Model mas76 leads to message [ERROR: Setting model status to Solve error]

[romz-pl]

For version 1.12 of HiGHS, an for the following input file

time_limit = 300
presolve = on
solver = simplex
parallel = off

for the model mas76 , taken from the MIPLIB library, the following message was received in the output file:

ERROR:   MIP solver claims optimality, but with num/max/sum primal(1/1.00001e-06/1.00001e-06) infeasibilities
ERROR:   Setting model status to Solve error

What input parameters should I use to obtain the solution to the model mas76?

The following is the complete output file:

Running HiGHS 1.12.0 (git hash: n/a): Copyright (c) 2025 HiGHS under MIT licence terms
Set option presolve to "on"
Set option solver to "simplex"
Set option parallel to "off"
Set option time_limit to 300
Set option log_file to "HiGHS.log"
MIP mas76 has 12 rows; 151 cols; 1640 nonzeros; 150 integer variables (150 binary)
Coefficient ranges:
  Matrix  [1e+00, 1e+04]
  Cost    [1e-05, 1e+00]
  Bound   [1e+00, 1e+12]
  RHS     [2e+01, 2e+05]
WARNING: Problem has some excessively small costs
WARNING: Problem has some excessively large column bounds
WARNING:    Consider scaling the    bounds by 1e-6, or setting the user_bound_scale option to -20
Presolving model
12 rows, 150 cols, 1639 nonzeros  0s
12 rows, 148 cols, 1615 nonzeros  0s
Presolve reductions: rows 12(-0); columns 148(-3); nonzeros 1615(-25) 

Solving MIP model with:
   12 rows
   148 cols (145 binary, 2 integer, 0 implied int., 1 continuous, 0 domain fixed)
   1615 nonzeros

Src: B => Branching; C => Central rounding; F => Feasibility pump; H => Heuristic;
     I => Shifting; J => Feasibility jump; L => Sub-MIP; P => Empty MIP; R => Randomized rounding;
     S => Solve LP; T => Evaluate node; U => Unbounded; X => User solution; Y => HiGHS solution;
     Z => ZI Round; l => Trivial lower; p => Trivial point; u => Trivial upper; z => Trivial zero

        Nodes      |    B&B Tree     |            Objective Bounds              |  Dynamic Constraints |       Work      
Src  Proc. InQueue |  Leaves   Expl. | BestBound       BestSol              Gap |   Cuts   InLp Confl. | LpIters     Time

 J       0       0         0   0.00%   -inf            90710.514236       Large        0      0      0         0     0.0s
 R       0       0         0   0.00%   38893.903641    44088.987759      11.78%        0      0      0        70     0.0s
 L       0       0         0   0.00%   39030.304486    40005.054141       2.44%     1088     23     18       174     0.2s

53.7% inactive integer columns, restarting
Model after restart has 12 rows, 69 cols (68 bin., 0 int., 0 impl., 1 cont., 0 dom.fix.), and 676 nonzeros

         0       0         0   0.00%   39031.930632    40005.054141       2.43%       15      0      0      1533     0.3s
         0       0         0   0.00%   39031.930632    40005.054141       2.43%       15     15      4      1560     0.3s

Restarting search from the root node
Model after restart has 12 rows, 68 cols (67 bin., 0 int., 0 impl., 1 cont., 0 dom.fix.), and 664 nonzeros

      1358       0         0   0.00%   39059.196002    40005.054141       2.36%       14      0      0     19569     1.3s
      1358       0         0   0.00%   39059.196002    40005.054141       2.36%       14      5      2     19579     1.3s

Restarting search from the root node
Model after restart has 12 rows, 66 cols (65 bin., 0 int., 0 impl., 1 cont., 0 dom.fix.), and 640 nonzeros

