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Barrier Method and Crossover in Large-Scale LP Solving

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4 comments

  • Jaromił Najman
    Gurobi Staff Gurobi Staff

    Hi Zhongfan Gu,

    From my understanding, both approaches should theoretically yield the same optimal solution, but this does not seem to be the case here. Could someone please explain why this discrepancy might occur and suggest any strategies to ensure feasibility without the crossover step?

    Theoretically, yes, practically, no. The Barrier algorithm is quite prone to numerical challenges. The difference you see most likely comes from the fact that presolve performs slightly different if no crossover is requested (the presolve statistics are different). When crossover is turned on, Gurobi performs a few more presolve reductions by default, which in your case seem to help the Barrier algorithm.

    You could try setting Presolve=2 and/or BarHomogeneous=1 for your Crossover=0 run. Presolve=2 tells Gurobi to perform more presolve reductions on the model. BarHomogeneous is a more careful version of the standard Barrier algorithm, which should avoid the numerical trouble. The homogeneous Barrier algorithm checks for infeasibility and unboundedness at every iteration of the Barrier algorithm.

    In general, if there is no good reason for turning off Crossover, it is recommended to use it. The Crossover phase can clean up small constraint violations in the Barrier solution and can give a "cleaner" solution. "Cleaner" here means that more variables are at their bounds compared to a Barrier solution.

    Best regards, 
    Jaromił

    0
  • Zhongfan Gu
    First Comment
    First Question

    Hello Jaromił,

    Thank you very much for your insights in your previous response. Following your advice, I attempted to set Presolve to 2 and BarHomogeneous to 1 in order to improve the solve process. Unfortunately, these settings did not resolve the issue. Below is the solver log from my latest attempt:

    Solver Log with Presolve=2 and BarHomogeneous=1:

    Set parameter Username
    Set parameter Method to value 2
    Set parameter BarHomogeneous to value 1
    Set parameter Crossover to value 0
    Set parameter NodefileDir to value ""
    Set parameter Presolve to value 2
    Set parameter TuneTimeLimit to value 1e+100
    Academic license - for non-commercial use only - expires 2024-11-02
    Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (win64)

    CPU model: 13th Gen Intel(R) Core(TM) i7-13700K, instruction set [SSE2|AVX|AVX2]
    Thread count: 16 physical cores, 24 logical processors, using up to 24 threads

    Optimize a model with 4702180 rows, 2210651 columns and 19350520 nonzeros
    Model fingerprint: 0x34eacf5d
    Coefficient statistics:
      Matrix range     [2e-05, 1e+01]
      Objective range  [2e-03, 2e+02]
      Bounds range     [0e+00, 0e+00]
      RHS range        [2e-02, 8e+04]
    Presolve removed 1022585 rows and 3101192 columns (presolve time = 5s) ...
    Presolve removed 1022585 rows and 3117081 columns
    Presolve time: 8.21s
    Presolved: 1188066 rows, 1585099 columns, 11208382 nonzeros
    Elapsed ordering time = 6s
    Elapsed ordering time = 27s
    Elapsed ordering time = 30s
    Elapsed ordering time = 35s
    Elapsed ordering time = 40s
    Elapsed ordering time = 45s
    Ordering time: 46.57s

    Barrier statistics:
     Dense cols : 53
     Free vars  : 185912
     AA' NZ     : 2.455e+07
     Factor NZ  : 1.298e+09 (roughly 12.0 GB of memory)
     Factor Ops : 5.358e+12 (roughly 10 seconds per iteration)
     Threads    : 16

