我有一个ILP，可以解决一些小问题。对于这些小问题，Gurobi轻松收敛并返回了正确答案。但是，当涉及到更大的问题时，即使两天后它也不会收敛。我更改了许多参数，例如“ MIPFocus”，“ ImproveStartGap”，“剪切”，“ ImproveStartTime”，甚至是“启发式”。
您能帮我解决这个问题吗？有什么办法可以以最佳松散为代价更快地达到融合？有什么问题吗？
最好，阿米尔
仅供参考，此ILP具有10135个整数变量（其中大多数10044是二进制）。下面是我停止程序时的日志：
Academic license - for non-commercial use only
Optimize a model with 131848 rows, 20748 columns and 577874 nonzeros
Variable types: 0 continuous, 20748 integer (20657 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+05]
Objective range [4e+01, 8e+01]
Bounds range [1e+00, 1e+00]
RHS range [1e+00, 3e+05]
Presolve removed 23245 rows and 10613 columns
Presolve time: 1.67s
Presolved: 108603 rows, 10135 columns, 526215 nonzeros
Variable types: 0 continuous, 10135 integer (10044 binary)
Presolved: 10135 rows, 118738 columns, 536350 nonzeros
Root relaxation: objective 9.360000e+03, 10205 iterations, 0.79 seconds
Total elapsed time = 5.06s
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 9360.00000 0 299 - 9360.00000 - - 5s
0 0 9360.00000 0 223 - 9360.00000 - - 8s
0 2 9360.00000 0 150 - 9360.00000 - - 23s
30 31 9360.00000 9 188 - 9360.00000 - 64.8 25s
207 208 9360.00000 64 263 - 9360.00000 - 14.4 31s
400 399 9360.00000 109 298 - 9360.00000 - 10.3 36s
587 584 9360.00000 156 319 - 9360.00000 - 9.5 41s
804 794 9360.00000 209 363 - 9360.00000 - 8.8 47s
918 905 9360.00000 238 303 - 9360.00000 - 8.6 50s
1159 1133 9360.00000 294 288 - 9360.00000 - 8.3 56s
1281 1247 9360.00000 319 371 - 9360.00000 - 8.2 60s
1534 1471 9360.00000 23 208 - 9360.00000 - 8.1 66s
1809 1736 9360.00000 237 223 - 9360.00000 - 8.0 71s
1811 1737 9360.00000 89 670 - 9360.00000 - 8.0 87s
1812 1738 9360.00000 192 572 - 9360.00000 - 8.0 96s
1813 1739 9360.00000 93 572 - 9360.00000 - 8.0 109s
1814 1742 9360.00000 11 371 - 9360.00000 - 9.3 117s
1865 1775 9360.00000 19 399 - 9360.00000 - 9.5 120s
1967 1840 9360.00000 31 395 - 9360.00000 - 9.1 125s
2180 1984 9360.00000 56 435 - 9360.00000 - 9.1 130s
2383 2121 9360.00000 84 408 - 9360.00000 - 9.4 136s
2495 2197 9360.00000 97 403 - 9360.00000 - 9.5 140s
2712 2337 9360.00000 124 425 - 9360.00000 - 9.6 147s
2829 2416 9360.00000 137 448 - 9360.00000 - 9.6 151s
2957 2505 9360.00000 153 421 - 9360.00000 - 9.6 155s
3196 2660 9360.00000 183 389 - 9360.00000 - 9.6 164s
3291 2721 9360.00000 195 412 - 9360.00000 - 9.6 168s
3383 2789 9360.00000 208 424 - 9360.00000 - 9.8 173s
3475 2850 9360.00000 221 427 - 9360.00000 - 10.0 177s
3590 2909 9360.00000 235 433 - 9360.00000 - 10.0 182s
3716 2990 9360.00000 250 424 - 9360.00000 - 10.1 187s
3830 3054 9360.00000 266 398 - 9360.00000 - 10.2 192s
3987 3151 9360.00000 285 400 - 9360.00000 - 10.2 197s
4079 3212 9360.00000 299 409 - 9360.00000 - 10.2 203s
4294 3385 infeasible 327 - 9360.00000 - 10.2 208s
4489 3316 9360.00000 61 404 - 9360.00000 - 10.3 213s
4688 3528 9360.00000 104 410 - 9360.00000 - 10.4 219s
4953 3715 9360.00000 144 409 - 9360.00000 - 10.2 225s
5175 3864 9360.00000 187 413 - 9360.00000 - 10.2 232s
5455 4022 9360.00000 221 427 - 9360.00000 - 10.0 239s