      3156       0         0   0.00%   39085.543774    40005.054141       2.30%       10      0      0     34702     2.6s
      3156       0         0   0.00%   39085.543774    40005.054141       2.30%       10      4      2     34714     2.6s
     15789     971      5770  15.12%   39109.828317    40005.054141       2.24%     1569     11   9689    120944     7.6s
     29970    1636     12437  24.83%   39198.70587     40005.054141       2.02%     1718      9   9923    215771    12.6s
     45839    2290     19971  31.43%   39226.9893      40005.054141       1.94%     1204     15   9781    318934    17.8s
     60826    2810     27116  36.36%   39252.960148    40005.054141       1.88%     1163     19   9800    417225    22.8s
     77432    3339     35063  41.66%   39286.765604    40005.054141       1.80%     1335     15   9963    521996    27.8s
     91752    3744     41932  46.85%   39307.070225    40005.054141       1.74%     1271      6   9945    617903    33.0s
    105448    4105     48519  49.68%   39318.200148    40005.054141       1.72%     1069     13   9912    709776    38.0s
    119797    4432     55460  52.66%   39326.585998    40005.054141       1.70%     1148     15  10000    804387    43.0s
    132752    4721     61716  60.05%   39340.93637     40005.054141       1.66%     1094     13   9907    891330    48.0s
    145943    4952     68122  64.60%   39353.318877    40005.054141       1.63%     1253     10   9637    979368    53.0s
    158776    5212     74325  67.56%   39360.856445    40005.054141       1.61%     1203      9   9785     1065k    58.0s

        Nodes      |    B&B Tree     |            Objective Bounds              |  Dynamic Constraints |       Work      
Src  Proc. InQueue |  Leaves   Expl. | BestBound       BestSol              Gap |   Cuts   InLp Confl. | LpIters     Time

    172320    5455     80889  70.75%   39370.922183    40005.054141       1.59%     1167     19   9787     1157k    63.0s
    186481    5714     87753  72.84%   39380.443482    40005.054141       1.56%     1185      7   9975     1251k    68.0s
    199448    5894     94049  75.42%   39395.334452    40005.054141       1.52%     1167      7   9842     1338k    73.0s
    212068    6054    100195  77.02%   39405.713262    40005.054141       1.50%     1204     12   9833     1424k    78.0s
    225635    6067    106897  82.27%   39424.949246    40005.054141       1.45%     1187     12   9982     1514k    83.0s
    240014    6145    113960  84.46%   39442.413798    40005.054141       1.41%     1098     20   9999     1609k    88.0s
    252190    6104    119977  86.43%   39458.1665      40005.054141       1.37%     1105     16   9839     1693k    93.0s
    265929    6002    126793  88.42%   39479.499141    40005.054141       1.31%     1291      8   9935     1784k    98.0s
    277795    5901    132691  90.22%   39497.280005    40005.054141       1.27%     1264     12   9984     1867k   103.0s
    289226    5635    138468  92.07%   39525.356938    40005.054141       1.20%     1185     15   9826     1948k   108.0s
    298915    5228    143455  94.60%   39552.833956    40005.054141       1.13%     1271     10   9035     2022k   113.0s
    309274    4609    148885  96.08%   39595.691881    40005.054141       1.02%     1287      9   5939     2099k   118.0s
    316206    3999    152606  96.83%   39632.439401    40005.054141       0.93%     1316     14   4865     2160k   123.0s
    323970    2944    156950  98.39%   39693.530016    40005.054141       0.78%     1279     12   3532     2227k   128.0s
    330142    1134    160891  99.54%   39803.389563    40005.054141       0.50%     1195      7   1495     2292k   133.0s
    331932       0    162341 100.00%   40001.055374    40005.054141       0.01%     1154      9   1272     2314k   134.5s

Solving report
  Model             mas76
  Status            Optimal
  Primal bound      40005.054141
  Dual bound        40001.055374
  Gap               0.01% (tolerance: 0.01%)
  P-D integral      2.05954656066
  Solution status   feasible
                    40005.054141 (objective)
                    0 (bound viol.)
                    0 (int. viol.)
                    0 (row viol.)
  Timing            134.50
  Max sub-MIP depth 5
  Nodes             331932
  Repair LPs        0
  LP iterations     2314385
                    8608 (strong br.)
                    142338 (separation)
                    116113 (heuristics)
ERROR:   MIP solver claims optimality, but with num/max/sum primal(1/1.00001e-06/1.00001e-06) infeasibilities
ERROR:   Setting model status to Solve error
Model name          : mas76
Model status        : Solve error
HiGHS run time      :        134.50

[jajhall]

Interesting, this is very close to being feasible, since the default MIP feasibility tolerance is 1e-6. I'll look at how the post-optimality feasibility check is computed. I wouldn't change any options to try to avoid this. Also, there's no point in setting presolve=on (as it's run by default) parallel=on (as it's off by default) or solver=simplex (as it's chosen by default).

[jajhall]

@fwesselm Did you say that there was a problem solving mas76 in your benchmarking?