                      Objective                Residual
    Iter       Primal          Dual         Primal    Dual     Compl     Time
       0   1.60479324e+11  7.57738388e+11  7.72e+06 1.07e+05  1.91e+08    73s
       1   1.21109862e+11  6.73035539e+11  6.61e+06 8.97e+04  1.62e+08    93s
       2   9.85913920e+10  6.11755544e+11  5.98e+06 7.33e+04  1.41e+08   107s
       3   6.00163845e+10  5.98520307e+11  4.89e+06 6.80e+04  1.21e+08   121s
       4   1.75191160e+10  3.52742091e+11  2.36e+06 4.11e+04  4.26e+07   137s
       5   3.41558696e+09  2.41070656e+11  1.54e+06 2.89e+04  2.36e+07   153s
       6  -4.61302970e+09  1.67298976e+11  1.08e+06 2.08e+04  1.46e+07   170s
       7  -9.20544135e+09  1.20751423e+11  8.04e+05 1.57e+04  1.00e+07   186s
       8  -1.19472908e+10  8.84384931e+10  6.29e+05 1.21e+04  7.37e+06   202s
       9  -1.36316037e+10  6.58322035e+10  5.09e+05 9.62e+03  5.70e+06   218s
      10  -1.48106222e+10  4.38253715e+10  4.17e+05 7.16e+03  4.32e+06   233s
      11  -1.52718259e+10  2.50266824e+10  2.81e+05 4.92e+03  2.80e+06   249s
      12  -1.47334706e+10  1.67201630e+10  2.50e+05 3.83e+03  2.26e+06   264s
      13  -1.33710472e+10  1.12803835e+10  2.02e+05 2.97e+03  1.70e+06   280s
      14  -1.14487986e+10  5.39878203e+09  1.53e+05 2.00e+03  1.13e+06   296s
      15  -9.61016574e+09  2.85600599e+09  1.23e+05 1.39e+03  7.80e+05   311s
      16  -7.16583140e+09  1.48600301e+09  8.48e+04 9.23e+02  4.71e+05   327s
      17  -5.29706871e+09  6.33326160e+08  5.93e+04 5.98e+02  2.86e+05   343s
      18  -4.34620399e+09  3.16007484e+08  4.75e+04 4.29e+02  2.01e+05   359s
      19  -3.25798216e+09  1.39257273e+08  3.48e+04 3.03e+02  1.32e+05   374s
      20  -2.30719920e+09  3.63081417e+07  2.38e+04 1.99e+02  7.97e+04   390s
      21  -9.82494673e+08 -9.82959191e+06  1.05e+04 8.36e+01  2.64e+04   406s
      22  -3.43912244e+08 -1.71192615e+07  3.13e+03 5.60e+01  8.39e+03   421s
      23  -1.53412626e+08 -1.66452817e+07  1.25e+03 1.17e+01  1.29e+03   437s
      24  -2.84053721e+07 -4.52684484e+06  2.45e+02 3.65e+00  1.49e+02   452s
      25  -8.75182272e+06 -1.93250344e+06  8.31e+01 1.88e+00  4.12e+01   469s
      26  -8.18685360e+06 -1.81224925e+06  7.83e+01 1.80e+00  3.84e+01   484s
      27  -5.40620236e+06 -9.76699295e+05  5.37e+01 1.19e+00  2.20e+01   503s
      28  -5.39494862e+06 -9.71119685e+05  5.36e+01 1.19e+00  2.19e+01   519s
      29  -4.80174437e+06 -8.02124470e+05  4.86e+01 1.09e+00  1.93e+01   535s
      30  -4.16117444e+06 -7.79402961e+05  4.36e+01 1.02e+00  1.65e+01   552s
      31  -4.15887303e+06 -7.78548837e+05  4.36e+01 1.02e+00  1.65e+01   569s
      32  -4.10914424e+06 -7.67597388e+05  4.31e+01 1.01e+00  1.63e+01   585s
      33  -4.10921280e+06 -7.80214595e+05  4.31e+01 1.01e+00  1.62e+01   602s
      34  -4.06349326e+06 -7.57262002e+05  4.25e+01 9.69e-01  1.56e+01   619s
      35  -4.03270130e+06 -7.17528269e+05  4.22e+01 9.41e-01  1.53e+01   636s
      36  -4.02500966e+06 -7.15853257e+05  4.21e+01 9.40e-01  1.52e+01   653s
      37  -3.98868806e+06 -7.13562049e+05  4.17e+01 9.36e-01  1.51e+01   669s