5683 4172 9360.00000 264 397 - 9360.00000 - 10.0 246s
5891 4318 9360.00000 300 395 - 9360.00000 - 10.0 254s
6211 4448 9360.00000 58 421 - 9360.00000 - 9.9 261s
6508 4642 9360.00000 110 472 - 9360.00000 - 9.9 268s
6856 4855 9360.00000 183 452 - 9360.00000 - 9.8 276s
7127 5068 9360.00000 231 397 - 9360.00000 - 9.9 285s
7508 5455 9360.00000 299 450 - 9360.00000 - 9.8 294s
7906 5732 9360.00000 350 400 - 9360.00000 - 9.7 303s
8105 5876 9360.00000 353 405 - 9360.00000 - 9.9 313s
8347 6093 9360.00000 362 366 - 9360.00000 - 10.1 323s
8657 6374 9360.00000 75 424 - 9360.00000 - 10.2 334s
8962 6663 9360.00000 135 506 - 9360.00000 - 10.3 345s
9380 7037 9360.00000 209 463 - 9360.00000 - 10.3 356s
9722 7363 9360.00000 302 445 - 9360.00000 - 10.4 368s
10215 7802 9360.00000 48 392 - 9360.00000 - 10.3 381s
10594 8171 9360.00000 128 488 - 9360.00000 - 10.3 394s
11142 8706 9360.00000 231 488 - 9360.00000 - 10.2 408s
11727 9203 infeasible 348 - 9360.00000 - 10.1 421s
12126 9573 9360.00000 112 489 - 9360.00000 - 10.2 435s
12631 10058 9360.00000 235 471 - 9360.00000 - 10.2 448s
13057 10467 9360.00000 313 509 - 9360.00000 - 10.3 461s
13442 10831 9360.00000 361 428 - 9360.00000 - 10.4 475s
14060 11357 9360.00000 62 399 - 9360.00000 - 10.3 489s
14714 11805 9360.00000 149 428 - 9360.00000 - 10.2 502s
15229 12295 9360.00000 258 458 - 9360.00000 - 10.1 516s
15794 12838 9360.00000 355 420 - 9360.00000 - 10.1 530s
16395 13384 infeasible 434 - 9360.00000 - 10.0 542s
16849 13726 9360.00000 124 497 - 9360.00000 - 10.1 555s
17364 14277 9360.00000 233 457 - 9360.00000 - 10.0 568s
17855 14758 9360.00000 327 432 - 9360.00000 - 10.0 582s
18446 15223 9360.00000 62 403 - 9360.00000 - 9.9 595s
19030 15662 9360.00000 152 434 - 9360.00000 - 9.9 608s
19502 16142 9360.00000 239 453 - 9360.00000 - 9.8 620s
20069 16702 9360.00000 355 432 - 9360.00000 - 9.8 633s
20643 17143 9360.06655 434 415 - 9360.00000 - 9.7 646s
21219 17545 9360.00000 89 493 - 9360.00000 - 9.7 658s
21694 17994 9360.00000 183 526 - 9360.00000 - 9.7 671s
22237 18517 9360.00000 302 462 - 9360.00000 - 9.6 683s
22822 18976 infeasible 383 - 9360.00000 - 9.5 695s
23246 19366 9360.00000 117 503 - 9360.00000 - 9.6 707s
23765 19879 9360.00000 212 484 - 9360.00000 - 9.5 720s
24139 20275 9360.00000 283 415 - 9360.00000 - 9.6 732s
24747 20695 infeasible 330 - 9360.00000 - 9.5 743s
25278 21165 9360.00000 90 434 - 9360.00000 - 9.5 755s
25714 21591 9360.00000 173 462 - 9360.00000 - 9.5 767s
26243 22075 9360.00000 296 396 - 9360.00000 - 9.4 779s
26830 22569 9360.00000 96 413 - 9360.00000 - 9.4 791s
27303 22968 9360.00000 188 438 - 9360.00000 - 9.4 802s
27692 23352 9360.00000 287 440 - 9360.00000 - 9.4 815s
28208 23839 9360.00000 50 370 - 9360.00000 - 9.4 826s
28753 24256 9360.00000 131 464 - 9360.00000 - 9.4 838s
29199 24630 9360.00000 71 408 - 9360.00000 - 9.4 850s
29586 25000 9360.00000 157 475 - 9360.00000 - 9.4 862s
30104 25497 9360.00000 247 428 - 9360.00000 - 9.3 874s
