我正在使用Gurobi版本8.1.0和Python API版本3.6解决MIP问题。我有两个模型，我认为它们的全局最优值是相等的。但是，我发现在我的模拟中它们并不相等。然后，我尝试使用其他模型（模型2）的解决方案热启动我认为解决方案不正确的模型（模型1）。换句话说，问题在于最大化目标函数，而model-1的目标值为42.3333，但我认为应该为42.8333。因此，我使用目标值为42.8333的模型2解决方案热启动到模型1。
奇怪的是，模型2的解决方案对于模型1而言不可行，因为目标值大于42.3333，并且问题是最大化。但是，事实证明这是可行的热启动，现在model-1的最佳值为42.8333。同一模型如何具有多个最优值？
Changed value of parameter timeLimit to 10800.0
Prev: 1e+100 Min: 0.0 Max: 1e+100 Default: 1e+100
Changed value of parameter LogFile to output/inconsistent_Model-1.log
Prev: gurobi.log Default:
Optimize a model with 11277 rows, 15150 columns and 165637 nonzeros
Model has 5050 general constraints
Variable types: 0 continuous, 15150 integer (5050 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e-02, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [1e+00, 5e+01]
Presolve removed 6167 rows and 7008 columns
Presolve time: 0.95s
Presolved: 5110 rows, 8142 columns, 37608 nonzeros
Presolved model has 3058 SOS constraint(s)
Variable types: 0 continuous, 8142 integer (4403 binary)
Warning: Markowitz tolerance tightened to 0.0625
Warning: Markowitz tolerance tightened to 0.125
Warning: Markowitz tolerance tightened to 0.25
Warning: Markowitz tolerance tightened to 0.5
Root relaxation: objective 4.333333e+01, 4856 iterations, 2.15 seconds
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 43.33333 0 587 - 43.33333 - - 3s
0 0 43.26667 0 243 - 43.26667 - - 4s
0 0 43.20000 0 1282 - 43.20000 - - 4s
0 0 43.20000 0 567 - 43.20000 - - 4s
0 0 43.18333 0 1114 - 43.18333 - - 5s
0 0 43.16543 0 2419 - 43.16543 - - 5s
0 0 43.15556 0 1575 - 43.15556 - - 5s
0 0 43.15333 0 2271 - 43.15333 - - 5s
0 0 43.13333 0 727 - 43.13333 - - 5s
0 0 43.12778 0 1698 - 43.12778 - - 5s
0 0 43.12500 0 1146 - 43.12500 - - 5s
0 0 43.12500 0 1911 - 43.12500 - - 6s
0 0 43.11927 0 1859 - 43.11927 - - 6s
0 0 43.11845 0 2609 - 43.11845 - - 7s
0 0 43.11845 0 2631 - 43.11845 - - 7s
0 0 43.11845 0 2642 - 43.11845 - - 7s
0 0 43.11845 0 2462 - 43.11845 - - 8s
0 0 43.11845 0 2529 - 43.11845 - - 8s
0 0 43.11845 0 2529 - 43.11845 - - 9s
0 2 43.11845 0 2531 - 43.11845 - - 14s
41 35 43.09874 17 957 - 43.09874 - 29.4 15s
94 84 42.93207 33 716 - 43.09874 - 22.1 31s
117 101 42.91940 40 2568 - 43.09874 - 213 37s
264 175 infeasible 92 - 43.09874 - 133 73s
273 181 infeasible 97 - 43.09874 - 277 77s
293 191 42.42424 17 1828 - 43.09874 - 280 90s
369 249 42.40111 52 2633 - 43.09874 - 311 105s
383 257 42.39608 59 3062 - 43.09874 - 329 152s
408 265 42.39259 65 2819 - 43.09874 - 386 162s
419 274 41.51399 66 2989 - 43.09874 - 401 170s
454 282 41.29938 71 3000 - 43.09874 - 390 182s
462 280 infeasible 74 - 43.09874 - 423 192s
479 287 infeasible 78 - 43.09874 - 419 204s
498 293 40.51287 81 2564 - 43.09874 - 435 207s
526 307 40.16638 86 2619 - 43.09874 - 419 227s
584 330 42.63100 33 621 - 43.09874 - 404 236s
628 333 infeasible 37 - 43.09874 - 394 252s
661 345 42.37500 26 25 - 43.09874 - 396 288s
684 353 infeasible 30 - 43.09874 - 426 290s
842 370 infeasible 69 - 43.09874 - 348 306s
944 379 infeasible 86 - 43.09874 - 321 370s
1009 395 42.36667 22 25 - 43.09874 - 350 409s
* 1031 243 3 42.3333333 43.09874 1.81% 343 409s
1056 203 43.00000 19 141 42.33333 43.09874 1.81% 362 411s
1194 222 cutoff 23 42.33333 43.00000 1.57% 325 430s
1199 219 cutoff 25 42.33333 43.00000 1.57% 349 450s
1202 212 cutoff 29 42.33333 43.00000 1.57% 361 472s
1211 200 infeasible 47 42.33333 42.91851 1.38% 380 498s
1226 169 infeasible 43 42.33333 42.91471 1.37% 395 511s
Cutting planes:
Gomory: 2
Cover: 15
Implied bound: 1
Clique: 26
MIR: 17
Inf proof: 1
Zero half: 8
Explored 1426 nodes (502432 simplex iterations) in 512.68 seconds
Thread count was 4 (of 4 available processors)
Solution count 1: 42.3333
Optimal solution found (tolerance 1.00e-04)
Warning: some integer variables take values larger than the maximum
supported value (2000000000)
Best objective 4.233333333333e+01, best bound 4.233333333333e+01, gap 0.0000%
除了上述内容，我还收到此警告：“找到了最佳解决方案（公差1.00e-04）警告：某些整数变量的值大于最大值支持值（2000000000）”。这是什么意思？非常感谢！
似乎您遇到了一些数字上的麻烦。根部松弛需要增加Markowitz耐受性，这表明基质条件不佳。正如您在两种不同的“最佳”解决方案中所观察到的，这可能导致不一致。
关于太大值的警告表示，存在整数值的解值太大，以致无法可靠地检查整数可行性公差。如果您的变量的解决方案值在1e + 9范围内，则它们是否为整数可能不再重要。因此，您还可以通过使它们成为连续变量来简化模型。
您应该检查两个模型的两个解决方案中是否存在违规情况（请参阅here，以查看解决方案的实际可行性。