      38  -3.96695903e+06 -6.90377090e+05  4.16e+01 9.27e-01  1.50e+01   685s
      39  -3.96701175e+06 -6.90439169e+05  4.16e+01 9.27e-01  1.50e+01   702s
      40  -3.95809051e+06 -6.87089945e+05  4.15e+01 9.24e-01  1.49e+01   718s
      41  -3.92056759e+06 -6.80601808e+05  4.11e+01 9.19e-01  1.48e+01   735s
      42  -3.59511269e+06 -6.10259913e+05  3.85e+01 8.83e-01  1.37e+01   751s
      43  -3.56336018e+06 -5.79478465e+05  3.82e+01 8.65e-01  1.34e+01   767s
      44  -3.38574110e+06 -5.37438280e+05  3.65e+01 8.30e-01  1.27e+01   785s
      45  -3.14945437e+06 -5.14342101e+05  3.47e+01 8.21e-01  1.21e+01   802s
      46  -3.12510512e+06 -5.12717844e+05  3.45e+01 8.18e-01  1.20e+01   818s
      47  -3.11779672e+06 -5.12325358e+05  3.44e+01 8.18e-01  1.20e+01   835s
      48  -3.11771320e+06 -5.15607238e+05  3.44e+01 8.18e-01  1.20e+01   851s
      49  -3.11724946e+06 -5.15736737e+05  3.44e+01 8.18e-01  1.20e+01   867s
      50  -2.95164538e+06 -5.08777015e+05  3.30e+01 8.14e-01  1.16e+01   883s
      51  -2.95042652e+06 -5.11441072e+05  3.30e+01 8.13e-01  1.15e+01   900s
      52  -2.94344853e+06 -5.07088636e+05  3.29e+01 8.09e-01  1.15e+01   916s
      53  -2.94283875e+06 -5.07043143e+05  3.29e+01 8.09e-01  1.15e+01   932s
      54  -2.69681566e+06 -4.74089018e+05  3.06e+01 7.83e-01  1.07e+01   948s
      55  -2.69677371e+06 -4.77322909e+05  3.06e+01 7.83e-01  1.07e+01   964s
      56  -2.69489436e+06 -4.77037944e+05  3.05e+01 7.83e-01  1.07e+01   980s
      57  -2.69487857e+06 -4.77233905e+05  3.05e+01 7.83e-01  1.07e+01   997s
      58  -2.65265231e+06 -4.62995752e+05  3.02e+01 7.76e-01  1.05e+01  1014s
      59  -2.63543433e+06 -4.60964416e+05  3.00e+01 7.72e-01  1.05e+01  1030s
      60  -2.63518532e+06 -4.60851863e+05  3.00e+01 7.72e-01  1.05e+01  1047s
      61  -2.61846361e+06 -4.51169956e+05  2.99e+01 7.65e-01  1.04e+01  1063s
      62  -2.61755578e+06 -4.49731201e+05  2.99e+01 7.65e-01  1.04e+01  1080s
      63  -2.61766325e+06 -4.49864132e+05  2.99e+01 7.65e-01  1.04e+01  1097s
      64  -2.61765269e+06 -4.49864100e+05  2.99e+01 7.65e-01  1.04e+01  1113s
      65  -2.61729669e+06 -4.49742897e+05  2.99e+01 7.64e-01  1.04e+01  1130s
      66  -2.61698651e+06 -4.49547872e+05  2.98e+01 7.64e-01  1.03e+01  1146s
      67  -2.61186068e+06 -4.47552723e+05  2.98e+01 7.63e-01  1.03e+01  1162s
      68  -2.61153466e+06 -4.47390110e+05  2.98e+01 7.63e-01  1.03e+01  1179s
      69  -2.61150254e+06 -4.47374768e+05  2.98e+01 7.63e-01  1.03e+01  1195s
      70  -2.61035489e+06 -4.46276398e+05  2.98e+01 7.62e-01  1.03e+01  1211s
      71  -2.60997570e+06 -4.46233704e+05  2.98e+01 7.62e-01  1.03e+01  1227s
      72  -2.60971095e+06 -4.46541649e+05  2.98e+01 7.62e-01  1.03e+01  1244s
      73  -2.55590200e+06 -4.30380743e+05  2.93e+01 7.51e-01  1.01e+01  1261s
      74  -2.54858034e+06 -4.28133320e+05  2.92e+01 7.49e-01  1.01e+01  1277s
      75  -2.54856964e+06 -4.28116394e+05  2.92e+01 7.49e-01  1.01e+01  1294s
      76  -2.49577564e+06 -4.21757482e+05  2.87e+01 7.44e-01  9.90e+00  1310s
