分析紙漿中 CBC 求解器的日志

Question

我正在嘗試使用 CBC 求解器解決紙漿中的優化問題。

這是日志和我想從日志中了解的幾個問題：

Welcome to the CBC MILP Solver 
Version: 2.9.9 
Build Date: Aug 21 2017 

command line - /usr/bin/cbc /tmp/ae38591e7b4f4185adc4ac18aa1c8361-pulp.mps max threads 4 timeMode elapsed branch printingOptions all solution /tmp/ae38591e7b4f4185adc4ac18aa1c8361-pulp.sol (default strategy 1)
At line 2 NAME          MODEL
At line 3 ROWS
At line 2681 COLUMNS
At line 126513 RHS
At line 129190 BOUNDS
At line 153239 ENDATA
Problem MODEL has 2676 rows, 24048 columns and 72144 elements
Coin0008I MODEL read with 0 errors
threads was changed from 0 to 4
Option for timeMode changed from cpu to elapsed
Continuous objective value is 72032.6 - 0.15 seconds
Cgl0008I 2672 inequality constraints converted to equality constraints
Cgl0004I processed model has 2676 rows, 10688 columns (10688 integer (10688 of which binary)) and 26720 elements
Cutoff increment increased from 1e-05 to 4.9999
Cbc0038I Initial state - 4 integers unsatisfied sum - 1.3913
Cbc0038I Pass   1: suminf.    0.69565 (2) obj. -72018.7 iterations 763
Cbc0038I Solution found of -71960
Cbc0038I Before mini branch and bound, 10682 integers at bound fixed and 0 continuous
Cbc0038I Full problem 2676 rows 10688 columns, reduced to 2 rows 3 columns
Cbc0038I Mini branch and bound improved solution from -71960 to -72000 (2.00 seconds)
Cbc0038I Round again with cutoff of -72007.8
Cbc0038I Reduced cost fixing fixed 3805 variables on major pass 2
Cbc0038I Pass   2: suminf.    0.69565 (2) obj. -72029.1 iterations 17
Cbc0038I Pass   3: suminf.    0.59203 (2) obj. -72007.8 iterations 850
Cbc0038I Pass   4: suminf.    1.39130 (6) obj. -72007.8 iterations 417
Cbc0038I Pass   5: suminf.    0.69565 (2) obj. -72009.1 iterations 556
Cbc0038I Pass   6: suminf.    0.74131 (2) obj. -72007.8 iterations 588
Cbc0038I Pass   7: suminf.    0.69565 (2) obj. -72009.1 iterations 610
Cbc0038I Pass   8: suminf.    1.81303 (8) obj. -72007.8 iterations 504
Cbc0038I Pass   9: suminf.    0.69565 (2) obj. -72009.1 iterations 922
Cbc0038I Pass  10: suminf.    0.74131 (2) obj. -72007.8 iterations 636
Cbc0038I Pass  11: suminf.    1.79138 (8) obj. -72007.8 iterations 340
Cbc0038I Pass  12: suminf.    0.69565 (2) obj. -72009.1 iterations 409
Cbc0038I Pass  13: suminf.    0.74131 (2) obj. -72007.8 iterations 584
Cbc0038I Pass  14: suminf.    2.90875 (8) obj. -72007.8 iterations 260
Cbc0038I Pass  15: suminf.    0.69565 (2) obj. -72009.1 iterations 1376
Cbc0038I Pass  16: suminf.    0.74131 (2) obj. -72007.8 iterations 597
Cbc0038I Pass  17: suminf.    1.79138 (8) obj. -72007.8 iterations 349
Cbc0038I Pass  18: suminf.    0.69565 (2) obj. -72009.1 iterations 449
Cbc0038I Pass  19: suminf.    0.74131 (2) obj. -72007.8 iterations 621
Cbc0038I Pass  20: suminf.    2.90875 (8) obj. -72007.8 iterations 311
Cbc0038I Pass  21: suminf.    0.69565 (2) obj. -72009.1 iterations 931
Cbc0038I Pass  22: suminf.    0.74131 (2) obj. -72007.8 iterations 627
Cbc0038I Pass  23: suminf.    2.90875 (8) obj. -72007.8 iterations 302
Cbc0038I Pass  24: suminf.    0.69565 (2) obj. -72009.1 iterations 554
Cbc0038I Pass  25: suminf.    0.74131 (2) obj. -72007.8 iterations 552
Cbc0038I Pass  26: suminf.    1.81303 (8) obj. -72007.8 iterations 303
Cbc0038I Pass  27: suminf.    0.69565 (2) obj. -72009.1 iterations 791
Cbc0038I Pass  28: suminf.    0.74131 (2) obj. -72007.8 iterations 575
Cbc0038I Pass  29: suminf.    2.63482 (8) obj. -72007.8 iterations 387
Cbc0038I Pass  30: suminf.    0.69565 (2) obj. -72009.1 iterations 801
Cbc0038I Pass  31: suminf.    0.74131 (2) obj. -72007.8 iterations 582
Cbc0038I No solution found this major pass
Cbc0038I Before mini branch and bound, 10134 integers at bound fixed and 0 continuous
Cbc0038I Full problem 2676 rows 10688 columns, reduced to 15 rows 45 columns
Cbc0038I Mini branch and bound did not improve solution (3.51 seconds)
Cbc0038I After 3.51 seconds - Feasibility pump exiting with objective of -72000 - took 1.65 seconds
Cbc0012I Integer solution of -72000 found by feasibility pump after 0 iterations and 0 nodes (3.52 seconds)
Cbc0038I Full problem 2676 rows 10688 columns, reduced to 2 rows 2 columns
Cbc0013I At root node, 0 cuts changed objective from -72032.609 to -72032.609 in 1 passes
Cbc0014I Cut generator 0 (Probing) - 0 row cuts average 0.0 elements, 0 column cuts (0 active)  in 0.012 seconds - new frequency is -100
Cbc0014I Cut generator 1 (Gomory) - 0 row cuts average 0.0 elements, 0 column cuts (0 active)  in 0.004 seconds - new frequency is -100
Cbc0014I Cut generator 2 (Knapsack) - 0 row cuts average 0.0 elements, 0 column cuts (0 active)  in 0.004 seconds - new frequency is -100