[jajhall]

This infeasibility is with respect to a bound of 157345, so the violation (1e-11) of the feasibility tolerance is 1e17 less than the bound - so the violation is less than double precision rounding. Hence using a different expression to compute the infeasibility (in the MIP solver and in the checking) can be the cause.

Although it's in Miplib 2017, it's a badly scaled MIP

[fwesselm]

@fwesselm Did you say that there was a problem solving mas76 in your benchmarking?

No, as far as I remember, there was no issue with mas76. I can double-check.

[romz-pl]

Also, there's no point in setting presolve=on (as it's run by default)

According to the HiGHS documentation, for parameter presolve, the parameter parallel and the parameter solver there is Default: "choose". This is why I set

presolve = on
solver = simplex
parallel = off

In that context, what is the meaning of Default: "choose"?

[jajhall]

"choose" allows us to change the behaviour when, for example, we introduce a mechanism to decide which form of LP solver to use based on model properties. However, at present simplex will always be chosen.

I was sloppy in using the word "default", sorry

[romz-pl]

WARNING: Problem has some excessively small costs
WARNING: Problem has some excessively large column bounds
WARNING: Consider scaling the bounds by 1e-6, or setting the user_bound_scale option to -20

Based on the warning from the previous run, the user_bound_scale parameter was set to -20.

The full output report is shown below:

Running HiGHS 1.12.0 (git hash: n/a): Copyright (c) 2025 HiGHS under MIT licence terms
Set option parallel to "off"
Set option time_limit to 300
Set option user_bound_scale to -20
Set option log_file to "HiGHS.log"
MIP mas76 has 12 rows; 151 cols; 1640 nonzeros; 150 integer variables (150 binary)
Assessing costs and bounds after applying user_bound_scale option value of -20
Coefficient ranges:
  Matrix  [1e-06, 1e+00]
  Cost    [1e-11, 1e+00]
  Bound   [1e+00, 1e+06]
  RHS     [1e-05, 2e-01]
WARNING: User-scaled problem has some excessively small costs
WARNING: User-scaled problem has some excessively small row bounds
Presolving model
12 rows, 150 cols, 1639 nonzeros  0s
12 rows, 148 cols, 1615 nonzeros  0s
Presolve reductions: rows 12(-0); columns 148(-3); nonzeros 1615(-25) 

Solving MIP model with:
   12 rows
   148 cols (145 binary, 2 integer, 0 implied int., 1 continuous, 0 domain fixed)
   1615 nonzeros

Src: B => Branching; C => Central rounding; F => Feasibility pump; H => Heuristic;
     I => Shifting; J => Feasibility jump; L => Sub-MIP; P => Empty MIP; R => Randomized rounding;
     S => Solve LP; T => Evaluate node; U => Unbounded; X => User solution; Y => HiGHS solution;
     Z => ZI Round; l => Trivial lower; p => Trivial point; u => Trivial upper; z => Trivial zero

        Nodes      |    B&B Tree     |            Objective Bounds              |  Dynamic Constraints |       Work      
Src  Proc. InQueue |  Leaves   Expl. | BestBound       BestSol              Gap |   Cuts   InLp Confl. | LpIters     Time

 J       0       0         0   0.00%   -inf            0.074658816        Large        0      0      0         0     0.0s
 R       0       0         0   0.00%   0.037092117     0.0420465353      11.78%        0      0      0        41     0.0s
 L       0       0         0   0.00%   0.0372177601    0.0381517927       2.45%      212     24      6       141     0.1s

53.7% inactive integer columns, restarting
Model after restart has 12 rows, 69 cols (68 bin., 0 int., 0 impl., 1 cont., 0 dom.fix.), and 676 nonzeros

         0       0         0   0.00%   0.037218511     0.0381517927       2.45%       14      0      0       893     0.2s
         0       0         0   0.00%   0.037218511     0.0381517927       2.45%       14     14      4       916     0.2s
 L       0       0         0   0.00%   0.0372231912    0.0381517927       2.43%       27     25      4       946     0.3s
 L     176      30        72   1.56%   0.0372258365    0.0381517927       2.43%      134     23   1394      7663     0.8s

Restarting search from the root node
Model after restart has 12 rows, 66 cols (65 bin., 0 int., 0 impl., 1 cont., 0 dom.fix.), and 640 nonzeros