      77  -2.49429894e+06 -4.22157375e+05  2.87e+01 7.44e-01  9.89e+00  1326s
      78  -2.49420023e+06 -4.22117884e+05  2.87e+01 7.44e-01  9.89e+00  1342s
      79  -2.46348056e+06 -4.20766591e+05  2.84e+01 7.43e-01  9.82e+00  1359s
      80  -2.44563763e+06 -4.20462693e+05  2.82e+01 7.42e-01  9.77e+00  1375s
      81  -2.40338790e+06 -4.09556693e+05  2.78e+01 7.30e-01  9.57e+00  1391s
      82  -2.40337958e+06 -4.09537887e+05  2.78e+01 7.30e-01  9.57e+00  1408s
      83  -2.40327229e+06 -4.09507703e+05  2.78e+01 7.30e-01  9.57e+00  1424s
      84  -2.37564141e+06 -3.98120519e+05  2.75e+01 7.21e-01  9.42e+00  1441s
      85  -2.32336000e+06 -3.79622950e+05  2.71e+01 7.09e-01  9.20e+00  1457s
      86  -2.32327542e+06 -3.79596001e+05  2.71e+01 7.09e-01  9.20e+00  1473s
      87  -2.31977989e+06 -3.78777766e+05  2.70e+01 7.08e-01  9.18e+00  1489s
      88  -2.15466741e+06 -3.47562192e+05  2.54e+01 6.77e-01  8.56e+00  1505s
      89  -2.15127581e+06 -3.41822874e+05  2.53e+01 6.71e-01  8.50e+00  1521s
      90  -2.15134121e+06 -3.41851570e+05  2.53e+01 6.71e-01  8.50e+00  1538s
      91  -2.14335907e+06 -3.28429645e+05  2.52e+01 6.59e-01  8.38e+00  1554s
      92  -2.14332971e+06 -3.28418440e+05  2.52e+01 6.59e-01  8.38e+00  1571s
      93  -2.14340283e+06 -3.28447718e+05  2.52e+01 6.59e-01  8.38e+00  1587s
      94  -2.12446871e+06 -3.26303253e+05  2.50e+01 6.57e-01  8.32e+00  1603s
      95  -2.12097513e+06 -3.25610031e+05  2.50e+01 6.56e-01  8.30e+00  1619s
      96  -2.07242989e+06 -3.15183894e+05  2.45e+01 6.45e-01  8.11e+00  1635s
      97  -2.07107577e+06 -3.13938753e+05  2.45e+01 6.44e-01  8.09e+00  1651s
      98  -2.06415882e+06 -3.11963176e+05  2.44e+01 6.42e-01  8.06e+00  1668s
      99  -2.06382595e+06 -3.11846647e+05  2.44e+01 6.42e-01  8.05e+00  1684s
     100  -2.06320459e+06 -3.11758464e+05  2.44e+01 6.42e-01  8.05e+00  1700s
     101  -2.06303559e+06 -3.11734356e+05  2.44e+01 6.41e-01  8.05e+00  1716s
     102  -2.06251522e+06 -3.11652767e+05  2.44e+01 6.41e-01  8.05e+00  1732s
     103  -2.06232646e+06 -3.11684840e+05  2.44e+01 6.41e-01  8.05e+00  1748s
     104  -2.06219853e+06 -3.11638448e+05  2.44e+01 6.41e-01  8.05e+00  1764s
     105  -2.06048889e+06 -3.11369199e+05  2.44e+01 6.41e-01  8.04e+00  1781s
     106  -2.05935453e+06 -3.10543284e+05  2.44e+01 6.40e-01  8.03e+00  1797s
     107  -2.05771976e+06 -3.10122332e+05  2.44e+01 6.40e-01  8.03e+00  1813s
     108  -2.05532892e+06 -3.09211873e+05  2.43e+01 6.39e-01  8.01e+00  1829s
     109  -2.05521170e+06 -3.09175282e+05  2.43e+01 6.39e-01  8.01e+00  1845s
     110  -2.04880624e+06 -3.08132091e+05  2.43e+01 6.38e-01  7.99e+00  1862s
     111  -2.04657729e+06 -3.07600552e+05  2.42e+01 6.37e-01  7.98e+00  1878s
     112  -2.04658064e+06 -3.07601710e+05  2.42e+01 6.37e-01  7.98e+00  1894s
     113  -2.04651589e+06 -3.07598513e+05  2.42e+01 6.37e-01  7.98e+00  1911s
     114  -2.04653143e+06 -3.07604570e+05  2.42e+01 6.37e-01  7.98e+00  1927s
     115  -2.04587714e+06 -3.07430562e+05  2.42e+01 6.37e-01  7.98e+00  1944s
     116  -2.04319380e+06 -3.06168647e+05  2.42e+01 6.36e-01  7.96e+00  1960s

