[SCIP] Multiple LPs between two pricing iterations?

[Franzen, Christian]

Hi SCIP team.


I am currently working on a branch-and-price solver utilising SCIP 7.0.0 and I have a question regarding the column generation part of my solver. I am using Gurobi as LP solver and in the output I see, that SCIP is solving two different LPs between two pricing iterations:


...

08:42:03,246 DEBUG [ShortestPathPricer] - Added 23529 priced variables to MIP in node 1
Gurobi Optimizer version 9.0.0 build v9.0.0rc2 (win64)
Optimize a model with 48551 rows, 93664 columns and 1338605 nonzeros
Model fingerprint: 0x72a2c96a
Coefficient statistics:
  Matrix range     [1e+00, 2e+03]
  Objective range  [3e+01, 6e+05]
  Bounds range     [1e+00, 1e+05]
  RHS range        [1e+00, 2e+03]
Presolve removed 34948 rows and 46357 columns
Presolve time: 0.36s
Presolved: 13603 rows, 47307 columns, 572120 nonzeros

Iteration    Objective       Primal Inf.    Dual Inf.      Time
       0    3.0013561e+07   2.138206e+04   0.000000e+00      0s
Extra 4629 simplex iterations after uncrush
   39243    1.4968131e+08   0.000000e+00   0.000000e+00      5s

Solved in 39243 iterations and 4.82 seconds
Optimal objective  1.496813123e+08
Gurobi Optimizer version 9.0.0 build v9.0.0rc2 (win64)
Optimize a model with 53040 rows, 98153 columns and 1367851 nonzeros
Model fingerprint: 0xc710b0e7
Coefficient statistics:
  Matrix range     [1e+00, 2e+03]
  Objective range  [3e+01, 6e+05]
  Bounds range     [1e+00, 1e+05]
  RHS range        [1e+00, 2e+03]
Presolve removed 41331 rows and 53475 columns
Presolve time: 0.35s
Presolved: 11709 rows, 44678 columns, 555041 nonzeros

Iteration    Objective       Primal Inf.    Dual Inf.      Time
       0    3.2305583e+07   2.006420e+04   0.000000e+00      0s
Extra 3020 simplex iterations after uncrush
   35045    1.4972126e+08   0.000000e+00   0.000000e+00      4s

Solved in 35045 iterations and 4.18 seconds
Optimal objective  1.497212611e+08
 time | node  | left  |LP iter|LP it/n|mem/heur|mdpt |frac |vars |cons |cols |rows |cuts |confs|strbr|  dualbound   | primalbound  |  gap
  242s|     1 |     0 |103574 |     - |   649M |   0 | 738 |  92k|  53k|  69k|  53k|   0 |   0 |   0 |      --      | 1.562342e+08 |    Inf
08:42:12,462 DEBUG [ShortestPathPricer] - Starting pricing interation #2 in node 1...
...


In my case, the second LP always has a few more columns and rows, but the optimal objective value is the same for both. Is this by intention or is this a bug (maybe in den Gurobi interface, which is in beta state)? If it is by intention, can you tell me what is the reason for that?


Regards

Christian
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