      1754       0         0   0.00%   0.0372483569    0.0381517927       2.37%       20      0      0     24417     1.8s
      1754       0         0   0.00%   0.0372483569    0.0381517927       2.37%       20      3      2     24425     1.8s
 L    1754       0         0   0.00%   0.0372517482    0.0381509225       2.36%       95     30      2     24648     1.9s

Restarting search from the root node
Model after restart has 12 rows, 66 cols (65 bin., 0 int., 0 impl., 1 cont., 0 dom.fix.), and 640 nonzeros

      3523       0         0   0.00%   0.0372517482    0.0381509225       2.36%       16      0      0     44462     3.3s
      3523       0         0   0.00%   0.0372517482    0.0381509225       2.36%       16      3      2     44469     3.3s
 L    3523       0         0   0.00%   0.0372517482    0.0381509225       2.36%       96     34      2     44687     3.6s
     12868     617      4295  38.87%   0.0374328942    0.0381509225       1.88%      626     25   9869    142135     8.6s
     23331    1011      9275  55.91%   0.0374849932    0.0381509225       1.75%      702     27   9507    244532    13.6s
 L   27496    1146     11264  59.86%   0.0375186592    0.0381509225       1.66%      834     17   9933    285508    16.0s
HighsMipSolverData::transformNewIntegerFeasibleSolution tmpSolver.run();
     34742    1335     14742  69.60%   0.0375726713    0.0381509225       1.52%      804     33   9972    367162    21.0s
     41994    1416     18282  76.52%   0.0376145289    0.0381509225       1.41%      709     30   9970    447643    26.0s
     49742    1422     22087  82.00%   0.0376667176    0.0381509225       1.27%      935     12   9971    527706    31.0s
     57891    1209     26207  93.42%   0.0377593518    0.0381509225       1.03%      863     22   9877    610871    36.0s

        Nodes      |    B&B Tree     |            Objective Bounds              |  Dynamic Constraints |       Work      
Src  Proc. InQueue |  Leaves   Expl. | BestBound       BestSol              Gap |   Cuts   InLp Confl. | LpIters     Time

     65223     598     30116  98.29%   0.0378813673    0.0381509225       0.71%      920     10   4451    684388    41.0s
     67980       0     31779 100.00%   0.0381471097    0.0381509225       0.01%     1145     11   1861    716351    43.4s

Solving report
  Model             mas76
  Status            Optimal
  Primal bound      0.0381509224892
  Dual bound        0.038147109715
  Gap               0.00999% (tolerance: 0.01%)
  P-D integral      0.668114738835
  Solution status   feasible
                    0.0381509224892 (objective)
                    0 (bound viol.)
                    4.8827608623e-13 (int. viol.)
                    0 (row viol.)
  Timing            43.44
  Max sub-MIP depth 4
  Nodes             67980
  Repair LPs        1 (1 feasible; 0 iterations)
  LP iterations     716351
                    6864 (strong br.)
                    93255 (separation)
                    36417 (heuristics)
WARNING: Solution optimality conditions: After removing user scaling
    max      4.88e-13                                  integrality violations     (tolerance = 1e-06)
num/max      1 /    0.912 (relative      1 /  5.8e-06) primal infeasibilities     (tolerance = 1e-06)
After solving the user-scaled model, the unscaled solution has objective value 40004.1417
WARNING: User scaled problem solved to optimality, but unscaled solution does not satisfy feasibilty and optimality tolerances

[jajhall]

That's interesting to see. It looks as if a stray printf has been left in. I'll fix that

The primal infeasibility after removing the user scaling is to be expected. Indeed, I'm surprised that there aren't more.

[romz-pl]

Setting the parameter mip_rel_gap = 0 the output of the HiGHS is the following

Running HiGHS 1.12.0 (git hash: n/a): Copyright (c) 2025 HiGHS under MIT licence terms
Set option parallel to "off"
Set option time_limit to 300
Set option user_bound_scale to -20
Set option log_file to "HiGHS.log"
Set option mip_rel_gap to 0
MIP mas76 has 12 rows; 151 cols; 1640 nonzeros; 150 integer variables (150 binary)
Assessing costs and bounds after applying user_bound_scale option value of -20
Coefficient ranges:
  Matrix  [1e-06, 1e+00]
  Cost    [1e-11, 1e+00]
  Bound   [1e+00, 1e+06]
  RHS     [1e-05, 2e-01]
WARNING: User-scaled problem has some excessively small costs
WARNING: User-scaled problem has some excessively small row bounds
Presolving model
12 rows, 150 cols, 1639 nonzeros  0s
12 rows, 148 cols, 1615 nonzeros  0s
Presolve reductions: rows 12(-0); columns 148(-3); nonzeros 1615(-25) 

