• Gurobi Staff

Hi Suyue,

There are multiple things to consider here.

You can see the warning

Warning for adding variables: zero or small (< 1e-13) coefficients, ignored

Gurobi sets very small coefficients to $$0$$. If these coefficients play a significant role for the solution of your model then you might want to re-scale and/or reformulate your model. For re-scaling, please have a look at our Guidelines for Numerical Issues and for improving model formulation please have a look at our Tech Talk about strong MIP formulations.

From the log, it is not clear whether it is the best objective that should be improved or the best bound. Do you have an idea about the optimal objective value for your model?

Could you construct a smaller version of the model? This would make it way easier for you to analyze what actually makes the model so hard (and possibly finding suiting parameters). I would guess that reducing the size of the model by a factor of 10 should already be good enough to make it "analyzable by hand".

Best regards,
Jaromił

It seems that the model has numerical issues, as the binary variables could oscilate during the branch-and-bound.Here is the possible problem syntax(written in MATLAB with yalmip):

Pw_q==Pw+zetaw_pos.*(repmat(Pw_max,1,T)-Pw)-zetaw_neg.*Pw;

This syntax aims to introduce a box uncertainty set of wind turbine power to indicate whether the output power touches the upper boundary or the lower boundary.I think the problem lies in the boundary set:when the upper boundary and lower boundary remain same(say both are 0), the binary variable(zetaw_pos and zetaw_neg) can either be 0 or 1.And that may lead to the slow descent of the gap.

And after I revised the boundary to avoid this problem,the efficient do promote a lot,as gurobi is able to get a solution in about 60s.But the solving process is somekind weird as the solution is concluedd when the gap is very big:

Removed 217 duplicated or redundant inequalitiesTransfered 2476 inequalities to equalitiesSet parameter UsernameSet parameter MIPGap to value 0.03Set parameter CrossoverBasis to value 0Set parameter MIPFocus to value 3Set parameter NodefileDir to value ""Set parameter NoRelHeurTime to value 5Set parameter PreSOS2BigM to value 0Set parameter TuneTrials to value 3Academic license - for non-commercial use only - expires 2023-12-04Warning for adding variables: zero or small (< 1e-13) coefficients, ignoredGurobi Optimizer version 9.5.0 build v9.5.0rc5 (win64)Thread count: 8 physical cores, 16 logical processors, using up to 16 threadsOptimize a model with 29167 rows, 14644 columns and 409035 nonzerosModel fingerprint: 0x51c1326dVariable types: 8817 continuous, 5827 integer (5827 binary)Coefficient statistics:  Matrix range     [1e-03, 1e+04]  Objective range  [1e+01, 1e+03]  Bounds range     [1e+00, 1e+00]  RHS range        [3e-14, 1e+04]Presolve removed 25656 rows and 10950 columnsPresolve time: 0.11sPresolved: 3511 rows, 3694 columns, 13776 nonzerosVariable types: 1889 continuous, 1805 integer (1803 binary)Found heuristic solution: objective -2581.451134Starting NoRel heuristicFound heuristic solution: objective -2581.452201Found heuristic solution: objective -2581.452342Elapsed time for NoRel heuristic: 6s (best bound -5.8162e+06)Root relaxation presolve removed 936 rows and 936 columnsRoot relaxation presolved: 2575 rows, 2758 columns, 11904 nonzerosRoot simplex log...Iteration    Objective       Primal Inf.    Dual Inf.      Time       0   -1.4283703e+07   1.533155e+04   0.000000e+00      6s    1292   -5.8162046e+06   0.000000e+00   0.000000e+00      6s    1300   -5.8162046e+06   0.000000e+00   0.000000e+00      6sExtra simplex iterations after uncrush: 8Root relaxation: objective -5.816205e+06, 1300 iterations, 0.03 seconds (0.06 work units)    Nodes    |    Current Node    |     Objective Bounds      |     Work Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time     0     0 -5816204.6    0  396 -2581.4523 -5816204.6      -     -    6s     0     0 -4667065.4    0  407 -2581.4523 -4667065.4      -     -    6s     0     0 -4667065.4    0  396 -2581.4523 -4667065.4      -     -    7s     0     0 -4644213.9    0  407 -2581.4523 -4644213.9      -     -    7s     0     0 -4435929.5    0  420 -2581.4523 -4435929.5      -     -    7s     0     0 -4434038.3    0  422 -2581.4523 -4434038.3      -     -    7s     0     0 -4433861.8    0  421 -2581.4523 -4433861.8      -     -    7s     0     0 -3869708.8    0  476 -2581.4523 -3869708.8      -     -    8s     0     0 -3834164.1    0  484 -2581.4523 -3834164.1      -     -    8s     0     0 -3584812.6    0  483 -2581.4523 -3584812.6      -     -    8s     0     0 -3584812.6    0  494 -2581.4523 -3584812.6      -     -    8s     0     0 -3584812.6    0  498 -2581.4523 -3584812.6      -     -    8s     0     0 -3565604.2    0  458 -2581.4523 -3565604.2      -     -   10s     0     0 -3426214.4    0  466 -2581.4523 -3426214.4      -     -   10s     0     0 -3426214.4    0  466 -2581.4523 -3426214.4      -     -   10s     0     0 -3388726.0    0  464 -2581.4523 -3388726.0      -     -   12s     0     0 -3387450.6    0  480 -2581.4523 -3387450.6      -     -   12s     0     0 -3387450.6    0  480 -2581.4523 -3387450.6      -     -   12s     0     0 -3387450.6    0  498 -2581.4523 -3387450.6      -     -   12s     0     0 -3291074.8    0  480 -2581.4523 -3291074.8      -     -   13s     0     0 -3280952.8    0  468 -2581.4523 -3280952.8      -     -   13s     0     0 -3280952.8    0  474 -2581.4523 -3280952.8      -     -   13s     0     0 -3224916.2    0  460 -2581.4523 -3224916.2      -     -   15s     0     0 -3219546.1    0  476 -2581.4523 -3219546.1      -     -   15s     0     0 -3219546.1    0  480 -2581.4523 -3219546.1      -     -   15s     0     0 -3189232.9    0  482 -2581.4523 -3189232.9      -     -   17s     0     0 -3142551.3    0  500 -2581.4523 -3142551.3      -     -   17s     0     0 -3116673.0    0  498 -2581.4523 -3116673.0      -     -   17s     0     0 -3116673.0    0  504 -2581.4523 -3116673.0      -     -   17s     0     0 -3116673.0    0  512 -2581.4523 -3116673.0      -     -   17s     0     0 -3104159.6    0  513 -2581.4523 -3104159.6      -     -   18s     0     0 -2972930.7    0  442 -2581.4523 -2972930.7      -     -   19s     0     2 -2972930.7    0  437 -2581.4523 -2972930.7      -     -   19s     3     8 -2671571.3    2  429 -2581.4523 -2879395.7      -   290   20sH  211   125                    -2581.543570 -2167624.8      -   248   24s   310   181 -2121977.3   12  354 -2581.5436 -2131973.4      -   221   25s  1145   859 infeasible   19      -2581.5436 -1974983.3      -   173   30s  1467  1051 -1697276.1   18  313 -2581.5436 -1702983.2      -   165   36s  1476  1057 -1322251.6   13  322 -2581.5436 -1322251.6      -   164   41s  1484  1062 -1191543.2   12  328 -2581.5436 -1191543.2      -   163   45s  1503  1076 -1083075.8    8  323 -2581.5436 -1083075.8      -   169   50s  1517  1085 -723153.77   18  337 -2581.5436 -723153.77      -   168   55s  1530  1094 -88330.910   21  279 -2581.5436 -88330.910  3322%   166   60s  1538  1097 -28053.295   29  218 -2581.5436 -28053.295   987%   175   65sCutting planes:  Learned: 1  Gomory: 13  Lift-and-project: 89  Cover: 131  Implied bound: 32  Clique: 26  MIR: 123  StrongCG: 4  Flow cover: 250  GUB cover: 17  Inf proof: 3  Zero half: 12  Network: 1  RLT: 4  Relax-and-lift: 14  BQP: 2Explored 1707 nodes (290334 simplex iterations) in 66.55 seconds (67.93 work units)Thread count was 16 (of 16 available processors)Solution count 10: -2581.54 -2581.54 -2581.45 ... -2581.45No other solutions better than -2581.54Optimal solution found (tolerance 3.00e-02)Best objective -2.581543575333e+03, best bound -2.581543575333e+03, gap 0.0000%

I'm wondering if there is still some numeric issues since the gap suddenly steps from 987% to 0.And by the way, the size of the model can't be reduced anymore since I have to construct the kkt condition of the model,which means I need to introduce a lot binaries to slack the complementary condition.