30660 25890 9600.00000 302 375 - 9360.00000 - 9.3 886s
30986 26191 9600.00000 309 399 - 9360.00000 - 9.5 899s
31374 26569 9600.00000 324 314 - 9360.00000 - 9.5 911s
31748 26902 9600.00000 324 346 - 9360.00000 - 9.5 923s
32341 27292 9360.00000 80 495 - 9360.00000 - 9.4 934s
32762 27690 9360.00000 159 528 - 9360.00000 - 9.5 947s
33288 28176 9360.00000 283 472 - 9360.00000 - 9.4 959s
33816 28698 infeasible 375 - 9360.00000 - 9.4 971s
34019 28872 9360.00000 382 355 - 9360.00000 - 9.5 982s
34249 29030 9360.00000 384 340 - 9360.00000 - 9.6 994s
34477 29168 9420.00000 407 370 - 9360.00000 - 9.7 1006s
34799 29473 infeasible 419 - 9360.00000 - 9.7 1018s
35163 29804 9360.00000 89 435 - 9360.00000 - 9.7 1031s
35749 30322 9360.00000 198 452 - 9360.00000 - 9.7 1044s
36357 30790 infeasible 295 - 9360.00000 - 9.6 1057s
36844 31266 9360.00000 147 473 - 9360.00000 - 9.6 1070s
37359 31755 9360.00000 226 463 - 9360.00000 - 9.6 1082s
37761 32178 9360.00000 328 494 - 9360.00000 - 9.6 1096s
38309 32576 9362.39601 376 479 - 9360.00000 - 9.6 1108s
38922 33011 infeasible 402 - 9360.00000 - 9.6 1120s
39313 33349 9360.00000 123 434 - 9360.00000 - 9.6 1132s
39891 33867 9360.00000 245 461 - 9360.00000 - 9.6 1145s
40260 34232 9360.00000 321 487 - 9360.00000 - 9.6 1157s
40817 34704 9360.00000 87 444 - 9360.00000 - 9.6 1169s
41151 35031 9360.00000 121 521 - 9360.00000 - 9.6 1182s
41732 35534 9360.00000 231 492 - 9360.00000 - 9.6 1196s
42304 35973 infeasible 321 - 9360.00000 - 9.6 1200s
Explored 42427 nodes (435518 simplex iterations) in 1200.24 seconds
Thread count was 8 (of 8 available processors)
Solution count 0
更新： 即使存在一个非常小的问题，并且连续变量而不是整数变量（469个二进制变量和15个连续变量），古罗比仍在寻找可行的解决方案。我认为必须采取一些措施以防止此问题并使古罗比收敛！小问题的日志：
Academic license - for non-commercial use only
Optimize a model with 2342 rows, 1206 columns and 8898 nonzeros
Variable types: 15 continuous, 1191 integer (1191 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+05]
Objective range [1e+00, 8e+02]
Bounds range [1e+00, 2e+01]
RHS range [1e+00, 3e+05]
Presolve removed 849 rows and 722 columns
Presolve time: 0.01s
Presolved: 1493 rows, 484 columns, 6414 nonzeros
Variable types: 15 continuous, 469 integer (469 binary)
Root relaxation: objective 2.160000e+03, 168 iterations, 0.00 seconds
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 2160.00000 0 19 - 2160.00000 - - 0s
0 0 2160.00000 0 44 - 2160.00000 - - 0s
0 0 2160.00000 0 57 - 2160.00000 - - 0s
0 0 2160.00000 0 46 - 2160.00000 - - 0s
0 0 2160.00000 0 31 - 2160.00000 - - 0s
0 0 2160.00000 0 28 - 2160.00000 - - 0s
0 0 2160.00000 0 49 - 2160.00000 - - 0s
0 0 2160.00000 0 42 - 2160.00000 - - 0s
0 0 2160.00000 0 59 - 2160.00000 - - 0s
0 0 2160.00000 0 41 - 2160.00000 - - 0s
0 2 2160.00000 0 41 - 2160.00000 - - 0s
10135 1630 2160.00000 36 12 - 2160.00000 - 8.7 5s
22631 2543 infeasible 40 - 2160.00000 - 12.8 10s
34157 2675 2160.00000 40 43 - 2160.00000 - 14.5 15s
47547 2906 infeasible 43 - 2160.00000 - 15.1 20s
61008 3057 2160.00000 36 30 - 2160.00000 - 15.3 25s