Solving MIP model with:
   12 rows
   148 cols (145 binary, 2 integer, 0 implied int., 1 continuous, 0 domain fixed)
   1615 nonzeros

Src: B => Branching; C => Central rounding; F => Feasibility pump; H => Heuristic;
     I => Shifting; J => Feasibility jump; L => Sub-MIP; P => Empty MIP; R => Randomized rounding;
     S => Solve LP; T => Evaluate node; U => Unbounded; X => User solution; Y => HiGHS solution;
     Z => ZI Round; l => Trivial lower; p => Trivial point; u => Trivial upper; z => Trivial zero

        Nodes      |    B&B Tree     |            Objective Bounds              |  Dynamic Constraints |       Work      
Src  Proc. InQueue |  Leaves   Expl. | BestBound       BestSol              Gap |   Cuts   InLp Confl. | LpIters     Time

 J       0       0         0   0.00%   -inf            0.074658816        Large        0      0      0         0     0.0s
 R       0       0         0   0.00%   0.037092117     0.0420465353      11.78%        0      0      0        41     0.0s
 L       0       0         0   0.00%   0.0372177601    0.0381517927       2.45%      212     24      6       141     0.1s

53.7% inactive integer columns, restarting
Model after restart has 12 rows, 69 cols (68 bin., 0 int., 0 impl., 1 cont., 0 dom.fix.), and 676 nonzeros

         0       0         0   0.00%   0.037218511     0.0381517927       2.45%       14      0      0       893     0.2s
         0       0         0   0.00%   0.037218511     0.0381517927       2.45%       14     14      4       916     0.2s
 L       0       0         0   0.00%   0.0372231912    0.0381517927       2.43%       27     25      4       946     0.3s

Restarting search from the root node
Model after restart has 12 rows, 65 cols (64 bin., 0 int., 0 impl., 1 cont., 0 dom.fix.), and 628 nonzeros

      1011       0         0   0.00%   0.0372258365    0.0381517927       2.43%       28      0      0     17917     1.2s
      1011       0         0   0.00%   0.0372258365    0.0381517927       2.43%       28      5      2     17933     1.2s
 L    1011       0         0   0.00%   0.037255748     0.0381517927       2.35%       99     32      2     18143     1.4s
 L    6234     453      2373  12.31%   0.037255748     0.0381509225       2.35%      529     38   9687     64613     3.8s
     17749    1054      7813  31.22%   0.0374055339    0.0381509225       1.95%      687     31   9723    171238     8.8s
     27933    1389     12729  41.18%   0.0374499314    0.0381509225       1.84%      704     20   9865    273487    13.8s
 L   29926    1456     13690  42.09%   0.0374587456    0.0381509225       1.81%      534     23   9653    293398    15.0s
     38364    1801     17728  48.29%   0.0374891332    0.0381509225       1.73%      581     30   9719    379582    20.0s
 L   42212    1912     19596  50.99%   0.0375044307    0.0381509225       1.69%      533     34   9671    418513    22.1s
     50251    2164     23481  54.83%   0.0375188451    0.0381509225       1.66%      837     20   9909    501585    27.1s
     58319    2391     27398  58.80%   0.037542246     0.0381509225       1.60%      527     35   9591    584336    32.5s
     66355    2548     31333  63.38%   0.0375609344    0.0381509225       1.55%      596     30   9852    670903    37.5s
 L   73912    2748     35003  67.25%   0.0375694207    0.0381509225       1.52%      718     14   9797    749275    42.6s
     81783    2849     38881  70.46%   0.0375821443    0.0381509225       1.49%      647     31   9841    836969    47.7s

        Nodes      |    B&B Tree     |            Objective Bounds              |  Dynamic Constraints |       Work      
Src  Proc. InQueue |  Leaves   Expl. | BestBound       BestSol              Gap |   Cuts   InLp Confl. | LpIters     Time

