调试帮助：Mixed Integer Linear Programming problem in Python PuLP

Question

我有一个 MILP 问题，我在 Python 中使用 PuLP 解决了这个问题，并且遇到了一些我无法理解的解算器的有趣行为。 我很想知道是什么导致了这个问题。

首先是关于问题陈述的一点点。 这是一个 transportation.network 问题，有一堆节点被连接起来，这样总成本最小，同时满足一些限制，比如禁用/强制某些车道。

当我使用 PuLP 的捆绑解算器解决问题时，它给了我以下解决方案。

objective = cost
opt_model.setObjective(objective)
opt_model.sense = plp.LpMinimize
opt_model.solve()
print(plp.LpStatus[opt_model.status])
print("objective=", opt_model.objective.value())


Optimal
objective= 20968423.09652282

我意识到 PuLP 使用的求解器版本是 2.9.0，但 COIN-OR 网站上的最新版本是 2.10.3，因此决定使用最新的 CBC 求解器。 当我这样做时，这个完全相同的问题在新求解器中变得不可行。

objective = cost
opt_model.setObjective(objective)
opt_model.sense = plp.LpMinimize
opt_model.solve(solver=plp.COIN_CMD(path='<path to solver>/cbc'))
print(plp.LpStatus[opt_model.status])
print("objective=", opt_model.objective.value())


Infeasible
objective= 18434742.025923416

然而，有趣的是，只有当我通过 PuLP 解决问题时，它才会给我一个问题。 如果我使用 PuLP 创建的 .lp 文件并使用下载的 cbc 二进制文件直接求解，它会求解并给出一个与 PuLP 求解器的答案非常接近的最佳答案！

Welcome to the CBC MILP Solver
Version: 2.10.3
Build Date: Dec 15 2019

command line - ./cbc writeLP_model_Partial.lp (default strategy 1)
Continuous objective value is 1.84347e+07 - 0.16 seconds
Cgl0003I 0 fixed, 0 tightened bounds, 854 strengthened rows, 338 substitutions
Cgl0003I 0 fixed, 0 tightened bounds, 630 strengthened rows, 0 substitutions
Cgl0003I 0 fixed, 0 tightened bounds, 278 strengthened rows, 0 substitutions
Cgl0003I 0 fixed, 0 tightened bounds, 100 strengthened rows, 0 substitutions
Cgl0004I processed model has 6676 rows, 5092 columns (5092 integer (3674 of which binary)) and 21162 elements
Cbc0038I Initial state - 435 integers unsatisfied sum - 73.1625
Cbc0038I Pass   1: (1.31 seconds) suminf.   54.06687 (218) obj. 2.10227e+07 iterations 631
Cbc0038I Pass   2: (1.31 seconds) suminf.   54.06685 (218) obj. 2.10227e+07 iterations 0
Cbc0038I Pass   3: (1.32 seconds) suminf.   54.06685 (218) obj. 2.10227e+07 iterations 0
Cbc0038I Pass   4: (1.33 seconds) suminf.   53.70259 (217) obj. 2.10265e+07 iterations 1
Cbc0038I Pass   5: (1.33 seconds) suminf.   53.70259 (217) obj. 2.10265e+07 iterations 0
Cbc0038I Pass   6: (1.33 seconds) suminf.   53.70259 (217) obj. 2.10265e+07 iterations 0
Cbc0038I Pass   7: (1.34 seconds) suminf.   53.70259 (217) obj. 2.10265e+07 iterations 0
Cbc0038I Pass   8: (1.34 seconds) suminf.   53.70259 (217) obj. 2.10265e+07 iterations 0
Cbc0038I Pass   9: (1.35 seconds) suminf.   53.70259 (217) obj. 2.10265e+07 iterations 0
Cbc0038I Pass  10: (1.35 seconds) suminf.   53.70259 (217) obj. 2.10265e+07 iterations 0
Cbc0038I Pass  11: (1.35 seconds) suminf.   53.70259 (217) obj. 2.10265e+07 iterations 0
Cbc0038I Pass  12: (1.36 seconds) suminf.   53.70259 (217) obj. 2.10265e+07 iterations 0
Cbc0038I Pass  13: (1.37 seconds) suminf.   47.92774 (193) obj. 2.24017e+07 iterations 444
Cbc0038I Pass  14: (1.38 seconds) suminf.   47.92774 (193) obj. 2.24017e+07 iterations 33
Cbc0038I Pass  15: (1.38 seconds) suminf.   47.92774 (193) obj. 2.24017e+07 iterations 0
Cbc0038I Pass  16: (1.39 seconds) suminf.   47.92774 (193) obj. 2.24017e+07 iterations 0
Cbc0038I Pass  17: (1.40 seconds) suminf.   47.92774 (193) obj. 2.34752e+07 iterations 355
Cbc0038I Pass  18: (1.41 seconds) suminf.   47.92774 (193) obj. 2.34752e+07 iterations 20
Cbc0038I Pass  19: (1.41 seconds) suminf.   47.92774 (193) obj. 2.34752e+07 iterations 0
Cbc0038I Pass  20: (1.42 seconds) suminf.   47.92774 (193) obj. 2.34752e+07 iterations 0
Cbc0038I Pass  21: (1.42 seconds) suminf.   47.92774 (193) obj. 2.34752e+07 iterations 0
Cbc0038I Pass  22: (1.42 seconds) suminf.   47.92774 (193) obj. 2.34752e+07 iterations 0
Cbc0038I Pass  23: (1.43 seconds) suminf.   47.92774 (193) obj. 2.34752e+07 iterations 0
Cbc0038I Pass  24: (1.43 seconds) suminf.   47.92774 (193) obj. 2.34752e+07 iterations 0
Cbc0038I Pass  25: (1.44 seconds) suminf.   47.92774 (193) obj. 2.34752e+07 iterations 0
Cbc0038I Pass  26: (1.44 seconds) suminf.   47.92774 (193) obj. 2.34752e+07 iterations 0
Cbc0038I Pass  27: (1.46 seconds) suminf.   44.63425 (184) obj. 2.45218e+07 iterations 368
Cbc0038I Pass  28: (1.47 seconds) suminf.   44.63425 (184) obj. 2.45218e+07 iterations 17
Cbc0038I Pass  29: (1.47 seconds) suminf.   44.63425 (184) obj. 2.45218e+07 iterations 0
Cbc0038I Pass  30: (1.48 seconds) suminf.   44.63425 (184) obj. 2.45218e+07 iterations 0
Cbc0038I Rounding solution of 2.09662e+07 is better than previous of 1e+50