    Barrier performed 116 iterations in 1960.01 seconds (3166.22 work units)
    Numerical trouble encountered

    Hmm, something went wrong!

    ans =

        'Numerical problems (learn to debug) (GUROBI)'

    As you can see, the problem still remains unresolved. Could you provide further guidance on how to proceed? Any additional suggestions or tweaks that could help make the model solvable without the crossover step would be greatly appreciated.

    Besides, I agree with your suggestion that we should not disable the crossover step unless there's a compelling reason to do so. However, I'm encountering a significant issue with the solve time when I modify constraints on just 8 variables.

    When I change the upper bounds of these variables (either increasing or decreasing them), the crossover phase takes more than 400,000 seconds and continues to run, which severely impacts the efficiency of the program. This has forced me to look into other methods to reduce solve time, such as disabling the crossover step, although I understand this affects the numerical stability of the barrier method.

    Given that the barrier method is highly sensitive to numerical stability, I was wondering if you could advise on how to identify the specific values that are causing instability within the barrier method. Are there diagnostic tools or methods available to pinpoint these problematic values?

    Any guidance on improving the solve time while maintaining the integrity of the solution would be greatly appreciated.

    Thank you once again for your support.

    Best regards,

    Zhongfan Gu

    1
  • Jaromił Najman
    Gurobi Staff Gurobi Staff

    Hi Zhongfan Gu,

    As you can see, the problem still remains unresolved. Could you provide further guidance on how to proceed?

    That's interesting. You could try running without the Presolve=2 setting, but only with BarHomogeneous=1.

    Besides, I agree with your suggestion that we should not disable the crossover step unless there's a compelling reason to do so. However, I'm encountering a significant issue with the solve time when I modify constraints on just 8 variables.

    When I change the upper bounds of these variables (either increasing or decreasing them), the crossover phase takes more than 400,000 seconds and continues to run, which severely impacts the efficiency of the program. This has forced me to look into other methods to reduce solve time, such as disabling the crossover step, although I understand this affects the numerical stability of the barrier method.

    This sounds very suspicious. Could you please share the models, such that we could have a look on our side? In particular, could you share MPS files of the model that solves nicely with Crossover turned on and the model where you modify the constraints/variables? Could you please then point to which constraints/variables you exactly modify? You can generate MPS files via the write method. Note that uploading files in the Community Forum is not possible but we discuss an alternative in Posting to the Community Forum.

    Are there diagnostic tools or methods available to pinpoint these problematic values?

    You could try experimenting with the NumericFocus parameter. This would however not pinpoint the source of numerical issues. We provide a Python open source package called gurobi-modelanalyzer, which you might want to try out to find the source of numerical trouble in your model. See the corresponding docs for additional information.

    Best regards, 
    Jaromił

    0
  • Zhongfan Gu
    First Comment
    First Question

    Hello Jaromił,

    Firstly, I would like to extend my sincere gratitude for your assistance.

    I have attempted setting BarHomogeneous=1 as suggested, but unfortunately, this does not seem to help with the correct solving of the program.

    Below are the specific solver logs:

    Set parameter Username
    Set parameter Method to value 2
    Set parameter BarHomogeneous to value 1
    Set parameter Crossover to value 0
    Set parameter NodefileDir to value ""
    Set parameter TuneTimeLimit to value 1e+100
    Academic license - for non-commercial use only - expires 2024-11-02
    Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (win64)

    CPU model: 13th Gen Intel(R) Core(TM) i7-13700K, instruction set [SSE2|AVX|AVX2]
    Thread count: 16 physical cores, 24 logical processors, using up to 24 threads

    Optimize a model with 4702180 rows, 2210651 columns and 19350520 nonzeros
    Model fingerprint: 0x34eacf5d
    Coefficient statistics:
      Matrix range     [2e-05, 1e+01]
      Objective range  [2e-03, 2e+02]
      Bounds range     [0e+00, 0e+00]
      RHS range        [2e-02, 8e+04]
    Presolve removed 1022585 rows and 3117081 columns
    Presolve time: 4.72s
    Presolved: 1188066 rows, 1585099 columns, 11208382 nonzeros
    Elapsed ordering time = 6s
    Elapsed ordering time = 29s
    Elapsed ordering time = 30s
    Elapsed ordering time = 35s
    Elapsed ordering time = 40s
    Elapsed ordering time = 45s
    Ordering time: 50.03s

    Barrier statistics:
     Dense cols : 53
     Free vars  : 185912
     AA' NZ     : 2.455e+07
     Factor NZ  : 1.298e+09 (roughly 12.0 GB of memory)
     Factor Ops : 5.358e+12 (roughly 10 seconds per iteration)
     Threads    : 16