     88803    2975     42324  73.09%   0.037593404     0.0381509225       1.46%      645     18   9991    915973    52.7s
     96116    3043     45943  76.80%   0.0376064558    0.0381509225       1.43%      709     28   9923    994945    57.7s
    104180    3173     49903  79.79%   0.0376188783    0.0381509225       1.39%      657     26   9770     1078k    62.7s
    111775    3249     53658  82.22%   0.0376351594    0.0381509225       1.35%      552     32   9868     1162k    67.8s
    121536    3307     58494  84.77%   0.0376481428    0.0381509225       1.32%      584     33   9941     1253k    73.0s
    129865    3337     62636  87.57%   0.0376656614    0.0381509225       1.27%      723     17   9868     1336k    78.0s
    137093    3287     66269  90.03%   0.0376797008    0.0381509225       1.24%      766     21   9910     1416k    83.0s
    144673    3229     70080  91.40%   0.0377009537    0.0381509225       1.18%      671     27   9750     1497k    88.0s
    152900    3107     74238  93.00%   0.0377243108    0.0381509225       1.12%      605     42   9934     1578k    93.0s
    160322    2924     78032  94.25%   0.0377466444    0.0381509225       1.06%      912     18   9678     1655k    98.0s
    168206    2703     82077  95.81%   0.0377744944    0.0381509225       0.99%      670     23   9668     1733k   103.0s
    174597    2314     85461  96.88%   0.0378060261    0.0381509225       0.90%      817     19   7817     1806k   108.0s
    181853    1849     89310  98.13%   0.0378445484    0.0381509225       0.80%      883     23   8350     1881k   113.0s
    186722    1017     92162  99.07%   0.0379317639    0.0381509225       0.57%      859     24   2816     1944k   118.0s
    188405       0     93514 100.00%   0.0381509225    0.0381509225       0.00%      881     21    972     1974k   120.7s

Solving report
  Model             mas76
  Status            Optimal
  Primal bound      0.0381509224892
  Dual bound        0.0381509224892
  Gap               0%
  P-D integral      1.69234805115
  Solution status   feasible
                    0.0381509224892 (objective)
                    0 (bound viol.)
                    5.62883073485e-13 (int. viol.)
                    0 (row viol.)
  Timing            120.71
  Max sub-MIP depth 4
  Nodes             188405
  Repair LPs        0
  LP iterations     1974177
                    6994 (strong br.)
                    222651 (separation)
                    99004 (heuristics)
WARNING: Solution optimality conditions: After removing user scaling
    max      5.63e-13                                  integrality violations     (tolerance = 1e-06)
num/max      1 /    0.912 (relative      1 /  5.8e-06) primal infeasibilities     (tolerance = 1e-06)
After solving the user-scaled model, the unscaled solution has objective value 40004.1417
WARNING: User scaled problem solved to optimality, but unscaled solution does not satisfy feasibilty and optimality tolerances

The value listed in miplib for mas76 is 40005.05398999999 but the value listed in HiGHS is 40004.1417.

What are your thoughts on this discrepancy?

[jajhall]

This will be a consequence of scaling the bounds down by 2^20~10^6 and the resultant primal infeasibility.

Specifically, if you scale the bounds down by 10^6 and solve to the MIP feasibility tolerance of 10^-6, then infeasibilities of this value will be scaled up by 10^6 when the user scaling is removed.

What happens if you set user_bound_scale=-10?

[romz-pl]

Setting the parameter user_bound_scale = -10 the output is the following:

Running HiGHS 1.12.0 (git hash: n/a): Copyright (c) 2025 HiGHS under MIT licence terms
Set option parallel to "off"
Set option time_limit to 300
Set option user_bound_scale to -10
Set option log_file to "HiGHS.log"
Set option mip_rel_gap to 0
MIP mas76 has 12 rows; 151 cols; 1640 nonzeros; 150 integer variables (150 binary)
Assessing costs and bounds after applying user_bound_scale option value of -10
Coefficient ranges:
  Matrix  [1e-03, 1e+01]
  Cost    [1e-08, 1e+00]
  Bound   [1e+00, 1e+09]
  RHS     [1e-02, 2e+02]
WARNING: User-scaled problem has some excessively small costs
WARNING: User-scaled problem has some excessively large column bounds
WARNING:    Consider setting the user_bound_scale option to -20
Presolving model
12 rows, 150 cols, 1639 nonzeros  0s
12 rows, 148 cols, 1615 nonzeros  0s
Presolve reductions: rows 12(-0); columns 148(-3); nonzeros 1615(-25) 

Solving MIP model with:
   12 rows
   148 cols (145 binary, 2 integer, 0 implied int., 1 continuous, 0 domain fixed)
   1615 nonzeros