• Gurobi Staff

I'm wondering if there is still some numeric issues since the gap suddenly steps from 987% to 0.

While quite rare, it is not unusual behavior, especially for more complex models. It is possible that a heuristic or a B&B dive finds some information which allows to prune a big chunk of the tree resulting in big MIPGap jumps.

You can see that the No Relaxation Heuristic found a very good solution very quickly. This can lead to impactful presolve reductions which ultimately lead to quicker convergence.

You should definitely check whether the solution computed by Gurobi satisfies the needs of your application.

The RHS range of your constraints is questionable

RHS range        [3e-14, 1e+04]

It would be best to clean it up manually before optimizing and set very small coefficients to $$0$$ or re-scale the model as suggested in my previous comment.

The same applies regarding the Warning

Warning for adding variables: zero or small (< 1e-13) coefficients, ignored

And at least, you have the option to update to v10 to profit from performance improvements and bug fixes.

Thank you, Jaromil

I will try to clean up very small coefficients and pay attention to the numeric issues.Thank you for your kindly comment again!

Hi Jaromil

Unfortunately the MILP model can find a solution in less than 10 min,but i'm still not satisfied with the efficiency.After I revised problems you mentioned above, it seems that the heuristics model find the solution from the beginning but it struggles to find the best bound.Here is the log:

Set parameter UsernameSet parameter MIPGap to value 0.01Set parameter CrossoverBasis to value 0Set parameter MIPFocus to value 3Set parameter NodefileDir to value ""Set parameter NoRelHeurTime to value 20Set parameter Cuts to value 3Set parameter PreSOS2BigM to value 0Set parameter TuneTrials to value 3Academic license - for non-commercial use only - expires 2024-06-06Gurobi Optimizer version 10.0.1 build v10.0.1rc0 (win64)CPU model: 11th Gen Intel(R) Core(TM) i7-11800H @ 2.30GHz, instruction set [SSE2|AVX|AVX2|AVX512]Thread count: 8 physical cores, 16 logical processors, using up to 16 threadsOptimize a model with 33808 rows, 14585 columns and 315796 nonzerosModel fingerprint: 0x73e9d9e9Variable types: 8130 continuous, 6455 integer (6455 binary)Coefficient statistics:  Matrix range     [3e-04, 1e+04]  Objective range  [3e-01, 2e+02]  Bounds range     [1e+00, 1e+00]  RHS range        [1e-03, 1e+04]Presolve removed 29486 rows and 10511 columnsPresolve time: 0.41sPresolved: 4322 rows, 4074 columns, 14508 nonzerosVariable types: 2510 continuous, 1564 integer (1564 binary)Starting NoRel heuristicFound phase-1 solution: relaxation 34839.7Found phase-1 solution: relaxation 34825.8Found phase-1 solution: relaxation 34536.8Found phase-1 solution: relaxation 34473.5Found phase-1 solution: relaxation 7818.41Found phase-1 solution: relaxation 7461.44Found phase-1 solution: relaxation 6905.05Found phase-1 solution: relaxation 6068.39Found phase-1 solution: relaxation 5208.38Found phase-1 solution: relaxation 2641.62Found phase-1 solution: relaxation 2615.4Found phase-1 solution: relaxation 2246.63Found phase-1 solution: relaxation 1988.52Found phase-1 solution: relaxation 1772.27Found phase-1 solution: relaxation 1718.13Found phase-1 solution: relaxation 1564.16Found phase-1 solution: relaxation 1451.22Found phase-1 solution: relaxation 1451.21Found phase-1 solution: relaxation 1450.87Found phase-1 solution: relaxation 1449.03Found phase-1 solution: relaxation 1449.01Found phase-1 solution: relaxation 1355.37Found phase-1 solution: relaxation 1292.59Found phase-1 solution: relaxation 1255.96Found phase-1 solution: relaxation 1252.97Found phase-1 solution: relaxation 1219.44Found phase-1 solution: relaxation 1057.55Found phase-1 solution: relaxation 954.437Found phase-1 solution: relaxation 937.607Found phase-1 solution: relaxation 880.965Found phase-1 solution: relaxation 814.701Found phase-1 solution: relaxation 807.84Found phase-1 solution: relaxation 799.182Found phase-1 solution: relaxation 765.258Found phase-1 solution: relaxation 704.463Found phase-1 solution: relaxation 680.014Found phase-1 solution: relaxation 676.414Found phase-1 solution: relaxation 645.723Found phase-1 solution: relaxation 645.72Found phase-1 solution: relaxation 642.346Found phase-1 solution: relaxation 629.765Found phase-1 solution: relaxation 616.697Found phase-1 solution: relaxation 604.417Found phase-1 solution: relaxation 600.956Found phase-1 solution: relaxation 578.192Found phase-1 solution: relaxation 574.722Found phase-1 solution: relaxation 574.717Found phase-1 solution: relaxation 502.014Found phase-1 solution: relaxation 501.626Found phase-1 solution: relaxation 493.187Found phase-1 solution: relaxation 493.184Found phase-1 solution: relaxation 473.362Found phase-1 solution: relaxation 473.076Found phase-1 solution: relaxation 473.075Found phase-1 solution: relaxation 472.934Found phase-1 solution: relaxation 472.647Found phase-1 solution: relaxation 462.699Found phase-1 solution: relaxation 462.695Found phase-1 solution: relaxation 439.008Found phase-1 solution: relaxation 436.682Found phase-1 solution: relaxation 320.432Found phase-1 solution: relaxation 318.201Found phase-1 solution: relaxation 313.778Found phase-1 solution: relaxation 313.19Found phase-1 solution: relaxation 313.073Found phase-1 solution: relaxation 312.901Found phase-1 solution: relaxation 311.792Found phase-1 solution: relaxation 308.126Found phase-1 solution: relaxation 285.554Found phase-1 solution: relaxation 279.175Found phase-1 solution: relaxation 278.367Found phase-1 solution: relaxation 271.357Found phase-1 solution: relaxation 229.721Found phase-1 solution: relaxation 131.886Found phase-1 solution: relaxation 108.55Found phase-1 solution: relaxation 108.537Found phase-1 solution: relaxation 108.221Found phase-1 solution: relaxation 108.22Found phase-1 solution: relaxation 108.207Found phase-1 solution: relaxation 108.207Found phase-1 solution: relaxation 107.663Found phase-1 solution: relaxation 86.6035Found phase-1 solution: relaxation 86.2127Found phase-1 solution: relaxation 83.6826Found phase-1 solution: relaxation 81.1013Found phase-1 solution: relaxation 77.1161Found phase-1 solution: relaxation 72.7764Found phase-1 solution: relaxation 68.3536Found phase-1 solution: relaxation 67.9194Found phase-1 solution: relaxation 64.1304Found phase-1 solution: relaxation 58.6391Found phase-1 solution: relaxation 58.1782Found phase-1 solution: relaxation 51.0738Found phase-1 solution: relaxation 50.327Found phase-1 solution: relaxation 47.7701Found phase-1 solution: relaxation 47.7316Found phase-1 solution: relaxation 47.4314Found phase-1 solution: relaxation 46.3485Found phase-1 solution: relaxation 45.761Found phase-1 solution: relaxation 42.9752Found phase-1 solution: relaxation 42.867Found phase-1 solution: relaxation 42.705Found phase-1 solution: relaxation 42.6603Found phase-1 solution: relaxation 42.4227Found phase-1 solution: relaxation 42.3405Found phase-1 solution: relaxation 36.7601Found phase-1 solution: relaxation 34.053Found phase-1 solution: relaxation 0Found heuristic solution: objective -2071.378493Transition to phase 2Found heuristic solution: objective -4318.593812Found heuristic solution: objective -6168.785979Found heuristic solution: objective -6248.871868Found heuristic solution: objective -6963.104062Found heuristic solution: objective -7138.650896Found heuristic solution: objective -8039.967780Found heuristic solution: objective -10902.59250Found heuristic solution: objective -12139.52933Found heuristic solution: objective -12219.61522Found heuristic solution: objective -15226.24593Found heuristic solution: objective -15241.18757Found heuristic solution: objective -16367.48261Found heuristic solution: objective -19389.05496Found heuristic solution: objective -21158.74883Found heuristic solution: objective -21353.13808Found heuristic solution: objective -22494.49922Found heuristic solution: objective -22814.05203Elapsed time for NoRel heuristic: 5s (best bound -85144.4)Found heuristic solution: objective -23036.66308Found heuristic solution: objective -23375.82982Found heuristic solution: objective -23375.82983Found heuristic solution: objective -23375.82985Elapsed time for NoRel heuristic: 10s (best bound -85144.4)Found heuristic solution: objective -23375.82986Elapsed time for NoRel heuristic: 15s (best bound -85144.4)Found heuristic solution: objective -23375.82986Elapsed time for NoRel heuristic: 22s (best bound -85144.4)Root relaxation presolve removed 1509 rows and 1509 columnsRoot relaxation presolved: 2813 rows, 2565 columns, 11488 nonzerosRoot simplex log...Iteration    Objective       Primal Inf.    Dual Inf.      Time       0   -7.4861268e+05   4.108696e+06   0.000000e+00     22s    1641   -8.5144387e+04   0.000000e+00   0.000000e+00     22s    1673   -8.5144387e+04   0.000000e+00   0.000000e+00     22sExtra simplex iterations after uncrush: 32Root relaxation: objective -8.514439e+04, 1673 iterations, 0.06 seconds (0.05 work units)    Nodes    |    Current Node    |     Objective Bounds      |     Work Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time     0     0 -85144.387    0  590 -23375.830 -85144.387   264%     -   23s     0     0 -54204.462    0  785 -23375.830 -54204.462   132%     -   25s     0     0 -54204.462    0  781 -23375.830 -54204.462   132%     -   25s     0     0 -51715.194    0  753 -23375.830 -51715.194   121%     -   25s     0     0 -51715.194    0  753 -23375.830 -51715.194   121%     -   25s     0     0 -51713.960    0  738 -23375.830 -51713.960   121%     -   25s     0     0 -51713.960    0  763 -23375.830 -51713.960   121%     -   25s     0     0 -51571.622    0  737 -23375.830 -51571.622   121%     -   25s     0     0 -51571.622    0  762 -23375.830 -51571.622   121%     -   25s     0     0 -51571.622    0  765 -23375.830 -51571.622   121%     -   25s     0     0 -49984.710    0  794 -23375.830 -49984.710   114%     -   27s     0     0 -48896.257    0  802 -23375.830 -48896.257   109%     -   28s     0     0 -48525.927    0  718 -23375.830 -48525.927   108%     -   30s     0     0 -48525.927    0  721 -23375.830 -48525.927   108%     -   30s     0     0 -46779.528    0  674 -23375.830 -46779.528   100%     -   30s     0     0 -46779.409    0  671 -23375.830 -46779.409   100%     -   30s     0     0 -46612.486    0  693 -23375.830 -46612.486  99.4%     -   30s     0     0 -46576.799    