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<p><span style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;">Hi SCIP team.</span><br>
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<p><span>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:</span></p>
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<p><span style="font-family:Consolas,Courier,monospace">...</span></p>
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<div><span style="font-family:Consolas,Courier,monospace">08:42:03,246 DEBUG [ShortestPathPricer] - Added 23529 priced variables to MIP in node 1</span></div>
<div><span style="font-family:Consolas,Courier,monospace">Gurobi Optimizer version 9.0.0 build v9.0.0rc2 (win64)</span></div>
<div><span style="font-family:Consolas,Courier,monospace">Optimize a model with 48551 rows, 93664 columns and 1338605 nonzeros</span></div>
<div><span style="font-family:Consolas,Courier,monospace">Model fingerprint: 0x72a2c96a</span></div>
<div><span style="font-family:Consolas,Courier,monospace">Coefficient statistics:</span></div>
<div><span style="font-family:Consolas,Courier,monospace"> Matrix range [1e+00, 2e+03]</span></div>
<div><span style="font-family:Consolas,Courier,monospace"> Objective range [3e+01, 6e+05]</span></div>
<div><span style="font-family:Consolas,Courier,monospace"> Bounds range [1e+00, 1e+05]</span></div>
<div><span style="font-family:Consolas,Courier,monospace"> RHS range [1e+00, 2e+03]</span></div>
<div><span style="font-family:Consolas,Courier,monospace">Presolve removed 34948 rows and 46357 columns</span></div>
<div><span style="font-family:Consolas,Courier,monospace">Presolve time: 0.36s</span></div>
<div><span style="font-family:Consolas,Courier,monospace">Presolved: 13603 rows, 47307 columns, 572120 nonzeros</span></div>
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<div><span style="font-family:Consolas,Courier,monospace">Iteration Objective Primal Inf. Dual Inf. Time</span></div>
<div><span style="font-family:Consolas,Courier,monospace"> 0 3.0013561e+07 2.138206e+04 0.000000e+00 0s</span></div>
<div><span style="font-family:Consolas,Courier,monospace">Extra 4629 simplex iterations after uncrush</span></div>
<div><span style="font-family:Consolas,Courier,monospace"> 39243 1.4968131e+08 0.000000e+00 0.000000e+00 5s</span></div>
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<div><span style="font-family:Consolas,Courier,monospace">Solved in 39243 iterations and 4.82 seconds</span></div>
<div><span style="font-family:Consolas,Courier,monospace">Optimal objective 1.496813123e+08</span></div>
<div><span style="font-family:Consolas,Courier,monospace">Gurobi Optimizer version 9.0.0 build v9.0.0rc2 (win64)</span></div>
<div><span style="font-family:Consolas,Courier,monospace">Optimize a model with 53040 rows, 98153 columns and 1367851 nonzeros</span></div>
<div><span style="font-family:Consolas,Courier,monospace">Model fingerprint: 0xc710b0e7</span></div>
<div><span style="font-family:Consolas,Courier,monospace">Coefficient statistics:</span></div>
<div><span style="font-family:Consolas,Courier,monospace"> Matrix range [1e+00, 2e+03]</span></div>
<div><span style="font-family:Consolas,Courier,monospace"> Objective range [3e+01, 6e+05]</span></div>
<div><span style="font-family:Consolas,Courier,monospace"> Bounds range [1e+00, 1e+05]</span></div>
<div><span style="font-family:Consolas,Courier,monospace"> RHS range [1e+00, 2e+03]</span></div>
<div><span style="font-family:Consolas,Courier,monospace">Presolve removed 41331 rows and 53475 columns</span></div>
<div><span style="font-family:Consolas,Courier,monospace">Presolve time: 0.35s</span></div>
<div><span style="font-family:Consolas,Courier,monospace">Presolved: 11709 rows, 44678 columns, 555041 nonzeros</span></div>
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<div><span style="font-family:Consolas,Courier,monospace">Iteration Objective Primal Inf. Dual Inf. Time</span></div>
<div><span style="font-family:Consolas,Courier,monospace"> 0 3.2305583e+07 2.006420e+04 0.000000e+00 0s</span></div>
<div><span style="font-family:Consolas,Courier,monospace">Extra 3020 simplex iterations after uncrush</span></div>
<div><span style="font-family:Consolas,Courier,monospace"> 35045 1.4972126e+08 0.000000e+00 0.000000e+00 4s</span></div>
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<div><span style="font-family:Consolas,Courier,monospace">Solved in 35045 iterations and 4.18 seconds</span></div>
<div><span style="font-family:Consolas,Courier,monospace">Optimal objective 1.497212611e+08</span></div>
<div><span style="font-family:Consolas,Courier,monospace"> time | node | left |LP iter|LP it/n|mem/heur|mdpt |frac |vars |cons |cols |rows |cuts |confs|strbr| dualbound | primalbound | gap </span></div>
<div><span style="font-family:Consolas,Courier,monospace"> 242s| 1 | 0 |103574 | - | 649M | 0 | 738 | 92k| 53k| 69k| 53k| 0 | 0 | 0 | -- | 1.562342e+08 | Inf </span></div>
<div><span style="font-family:Consolas,Courier,monospace">08:42:12,462 DEBUG [ShortestPathPricer] - Starting pricing interation #2 in node 1...</span></div>
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<span style="font-family:Consolas,Courier,monospace">...</span>
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<p><span>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?</span></p>
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<p><span>Regards</span></p>
<p><span>Christian</span></p>
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