Src: B => Branching; C => Central rounding; F => Feasibility pump; H => Heuristic;
     I => Shifting; J => Feasibility jump; L => Sub-MIP; P => Empty MIP; R => Randomized rounding;
     S => Solve LP; T => Evaluate node; U => Unbounded; X => User solution; Y => HiGHS solution;
     Z => ZI Round; l => Trivial lower; p => Trivial point; u => Trivial upper; z => Trivial zero

        Nodes      |    B&B Tree     |            Objective Bounds              |  Dynamic Constraints |       Work      
Src  Proc. InQueue |  Leaves   Expl. | BestBound       BestSol              Gap |   Cuts   InLp Confl. | LpIters     Time

 J       0       0         0   0.00%   -inf            83.28624987        Large        0      0      0         0     0.0s
 R       0       0         0   0.00%   37.98232777     43.05565211       11.78%        0      0      0        42     0.0s
 L       0       0         0   0.00%   38.11553172     39.06743569        2.44%     1090     23     17       146     0.2s

53.7% inactive integer columns, restarting
Model after restart has 12 rows, 69 cols (68 bin., 0 int., 0 impl., 1 cont., 0 dom.fix.), and 676 nonzeros

         0       0         0   0.00%   38.11711976     39.06743569        2.43%       15      0      0      1406     0.4s
         0       0         0   0.00%   38.11711976     39.06743569        2.43%       15     15      4      1437     0.4s
 L       0       0         0   0.00%   38.13637105     39.06743569        2.38%     1015     31      4      1556     0.6s
 L       0       0         0   0.00%   38.13637105     39.06743569        2.38%     1015     31      4      2125     0.7s

Restarting search from the root node
Model after restart has 12 rows, 67 cols (66 bin., 0 int., 0 impl., 1 cont., 0 dom.fix.), and 652 nonzeros

      1547       0         0   0.00%   38.14065018     39.06743569        2.37%        8      0      0     18366     1.6s
      1547       0         0   0.00%   38.14065018     39.06743569        2.37%        8      3      4     18370     1.6s

Restarting search from the root node
Model after restart has 12 rows, 67 cols (66 bin., 0 int., 0 impl., 1 cont., 0 dom.fix.), and 652 nonzeros

      4774       0         0   0.00%   38.17093927     39.06743569        2.29%       15      0      0     43046     3.9s
      4774       0         0   0.00%   38.17093927     39.06743569        2.29%       15      4      4     43060     3.9s
 L    4774       0         0   0.00%   38.17272155     39.0674347         2.29%     2141     34      4     43540     4.4s
     16000     759      5209  13.28%   38.24129309     39.0674347         2.11%     1804     16   9839    115973     9.4s
     28953    1409     11325  21.71%   38.27448921     39.0674347         2.03%     1536     13   9512    192810    14.4s
     41979    1979     17528  27.66%   38.3053785      39.0674347         1.95%     1412     12   9959    271783    19.4s
     54249    2444     23403  35.47%   38.31555441     39.0674347         1.92%     1455     18   9540    346368    24.4s
     65848    2830     28983  40.65%   38.33996037     39.0674347         1.86%     1499     10   9688    419529    29.7s
     77077    3198     34383  45.22%   38.35239566     39.0674347         1.83%     1527     10   9972    489929    34.7s
     89044    3546     40169  47.91%   38.36107091     39.0674347         1.81%     1491     10   9930    560327    39.7s
     99522    3830     45240  50.80%   38.3692051      39.0674347         1.79%     1465     11   9918    628333    44.7s

        Nodes      |    B&B Tree     |            Objective Bounds              |  Dynamic Constraints |       Work      
Src  Proc. InQueue |  Leaves   Expl. | BestBound       BestSol              Gap |   Cuts   InLp Confl. | LpIters     Time