0  710 -23375.830 -46576.799  99.3%     -   30s     0     0 -45061.350    0  673 -23375.830 -45061.350  92.8%     -   33s     0     0 -45051.543    0  691 -23375.830 -45051.543  92.7%     -   33s     0     0 -44832.460    0  677 -23375.830 -44832.460  91.8%     -   35s     0     0 -44832.460    0  677 -23375.830 -44832.460  91.8%     -   37s     0     0 -44832.460    0  464 -23375.830 -44832.460  91.8%     -   38s     0     0 -44832.460    0  568 -23375.830 -44832.460  91.8%     -   39sH    0     0                    -23375.82990 -44832.460  91.8%     -   39s     0     0 -44832.460    0  547 -23375.830 -44832.460  91.8%     -   39s     0     0 -44832.460    0  481 -23375.830 -44832.460  91.8%     -   39s     0     0 -44832.460    0  454 -23375.830 -44832.460  91.8%     -   39s     0     0 -44832.460    0  417 -23375.830 -44832.460  91.8%     -   39s     0     0 -44832.460    0  422 -23375.830 -44832.460  91.8%     -   39s     0     0 -44832.460    0  422 -23375.830 -44832.460  91.8%     -   39s     0     0 -44475.327    0  486 -23375.830 -44475.327  90.3%     -   41s     0     0 -43343.206    0  490 -23375.830 -43343.206  85.4%     -   41s     0     0 -43343.206    0  472 -23375.830 -43343.206  85.4%     -   41s     0     0 -42622.193    0  495 -23375.830 -42622.193  82.3%     -   43s     0     0 -42113.386    0  513 -23375.830 -42113.386  80.2%     -   43s     0     0 -42113.386    0  603 -23375.830 -42113.386  80.2%     -   43s     0     0 -42062.210    0  604 -23375.830 -42062.210  79.9%     -   43s     0     0 -41097.172    0  600 -23375.830 -41097.172  75.8%     -   44s     0     0 -41097.172    0  600 -23375.830 -41097.172  75.8%     -   44s     0     0 -40946.632    0  587 -23375.830 -40946.632  75.2%     -   44s     0     0 -40660.983    0  590 -23375.830 -40660.983  73.9%     -   45s     0     0 -40660.983    0  593 -23375.830 -40660.983  73.9%     -   45s     0     0 -40579.997    0  619 -23375.830 -40579.997  73.6%     -   45s     0     0 -40579.997    0  628 -23375.830 -40579.997  73.6%     -   45sH    0     0                    -23375.82994 -40560.103  73.5%     -   46s     0     0 -40058.088    0  595 -23375.830 -40058.088  71.4%     -   46s     0     0 -39940.870    0  607 -23375.830 -39940.870  70.9%     -   46s     0     0 -39836.725    0  617 -23375.830 -39836.725  70.4%     -   46s     0     0 -39667.372    0  596 -23375.830 -39667.372  69.7%     -   47s     0     0 -39604.819    0  602 -23375.830 -39604.819  69.4%     -   47s     0     0 -39351.534    0  579 -23375.830 -39351.534  68.3%     -   48s     0     0 -39189.161    0  619 -23375.830 -39189.161  67.6%     -   48s     0     0 -39014.825    0  640 -23375.830 -39014.825  66.9%     -   48s     0     0 -39014.825    0  640 -23375.830 -39014.825  66.9%     -   48s     0     0 -38944.425    0  631 -23375.830 -38944.425  66.6%     -   49s     0     0 -38887.376    0  630 -23375.830 -38887.376  66.4%     -   50s     0     2 -38887.376    0  630 -23375.830 -38887.376  66.4%     -   51s    57    49 infeasible    9      -23375.830 -38285.425  63.8%  1216   55s   207   166 -37151.344   14  462 -23375.830 -37151.344  58.9%   827   60s   366   329 -35780.082   18  324 -23375.830 -36641.835  56.8%   658   65s   908   774 -35073.179   13  496 -23375.830 -36205.118  54.9%   468   70sH  920   774                    -23375.82999 -36193.893  54.8%   468   70s  1359  1182 -35345.520   16  364 -23375.830 -35781.545  53.1%   454   75s  1480  1185 -35620.140   20  443 -23375.830 -35732.148  52.9%   440   81s  1492  1193 -33575.356   18  558 -23375.830 -35732.148  52.9%   437   89s  1498  1197 -33230.431   22  565 -23375.830 -35732.148  52.9%   435   91s  1499  1198 -30087.971   13  528 -23375.830 -35732.148  52.9%   435   95s  1504  1201 -33219.850   22  538 -23375.830 -35732.148  52.9%   433  102s  1510  1205 -32609.905   27  577 -23375.830 -34912.325  49.4%   432  105s  1517  1210 -34346.471   14  554 -23375.830 -34346.471  46.9%   430  110s  1521  1212 -33896.066   17  529 -23375.830 -33896.066  45.0%   429  115s  1524  1214 -33759.697   17  576 -23375.830 -33759.697  44.4%   428  121s  1530  1218 -33174.026   18  527 -23375.830 -33174.026  41.9%   426  127s  1534  1221 -28235.239   16  545 -23375.830 -32660.098  39.7%   425  133s  1538  1224 -32471.002   23  545 -23375.830 -32471.002  38.9%   424  135s  1543  1227 -31821.621   15  567 -23375.830 -31821.621  36.1%   422  142s  1547  1230 -31660.990   19  530 -23375.830 -31660.990  35.4%   