Cbc0014I Cut generator 3 (Clique) - 0 row cuts average 0.0 elements, 0 column cuts (0 active)  in 0.000 seconds - new frequency is -100
Cbc0014I Cut generator 4 (MixedIntegerRounding2) - 0 row cuts average 0.0 elements, 0 column cuts (0 active)  in 0.002 seconds - new frequency is -100
Cbc0014I Cut generator 5 (FlowCover) - 0 row cuts average 0.0 elements, 0 column cuts (0 active)  in 0.000 seconds - new frequency is -100
Cbc0010I After 0 nodes, 1 on tree, -72000 best solution, best possible -72032.609 (4.57 seconds)
Cbc0038I Full problem 2676 rows 10688 columns, reduced to 955 rows 3443 columns
Cbc0044I Reduced cost fixing - 955 rows, 3443 columns - restarting search
Cbc0038I Unable to insert previous solution - using cutoff of -72000
Cbc0038I Initial state - 3 integers unsatisfied sum - 1.04348
Cbc0038I Pass   1: suminf.    0.68801 (4) obj. -72000 iterations 750
Cbc0038I Pass   2: suminf.    0.00018 (1) obj. -72000 iterations 531
Cbc0038I Solution found of -72000
Cbc0038I After further testing solution no better than previous of -72000
Cbc0038I Before mini branch and bound, 3437 integers at bound fixed and 0 continuous
Cbc0038I Full problem 955 rows 3443 columns, reduced to 2 rows 3 columns
Cbc0038I Mini branch and bound did not improve solution (18.74 seconds)
Cbc0038I Round again with cutoff of -72007.8
Cbc0038I Pass   3: suminf.    1.01084 (4) obj. -72007.8 iterations 0
Cbc0038I Pass   4: suminf.    0.46565 (3) obj. -72007.8 iterations 864
Cbc0038I Pass   5: suminf.    1.01084 (4) obj. -72007.8 iterations 976
Cbc0038I Pass   6: suminf.    1.65441 (7) obj. -72007.8 iterations 882
Cbc0038I Pass   7: suminf.    1.13162 (4) obj. -72007.8 iterations 813
Cbc0038I Pass   8: suminf.    0.92536 (2) obj. -72007.8 iterations 858
Cbc0038I Pass   9: suminf.    1.31344 (4) obj. -72007.8 iterations 1029
Cbc0038I Pass  10: suminf.    1.06565 (3) obj. -72007.8 iterations 857
Cbc0038I Pass  11: suminf.    1.31344 (4) obj. -72007.8 iterations 971
Cbc0038I Pass  12: suminf.    1.28587 (7) obj. -72007.8 iterations 980
Cbc0038I No solution found this major pass
Cbc0038I Before mini branch and bound, 3156 integers at bound fixed and 0 continuous
Cbc0038I Full problem 955 rows 3443 columns, reduced to 12 rows 37 columns
Cbc0038I Mini branch and bound did not improve solution (19.03 seconds)
Cbc0038I After 19.03 seconds - Feasibility pump exiting with objective of -72000 - took 0.97 seconds
Cbc0012I Integer solution of -72000 found by feasibility pump after 0 iterations and 0 nodes (19.03 seconds)
Cbc0038I Full problem 955 rows 3443 columns, reduced to 2 rows 2 columns
Cbc0013I At root node, 0 cuts changed objective from -72032.609 to -72032.609 in 1 passes
Cbc0014I Cut generator 0 (Probing) - 0 row cuts average 0.0 elements, 0 column cuts (0 active)  in 0.005 seconds - new frequency is -100
Cbc0014I Cut generator 1 (Gomory) - 0 row cuts average 0.0 elements, 0 column cuts (0 active)  in 0.001 seconds - new frequency is -100
Cbc0014I Cut generator 2 (Knapsack) - 0 row cuts average 0.0 elements, 0 column cuts (0 active)  in 0.003 seconds - new frequency is -100
Cbc0014I Cut generator 3 (Clique) - 0 row cuts average 0.0 elements, 0 column cuts (0 active)  in 0.000 seconds - new frequency is -100
Cbc0014I Cut generator 4 (MixedIntegerRounding2) - 0 row cuts average 0.0 elements, 0 column cuts (0 active)  in 0.001 seconds - new frequency is -100
Cbc0014I Cut generator 5 (FlowCover) - 0 row cuts average 0.0 elements, 0 column cuts (0 active)  in 0.001 seconds - new frequency is -100
Cbc0014I Cut generator 6 (TwoMirCuts) - 0 row cuts average 0.0 elements, 0 column cuts (0 active)  in 0.002 seconds - new frequency is -100
Cbc0010I After 0 nodes, 1 on tree, -72000 best solution, best possible -72029.13 (19.57 seconds)
Cbc0010I After 100 nodes, 45 on tree, -72000 best solution, best possible -72029.13 (21.76 seconds)
Cbc0010I After 200 nodes, 93 on tree, -72000 best solution, best possible -72029.13 (22.35 seconds)
Cbc0010I After 300 nodes, 146 on tree, -72000 best solution, best possible -72029.13 (22.91 seconds)
Cbc0010I After 400 nodes, 200 on tree, -72000 best solution, best possible -72029.13 (23.29 seconds)
Cbc0010I After 500 nodes, 249 on tree, -72000 best solution, best possible -72029.13 (23.73 seconds)
Cbc0010I After 600 nodes, 306 on tree, -72000 best solution, best possible -72029.13 (24.16 seconds)
Cbc0010I After 700 nodes, 356 on tree, -72000 best solution, best possible -72029.13 (24.55 seconds)
Cbc0010I After 800 nodes, 403 on tree, -72000 best solution, best possible -72029.13 (24.91 seconds)
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Cbc0010I After 256800 nodes, 12117 on tree, -72000 best solution, best possible -72029.13 (822.34 seconds)
C

