413797, 163640, 491733, 212409, 556786, 103608, 247427, 443322, 208464, 561173], [235204, 46693, 163476, 153805, 213849, 71333, 229266, 272011, 320118, 225844, 206849, 89028, 156178, 217517, 381057, 222751, 143532, 286282, 280163, 270296, 370743, 237099, 86738, 414364, 0, 208101, 219280, 101025, 259858, 260053, 214484, 274518, 217001, 318654, 159780, 391112, 279361, 131548, 271564, 233971], [275271, 204251, 79788, 162481, 411617, 272261, 429328, 90917, 158889, 383011, 408806, 287097, 218494, 376220, 451860, 259395, 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# Initialize Model
m = GEKKO(remote=False)
m.options.SOLVER = 1
m.options.IMODE = 3
# VARIABLES
print("Creating variables...")
# warehouse locations
warehouses_to_hexagon_vars = []
for dks_id in range(n_warehouses):
warehouses_to_hexagon_vars.append([m.Var(value=0, lb=0, ub=1, integer=True, name=f"dk_{dks_id}_{hex_id}")
for hex_id in df_aggreg["hex_id_basic"].unique()])
# hexagon assigned to warehouse
hexagon_to_warehouse_vars = []
for hex_id in df_aggreg["hex_id_basic"].unique():
hexagon_to_warehouse_vars.append([m.Var(value=0, lb=0, ub=1, integer=True, name=f"hx_{hex_id}_{dks_id}")
for dks_id in range(n_warehouses)])
# CONSTRAINTS
# A warehouse located only in one hexagon
print("Creating constraints...")
for dks_vars in warehouses_to_hexagon_vars:
m.Equation(m.sum(dks_vars) == 1)
# One hexagon contains at most one warehouse
for hex_id in df_aggreg["hex_id_basic"].unique():
m.Equation(m.sum([dks_vars[hex_id] for dks_vars in warehouses_to_hexagon_vars]) <= 1)
# One hexagon assigned only to one warehouse
for hex_vars in hexagon_to_warehouse_vars:
m.Equation(m.sum(hex_vars) == 1)
# WARM START
for dks_id in range(n_warehouses):
warehouses_to_hexagon_vars[dks_id][randint(0, len(warehouses_to_hexagon_vars[dks_id]) - 1)].value = 1
for hex_id in range(len(hexagon_to_warehouse_vars)):
hexagon_to_warehouse_vars[hex_id][randint(0, n_warehouses - 1)].value = 1
# Set objective function
print("Creating objective function...")
for wh_id in range(n_warehouses):
for hex_id_1 in df_aggreg["hex_id_basic"].unique():
for hex_id_2 in df_aggreg["hex_id_basic"].unique():
distance_hexagon_to_warehouse = int(distance_matrix[hex_id_1][hex_id_2])
demand_hexagon = df_aggreg.loc[df_aggreg["hex_id_basic"] == hex_id_2, "value"].values[0]
m.Obj(warehouses_to_hexagon_vars[wh_id][hex_id_1] *
hexagon_to_warehouse_vars[hex_id_2][wh_id] *
distance_hexagon_to_warehouse *
demand_hexagon)
# Solve simulation
m.solve()
I've implemented a parallel solution in which I run the same model n times but with a different initial solution each. Once all models have been solved, I take the solution with lowest objective value.