421  147s  1552  1233 -31369.953   14  523 -23375.830 -31369.953  34.2%   420  150s  1557  1236 -31285.659   16  515 -23375.830 -31285.659  33.8%   419  155s  1565  1242 -30641.469   20  555 -23375.830 -30776.959  31.7%   417  161s  1566  1242 -30734.749   26  546 -23375.830 -30734.749  31.5%   416  165s  1576  1249 -30562.352   16  547 -23375.830 -30562.352  30.7%   414  170s  1580  1252 -30365.167   20  534 -23375.830 -30365.167  29.9%   413  176s  1587  1256 -30173.546   22  572 -23375.830 -30173.546  29.1%   411  180s  1593  1260 -30128.904   20  564 -23375.830 -30128.904  28.9%   409  185s  1601  1266 -30037.731   21  502 -23375.830 -30037.731  28.5%   407  191s  1610  1272 -29814.656   27  519 -23375.830 -29814.656  27.5%   405  195s  1615  1275 -29633.881   14  518 -23375.830 -29633.881  26.8%   404  200s  1621  1280 -29633.881   17  379 -23375.830 -29633.881  26.8%   464  205s  1632  1287 -29633.881   21  486 -23375.830 -29633.881  26.8%   461  210s  1638  1291 -29633.881   23  503 -23375.830 -29633.881  26.8%   459  216s  1640  1293 -29633.881   17  515 -23375.830 -29633.881  26.8%   458  221s  1645  1296 -29633.881   21  499 -23375.830 -29633.881  26.8%   457  228s  1648  1298 -29633.881   17  522 -23375.830 -29633.881  26.8%   456  231s  1650  1299 -29633.881   21  504 -23375.830 -29633.881  26.8%   456  235s  1654  1302 -29633.881   22  518 -23375.830 -29633.881  26.8%   454  240s  1661  1307 -29633.881   20  510 -23375.830 -29633.881  26.8%   453  246s  1663  1308 -29633.881   22  493 -23375.830 -29633.881  26.8%   452  263s  1667  1312 -29633.881   18  392 -23375.830 -29633.881  26.8%   472  265s  1678  1320 -29633.881   16  489 -23375.830 -29633.881  26.8%   469  271s  1680  1321 -29633.881   20  493 -23375.830 -29633.881  26.8%   468  275s  1683  1323 -29633.881   14  490 -23375.830 -29633.881  26.8%   468  302s  1687  1327 -29633.881   41  390 -23375.830 -29633.881  26.8%   479  305s  1749  1340 -29633.881   47  391 -23375.830 -29633.881  26.8%   506  310s  1813  1364 -29633.881   51  351 -23375.830 -29633.881  26.8%   533  315s  1878  1389 -29199.202   53  316 -23375.830 -29633.881  26.8%   568  320s  1929  1411 -29011.725   54  351 -23375.830 -29225.418  25.0%   589  325s  2023  1462 -26982.495   53  302 -23375.830 -28469.300  21.8%   619  330s  2157  1499 -24067.149   56  283 -23375.830 -27846.488  19.1%   640  336s  2273  1504 -25726.303   55  310 -23375.830 -27432.426  17.4%   669  341sH 2308  1429                    -23375.83000 -27298.528  16.8%   680  344s  2319  1435 -25933.386   57  294 -23375.830 -27270.183  16.7%   686  346s  2483  1389 -26170.034   56  275 -23375.830 -26773.903  14.5%   710  351s  2694  1326     cutoff   55      -23375.830 -26164.120  11.9%   730  356s  2871  1254 -24862.156   61  237 -23375.830 -25764.787  10.2%   732  360s  3172  1102 infeasible   62      -23375.830 -25025.324  7.06%   729  367s  3311  1017     cutoff   60      -23375.830 -24614.620  5.30%   726  371s  3672   833     cutoff   65      -23375.830 -23989.853  2.63%   699  375sCutting planes:  Learned: 1  Gomory: 4  Lift-and-project: 115  Cover: 506  Implied bound: 508  Projected implied bound: 10  Clique: 1679  MIR: 876  StrongCG: 8  Flow cover: 2199  Zero half: 87  Network: 6  RLT: 489  Relax-and-lift: 402  BQP: 74  PSD: 14Explored 3983 nodes (2705378 simplex iterations) in 377.83 seconds (467.16 work units)Thread count was 16 (of 16 available processors)Solution count 10: -23375.8 -23375.8 -23375.8 ... -23036.7Optimal solution found (tolerance 1.00e-02)Best objective -2.337583000142e+04, best bound -2.355547955495e+04, gap 0.7685%

Before the reformulation of the model,is there any possible way to improve the best bound?What' more,the log ends with arrays of 'infeasible' and 'cutoff',is this message indicate why the model moves very slow?

• Gurobi Staff

Before the reformulation of the model,is there any possible way to improve the best bound?

You could try combinations of the following parameters:

Is there a particular reason why you set PreSOS2BigM?

What' more, the log ends with arrays of 'infeasible' and 'cutoff', is this message indicate why the model moves very slow?

These are actually good messages. This means that the current node has been cutoff or that it is infeasible. This leads to a smaller tree which is good.

If nothing of this helps, I think that the last resort would be a stronger formulation. Maybe our Tech Talk on converting weak to strong MIP formulation is helpful.