                      Objective                Residual
    Iter       Primal          Dual         Primal    Dual     Compl     Time
       0   1.60479324e+11  7.57738388e+11  7.72e+06 1.07e+05  1.91e+08    73s
       1   1.21109862e+11  6.73035539e+11  6.61e+06 8.97e+04  1.62e+08    92s
       2   9.85913920e+10  6.11755544e+11  5.98e+06 7.33e+04  1.41e+08   106s
       3   6.00163845e+10  5.98520307e+11  4.89e+06 6.80e+04  1.21e+08   121s
       4   1.75191160e+10  3.52742091e+11  2.36e+06 4.11e+04  4.26e+07   137s
       5   3.41558696e+09  2.41070656e+11  1.54e+06 2.89e+04  2.36e+07   153s
       6  -4.61302970e+09  1.67298976e+11  1.08e+06 2.08e+04  1.46e+07   170s
       7  -9.20544135e+09  1.20751423e+11  8.04e+05 1.57e+04  1.00e+07   186s
       8  -1.19472908e+10  8.84384931e+10  6.29e+05 1.21e+04  7.37e+06   202s
       9  -1.36316037e+10  6.58322035e+10  5.09e+05 9.62e+03  5.70e+06   217s
      10  -1.48106222e+10  4.38253715e+10  4.17e+05 7.16e+03  4.32e+06   233s
      11  -1.52718259e+10  2.50266824e+10  2.81e+05 4.92e+03  2.80e+06   248s
      12  -1.47334706e+10  1.67201630e+10  2.50e+05 3.83e+03  2.26e+06   264s
      13  -1.33710472e+10  1.12803835e+10  2.02e+05 2.97e+03  1.70e+06   279s
      14  -1.14487986e+10  5.39878203e+09  1.53e+05 2.00e+03  1.13e+06   295s
      15  -9.61016574e+09  2.85600599e+09  1.23e+05 1.39e+03  7.80e+05   311s
      16  -7.16583140e+09  1.48600301e+09  8.48e+04 9.23e+02  4.71e+05   327s
      17  -5.29706871e+09  6.33326160e+08  5.93e+04 5.98e+02  2.86e+05   342s
      18  -4.34620399e+09  3.16007484e+08  4.75e+04 4.29e+02  2.01e+05   358s
      19  -3.25798216e+09  1.39257273e+08  3.48e+04 3.03e+02  1.32e+05   374s
      20  -2.30719920e+09  3.63081417e+07  2.38e+04 1.99e+02  7.97e+04   389s
      21  -9.82494673e+08 -9.82959191e+06  1.05e+04 8.36e+01  2.64e+04   405s
      22  -3.43912244e+08 -1.71192615e+07  3.13e+03 5.60e+01  8.39e+03   421s
      23  -1.53412626e+08 -1.66452817e+07  1.25e+03 1.17e+01  1.29e+03   436s
      24  -2.84053721e+07 -4.52684484e+06  2.45e+02 3.65e+00  1.49e+02   451s
      25  -8.75182272e+06 -1.93250344e+06  8.31e+01 1.88e+00  4.12e+01   468s
      26  -8.18685360e+06 -1.81224925e+06  7.83e+01 1.80e+00  3.84e+01   483s
      27  -5.40620236e+06 -9.76699295e+05  5.37e+01 1.19e+00  2.20e+01   503s
      28  -5.39494862e+06 -9.71119685e+05  5.36e+01 1.19e+00  2.19e+01   518s
      29  -4.80174437e+06 -8.02124470e+05  4.86e+01 1.09e+00  1.93e+01   534s
      30  -4.16117444e+06 -7.79402961e+05  4.36e+01 1.02e+00  1.65e+01   551s
      31  -4.15887303e+06 -7.78548837e+05  4.36e+01 1.02e+00  1.65e+01   568s
      32  -4.10914424e+06 -7.67597388e+05  4.31e+01 1.01e+00  1.63e+01   585s
      33  -4.10921280e+06 -7.80214595e+05  4.31e+01 1.01e+00  1.62e+01   601s
      34  -4.06349326e+06 -7.57262002e+05  4.25e+01 9.69e-01  1.56e+01   619s
      35  -4.03270130e+06 -7.17528269e+05  4.22e+01 9.41e-01  1.53e+01   636s
      36  -4.02500966e+06 -7.15853257e+05  4.21e+01 9.40e-01  1.52e+01   653s
      37  -3.98868806e+06 -7.13562049e+05  4.17e+01 9.36e-01  1.51e+01   669s
      38  -3.96695903e+06 -6.90377090e+05  4.16e+01 9.27e-01  1.50e+01   686s
      39  -3.96701175e+06 -6.90439169e+05  4.16e+01 9.27e-01  1.50e+01   703s
      40  -3.95809051e+06 -6.87089945e+05  4.15e+01 9.24e-01  1.49e+01   719s
      41  -3.92056759e+06 -6.80601808e+05  4.11e+01 9.19e-01  1.48e+01   735s
      42  -3.59511269e+06 -6.10259913e+05  3.85e+01 8.83e-01  1.37e+01   751s