1. 我們如何估計完成計算所需的時間？
2. 目前的進展是什么，我該如何解釋這一行 - 對於前

Cbc0010I After 800 nodes, 403 on tree, -72000 best solution, best possible -72029.13 (24.91 seconds)

3. 看來這個問題陷入了局部最優，有沒有辦法 f.netune /在某個間隙/間隔內找到最可行的解決方案？

如果您有任何問題，請告訴我？

Answer 1

1. 我們如何估計完成計算所需的時間？

我們不能。 只需使用不同的數據集運行您的模型。 這讓您了解解決方案的時間。

2. 目前的進展是什么，我如何解釋這一行 - 對於前`Cbc0010I 在 800 個節點之后，樹上有 403 個，-72000 最佳解決方案，最佳可能 -72029.13（24.91 秒）。

這意味着 CBC 忙了 25 秒。 節點計數（已處理節點和等待節點的數量）解釋起來有點技術性。 基本上，我們需要等到樹的大小開始縮小。 不幸的是，這種情況通常發生在搜索即將結束時。 當樹的大小變為零時，求解器就完成了。 找到的最佳解決方案是當前最佳解決方案。 最好的就是所說的：沒有比這更好的解決方案了。 這兩個數字應該越來越接近。 當間隙為零時，求解器完成。

3. 看來這個問題陷入了局部最優，有沒有辦法 f.netune /在某個間隙/間隔內找到最可行的解決方案？

術語局部最優更多地用於非線性規划。 但是，是的，有時這兩個界限（最好找到的和最好的）暫時不會移動。 更好的公式和更好的求解器可以提供幫助。 您的問題有 > 10k integer 個變量。 這已經不小了，可能需要在公式方面做一些工作和/或使用更強大的硬件（更多線程）的更好的求解器。

通常只報告 integer 個可行的解決方案。 如果您隨時對最佳非可行解感興趣，那么您需要使 model 具有彈性。 （總是讓它可行，但要付出很大的代價）。 請注意，CBC 在 19 秒后找到了一個可行的 integer 解決方案。 之后，如果您提前停止（例如在間隙或時間限制），它將始終返回最佳 integer 解決方案。