70483 3488 2160.00000 42 20 - 2160.00000 - 15.7 30s
81159 4625 2160.00000 34 23 - 2160.00000 - 15.8 35s
94894 6051 infeasible 43 - 2160.00000 - 16.0 40s
106278 6567 2160.00000 47 32 - 2160.00000 - 16.1 45s
118415 7154 2160.00000 40 9 - 2160.00000 - 16.4 50s
130278 7148 2160.00000 40 14 - 2160.00000 - 16.7 55s
141753 8045 2160.00000 38 21 - 2160.00000 - 16.8 60s
153321 8861 2160.00000 37 17 - 2160.00000 - 17.0 65s
163315 9327 infeasible 37 - 2160.00000 - 17.2 70s
174712 9284 2160.00000 43 22 - 2160.00000 - 17.4 75s
186989 9750 2160.00000 40 14 - 2160.00000 - 17.3 80s
199567 9980 2160.00000 47 17 - 2160.00000 - 17.3 85s
213163 10894 2160.00000 41 11 - 2160.00000 - 17.0 90s
225271 11352 infeasible 34 - 2160.00000 - 16.9 95s
237961 11732 2160.00000 45 7 - 2160.00000 - 16.8 100s
250844 11855 infeasible 46 - 2160.00000 - 16.7 105s
265028 13816 infeasible 51 - 2160.00000 - 16.8 110s
278712 14912 2160.00000 41 14 - 2160.00000 - 16.8 115s
290532 15964 2160.00000 43 27 - 2160.00000 - 16.8 120s
302974 17402 infeasible 44 - 2160.00000 - 16.8 125s
315002 18302 infeasible 42 - 2160.00000 - 16.8 130s
327409 19249 2160.00000 37 23 - 2160.00000 - 16.8 135s
339414 20128 2160.00000 50 16 - 2160.00000 - 16.8 140s
352135 20727 infeasible 45 - 2160.00000 - 16.8 145s
367381 21309 2160.00000 38 13 - 2160.00000 - 16.8 150s
7660856 348402 infeasible 49 - 2160.00000 - 15.9 3205s
7672378 348678 2160.00000 33 21 - 2160.00000 - 15.9 3210s
7685454 348828 2160.00000 37 18 - 2160.00000 - 15.9 3215s
7697794 348947 2160.00000 49 2 - 2160.00000 - 15.9 3220s
7707262 349326 2160.92308 40 31 - 2160.00000 - 15.9 3225s
7718583 349877 infeasible 40 - 2160.00000 - 15.9 3230s
7729574 350121 infeasible 40 - 2160.00000 - 15.9 3235s
7741901 350412 infeasible 44 - 2160.00000 - 15.9 3240s
7751253 350381 2160.00000 49 32 - 2160.00000 - 15.9 3245s
7763103 350489 2160.00000 37 26 - 2160.00000 - 15.9 3250s
7773839 350681 2160.00000 38 27 - 2160.00000 - 15.9 3255s
7786222 351217 infeasible 45 - 2160.00000 - 15.9 3260s
7797384 351803 infeasible 46 - 2160.00000 - 15.9 3265s
7808953 352474 2160.00000 51 12 - 2160.00000 - 15.9 3270s
7820291 353040 2160.00000 49 8 - 2160.00000 - 15.8 3275s
7831847 353412 2160.00000 54 2 - 2160.00000 - 15.8 3280s
7842631 354132 infeasible 50 - 2160.00000 - 15.8 3285s
7852436 354657 infeasible 47 - 2160.00000 - 15.8 3290s
7861503 354637 2160.00000 39 24 - 2160.00000 - 15.8 3295s
7874356 354907 2160.00000 41 9 - 2160.00000 - 15.8 3300s
Interrupt request received
Cutting planes:
Learned: 7
Gomory: 11
Cover: 18
Implied bound: 2
Clique: 10
MIR: 99
StrongCG: 6
Flow cover: 243
Inf proof: 6
Explored 7885073 nodes (124881023 simplex iterations) in 3303.69 seconds
Thread count was 8 (of 8 available processors)
Solution count 0
Solve interrupted
Best objective -, best bound 2.159999999845e+03, gap -
答案 0 :(得分：1)
您是否尝试过关闭预解析？ 将presolve设置为2并尝试。有时，预求解步骤会修剪一些可行的区域以加强公式，结果模型中只剩下一些可行的解决方案。
在许多情况下，关闭预解析器会有所帮助。
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