      43  -3.56336018e+06 -5.79478465e+05  3.82e+01 8.65e-01  1.34e+01   767s
      44  -3.38574110e+06 -5.37438280e+05  3.65e+01 8.30e-01  1.27e+01   785s
      45  -3.14945437e+06 -5.14342101e+05  3.47e+01 8.21e-01  1.21e+01   802s
      46  -3.12510512e+06 -5.12717844e+05  3.45e+01 8.18e-01  1.20e+01   818s
      47  -3.11779672e+06 -5.12325358e+05  3.44e+01 8.18e-01  1.20e+01   835s
      48  -3.11771320e+06 -5.15607238e+05  3.44e+01 8.18e-01  1.20e+01   851s
      49  -3.11724946e+06 -5.15736737e+05  3.44e+01 8.18e-01  1.20e+01   867s
      50  -2.95164538e+06 -5.08777015e+05  3.30e+01 8.14e-01  1.16e+01   883s
      51  -2.95042652e+06 -5.11441072e+05  3.30e+01 8.13e-01  1.15e+01   900s
      52  -2.94344853e+06 -5.07088636e+05  3.29e+01 8.09e-01  1.15e+01   916s
      53  -2.94283875e+06 -5.07043143e+05  3.29e+01 8.09e-01  1.15e+01   932s
      54  -2.69681566e+06 -4.74089018e+05  3.06e+01 7.83e-01  1.07e+01   948s
      55  -2.69677371e+06 -4.77322909e+05  3.06e+01 7.83e-01  1.07e+01   964s
      56  -2.69489436e+06 -4.77037944e+05  3.05e+01 7.83e-01  1.07e+01   980s
      57  -2.69487857e+06 -4.77233905e+05  3.05e+01 7.83e-01  1.07e+01   997s
      58  -2.65265231e+06 -4.62995752e+05  3.02e+01 7.76e-01  1.05e+01  1014s
      59  -2.63543433e+06 -4.60964416e+05  3.00e+01 7.72e-01  1.05e+01  1030s
      60  -2.63518532e+06 -4.60851863e+05  3.00e+01 7.72e-01  1.05e+01  1047s
      61  -2.61846361e+06 -4.51169956e+05  2.99e+01 7.65e-01  1.04e+01  1064s
      62  -2.61755578e+06 -4.49731201e+05  2.99e+01 7.65e-01  1.04e+01  1082s
      63  -2.61766325e+06 -4.49864132e+05  2.99e+01 7.65e-01  1.04e+01  1099s
      64  -2.61765269e+06 -4.49864100e+05  2.99e+01 7.65e-01  1.04e+01  1115s
      65  -2.61729669e+06 -4.49742897e+05  2.99e+01 7.64e-01  1.04e+01  1132s
      66  -2.61698651e+06 -4.49547872e+05  2.98e+01 7.64e-01  1.03e+01  1148s
      67  -2.61186068e+06 -4.47552723e+05  2.98e+01 7.63e-01  1.03e+01  1165s
      68  -2.61153466e+06 -4.47390110e+05  2.98e+01 7.63e-01  1.03e+01  1182s
      69  -2.61150254e+06 -4.47374768e+05  2.98e+01 7.63e-01  1.03e+01  1200s
      70  -2.61035489e+06 -4.46276398e+05  2.98e+01 7.62e-01  1.03e+01  1216s
      71  -2.60997570e+06 -4.46233704e+05  2.98e+01 7.62e-01  1.03e+01  1233s
      72  -2.60971095e+06 -4.46541649e+05  2.98e+01 7.62e-01  1.03e+01  1250s
      73  -2.55590200e+06 -4.30380743e+05  2.93e+01 7.51e-01  1.01e+01  1268s
      74  -2.54858034e+06 -4.28133320e+05  2.92e+01 7.49e-01  1.01e+01  1285s
      75  -2.54856964e+06 -4.28116394e+05  2.92e+01 7.49e-01  1.01e+01  1302s
      76  -2.49577564e+06 -4.21757482e+05  2.87e+01 7.44e-01  9.90e+00  1318s
      77  -2.49429894e+06 -4.22157375e+05  2.87e+01 7.44e-01  9.89e+00  1336s
      78  -2.49420023e+06 -4.22117884e+05  2.87e+01 7.44e-01  9.89e+00  1353s
      79  -2.46348056e+06 -4.20766591e+05  2.84e+01 7.43e-01  9.82e+00  1370s
      80  -2.44563763e+06 -4.20462693e+05  2.82e+01 7.42e-01  9.77e+00  1387s
      81  -2.40338790e+06 -4.09556693e+05  2.78e+01 7.30e-01  9.57e+00  1404s
      82  -2.40337958e+06 -4.09537887e+05  2.78e+01 7.30e-01  9.57e+00  1421s
      83  -2.40327229e+06 -4.09507703e+05  2.78e+01 7.30e-01  9.57e+00  1438s
      84  -2.37564141e+06 -3.98120519e+05  2.75e+01 7.21e-01  9.42e+00  1454s
      85  -2.32336000e+06 -3.79622950e+05  2.71e+01 7.09e-01  9.20e+00  1470s
      86  -2.32327542e+06 -3.79596001e+05  2.71e+01 7.09e-01  9.20e+00  1486s
      87  -2.31977989e+06 -3.78777766e+05  2.70e+01 7.08e-01  9.18e+00  1503s