    111228    4074     50936  54.14%   38.3808241      39.0674347         1.76%     1478      9   9809    700211    49.7s
    124423    4419     57331  57.96%   38.39297982     39.0674347         1.73%     1587     19   9810    778164    54.7s
    135896    4715     62897  61.67%   38.3983265      39.0674347         1.71%     1511     13   9777    848141    59.7s
    147144    4946     68383  64.32%   38.41064344     39.0674347         1.68%     1398     11   9570    917900    64.7s
    159181    5252     74223  67.10%   38.42199139     39.0674347         1.65%     1446     13   9746    990957    69.7s
    172355    5551     80622  70.26%   38.4300845      39.0674347         1.63%     1408      9   9943     1066k    74.7s
    183906    5760     86266  72.47%   38.44003948     39.0674347         1.61%     1406      8   9996     1136k    79.7s
    195364    5913     91894  74.41%   38.44961859     39.0674347         1.58%     1695      9   9927     1205k    84.7s
    207137    6060     97681  76.73%   38.45903886     39.0674347         1.56%     1518     16   9943     1274k    89.7s
    217961    6157    103023  78.41%   38.46986402     39.0674347         1.53%     1540     18   9795     1343k    95.1s
    230158    6248    109049  80.07%   38.47947138     39.0674347         1.50%     1637      9   9905     1415k   100.2s
    242532    6351    115156  82.76%   38.48920435     39.0674347         1.48%     1881      7   9936     1488k   105.2s
    253762    6419    120714  84.81%   38.49844113     39.0674347         1.46%     1455      9   9578     1557k   110.2s
    264125    6450    125863  85.64%   38.50901385     39.0674347         1.43%     1572     10   9847     1621k   115.2s
    276069    6407    131834  87.45%   38.52051206     39.0674347         1.40%     1503     13   9839     1690k   120.2s
    287961    6361    137776  89.16%   38.53313388     39.0674347         1.37%     1388      9   9951     1760k   125.2s
    298935    6340    143250  90.65%   38.54446191     39.0674347         1.34%     1274      9   9938     1826k   130.2s
    310501    6238    149056  92.09%   38.56683671     39.0674347         1.28%     1377      9   9974     1895k   135.2s
    321005    6042    154381  93.69%   38.58919754     39.0674347         1.22%     1447      6   9975     1960k   140.2s
    330564    5731    159299  94.82%   38.61212136     39.0674347         1.17%     1178     14   9805     2021k   145.2s

        Nodes      |    B&B Tree     |            Objective Bounds              |  Dynamic Constraints |       Work      
Src  Proc. InQueue |  Leaves   Expl. | BestBound       BestSol              Gap |   Cuts   InLp Confl. | LpIters     Time

    339401    5378    163881  95.86%   38.63689152     39.0674347         1.10%     1403     12   9661     2080k   150.2s
    347301    4876    168067  96.95%   38.67677936     39.0674347         1.00%     1308      9   8665     2135k   155.2s
    353524    4159    171523  97.83%   38.73137275     39.0674347         0.86%     1372     10   3841     2183k   160.2s
    357982    3323    174161  98.39%   38.77689303     39.0674347         0.74%     1330     10   2238     2224k   165.2s
    362747    1746    177320  99.24%   38.86525707     39.0674347         0.52%     1198      8   1286     2270k   170.2s
    365308       0    179471 100.00%   39.0674347      39.0674347         0.00%     1177     10   1079     2298k   172.9s

Solving report
  Model             mas76
  Status            Optimal
  Primal bound      39.0674346953
  Dual bound        39.0674346953
  Gap               0%
  P-D integral      2.67477351448
  Solution status   feasible
                    39.0674346953 (objective)
                    0 (bound viol.)
                    0 (int. viol.)
                    0 (row viol.)
  Timing            172.92
  Max sub-MIP depth 5
  Nodes             365308
  Repair LPs        0
  LP iterations     2298658
                    7830 (strong br.)
                    123887 (separation)
                    115058 (heuristics)
WARNING: Solution optimality conditions: After removing user scaling
    max             0                                  integrality violations     (tolerance = 1e-06)
num/max      1 /  0.00101 (relative      0 / 6.44e-09) primal infeasibilities     (tolerance = 1e-06)
After solving the user-scaled model, the unscaled solution has objective value 40005.053128
WARNING: User scaled problem solved to optimality, but unscaled solution does not satisfy feasibilty and optimality tolerances

The return value by HiGHS is 40005.053128.
Great!
Thank you for your help!

[jajhall]

Thanks, this has been an interesting and valuable discussion for me

[romz-pl]

I have noticed that setting the value of parameter mip_rel_gap = 0 and the value of parameter mip_abs_gap = 1e-06, for both set user_bound_scale=-10 and set user_bound_scale=-20, the value of the column BestBound is equal to the value of the column BestSol at the last iteration of the branch-and-bound algorithm.

Will you be making any improvements to this issue in future versions of HiGHS?