Cbc0038I Before mini branch and bound, 3925 integers at bound fixed and 1 continuous
Cbc0038I Mini branch and bound did not improve solution (1.50 seconds)
Cbc0038I After 1.50 seconds - Feasibility pump exiting with objective of 2.09662e+07 - took 0.25 seconds
Cbc0012I Integer solution of 20966181 found by feasibility pump after 0 iterations and 0 nodes (1.50 seconds)
Cbc0001I Search completed - best objective 20966181.27328906, took 0 iterations and 0 nodes (1.55 seconds)
Cbc0035I Maximum depth 0, 0 variables fixed on reduced cost
Cuts at root node changed objective from 2.09843e+07 to 2.09843e+07
Probing was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)
Gomory was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)
Knapsack was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)
Clique was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)
MixedIntegerRounding2 was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 s
econds)
FlowCover was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)
TwoMirCuts was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)
ZeroHalf was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)

Result - Optimal solution found

Objective value:                20966181.27328906
Enumerated nodes:               0
Total iterations:               0
Time (CPU seconds):             1.74
Time (Wallclock seconds):       1.82

Total time (CPU seconds):       1.85   (Wallclock seconds):       1.96

我在这里错过了什么？ 我尝试了不同的方法，比如将 PuLP 更新到最新版本，但这没有帮助。 是否有任何我需要更改的求解器选项？ 我是新手，所以不知道该尝试什么。

Answer 1

您很可能遇到了数值精度问题。 检查pulp 文档这一部分的第2 点。 您在约束参数和目标 function 系数中为浮点数使用了太多小数。 只需将所有参数四舍五入到 2 位或 3 位小数（或对您的问题有意义的任何值）。

这可以看出，因为您的目标 function 值很长 (18434742.025923416) 并且因为 CBC 给出了不同的目标作为最优目标（无论您使用哪种求解器，都应该只有一个最优目标 function 值）。