      88  -2.15466741e+06 -3.47562192e+05  2.54e+01 6.77e-01  8.56e+00  1520s
      89  -2.15127581e+06 -3.41822874e+05  2.53e+01 6.71e-01  8.50e+00  1536s
      90  -2.15134121e+06 -3.41851570e+05  2.53e+01 6.71e-01  8.50e+00  1553s
      91  -2.14335907e+06 -3.28429645e+05  2.52e+01 6.59e-01  8.38e+00  1570s
      92  -2.14332971e+06 -3.28418440e+05  2.52e+01 6.59e-01  8.38e+00  1586s
      93  -2.14340283e+06 -3.28447718e+05  2.52e+01 6.59e-01  8.38e+00  1603s
      94  -2.12446871e+06 -3.26303253e+05  2.50e+01 6.57e-01  8.32e+00  1620s
      95  -2.12097513e+06 -3.25610031e+05  2.50e+01 6.56e-01  8.30e+00  1636s
      96  -2.07242989e+06 -3.15183894e+05  2.45e+01 6.45e-01  8.11e+00  1653s
      97  -2.07107577e+06 -3.13938753e+05  2.45e+01 6.44e-01  8.09e+00  1670s
      98  -2.06415882e+06 -3.11963176e+05  2.44e+01 6.42e-01  8.06e+00  1687s
      99  -2.06382595e+06 -3.11846647e+05  2.44e+01 6.42e-01  8.05e+00  1704s
     100  -2.06320459e+06 -3.11758464e+05  2.44e+01 6.42e-01  8.05e+00  1721s
     101  -2.06303559e+06 -3.11734356e+05  2.44e+01 6.41e-01  8.05e+00  1738s
     102  -2.06251522e+06 -3.11652767e+05  2.44e+01 6.41e-01  8.05e+00  1756s
     103  -2.06232646e+06 -3.11684840e+05  2.44e+01 6.41e-01  8.05e+00  1773s
     104  -2.06219853e+06 -3.11638448e+05  2.44e+01 6.41e-01  8.05e+00  1791s
     105  -2.06048889e+06 -3.11369199e+05  2.44e+01 6.41e-01  8.04e+00  1808s
     106  -2.05935453e+06 -3.10543284e+05  2.44e+01 6.40e-01  8.03e+00  1826s
     107  -2.05771976e+06 -3.10122332e+05  2.44e+01 6.40e-01  8.03e+00  1843s
     108  -2.05532892e+06 -3.09211873e+05  2.43e+01 6.39e-01  8.01e+00  1862s
     109  -2.05521170e+06 -3.09175282e+05  2.43e+01 6.39e-01  8.01e+00  1882s
     110  -2.04880624e+06 -3.08132091e+05  2.43e+01 6.38e-01  7.99e+00  1899s
     111  -2.04657729e+06 -3.07600552e+05  2.42e+01 6.37e-01  7.98e+00  1916s
     112  -2.04658064e+06 -3.07601710e+05  2.42e+01 6.37e-01  7.98e+00  1933s
     113  -2.04651589e+06 -3.07598513e+05  2.42e+01 6.37e-01  7.98e+00  1949s
     114  -2.04653143e+06 -3.07604570e+05  2.42e+01 6.37e-01  7.98e+00  1966s
     115  -2.04587714e+06 -3.07430562e+05  2.42e+01 6.37e-01  7.98e+00  1983s
     116  -2.04319380e+06 -3.06168647e+05  2.42e+01 6.36e-01  7.96e+00  1999s

    Barrier performed 116 iterations in 1998.90 seconds (3150.40 work units)
    Numerical trouble encountered

    Hmm, something went wrong!

    ans =

        'Numerical problems (learn to debug) (GUROBI)'

    Furthermore, considering the reproducibility of the results, I have uploaded the program and log that exceeds 400,000 seconds during the Crossover phase in MPS format to a sharing website: https://doi.org/10.5281/zenodo.13921293 . I hope you can access the file.

    It should be noted that the uploaded file is an earlier version of the model and therefore does not correspond to the solver logs shown on the Gurobi community forum. The logs on the forum are from a model that has undergone parameter tuning, making it solvable with Crossover enabled. Given the age of the earlier version, it is difficult to trace back the exact parameter changes that made it solvable faster. However, I can confirm that the uploaded file reproduces the issue of the Crossover phase taking over 400,000 seconds.

    I hope to receive further help from you and look forward to your valuable insights.

    Best regards,

    Zhongfan Gu

    0

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