MPS Files (2)

As follow up on http://yetanothermathprogrammingconsultant.blogspot.com/2011/10/mps-files.html it is noted that Microsoft Solver Foundation also reads some MPS files incorrectly. E.g. consider the files:

C:\Users\erwin\Documents>type mip4mps.oml Model[   Decisions[Integers[0, Infinity], x],   Constraints[x <= 5],   Goals[Maximize[x]] ] C:\Users\erwin\Documents>type output.mps NAME          MODEL ROWS L  constrai N  goal_8ef COLUMNS     INTMARK   'MARKER'                 'INTORG'     x         constrai   1             goal_8ef  -1     INTMARK   'MARKER'                 'INTEND' RHS     RHS       constrai   5 BOUNDS ENDATA C:\Users\erwin\Documents>

The MPS file was generated from the OML file. If we inspect the MPS file we see no bounds on x. This means the variable x should be binary.

If we solve the MPS file with Solver Foundation we see:

C:\Users\erwin\Documents>"\Program Files (x86)\Microsoft Solver Foundation\3.0.2.10889\Bin\MSFCli.exe" +verbose 3 output.mps ===== Processing .\output.mps ===== Solution Quality: Optimal ===Solver Foundation Service Report=== Date: 11/21/2011 10:27:00 PM Version: Microsoft Solver Foundation 3.0.2.10889 Standard Edition Model Name: DefaultModel Capabilities Applied: MILP Solve Time (ms): 367 Total Time (ms): 489 Solve Completion Status: Optimal Solver Selected: Microsoft.SolverFoundation.Solvers.SimplexSolver Algorithm: Primal Arithmetic: Hybrid Variables: 1 -> 1 + 2 Rows: 2 -> 2 Nonzeros: 2 Eliminated Slack Variables: 0 Pricing (exact): SteepestEdge Pricing (double): SteepestEdge Basis: Slack Pivot Count: 1 Phase 1 Pivots: 0 + 0 Phase 2 Pivots: 1 + 0 Factorings: 4 + 1 Degenerate Pivots: 0 (0.00 %) Branches: 0 ===Solution Details=== Goals: goal_8ef: -5 Decisions: x: 5 ===== Finished .\output.mps: 00:00:00.5501834 =====

This is incorrect. The reported value of x=5 indicates x is not read as a binary variable. If we solve the MPS file with CBC we see:

C:\Users\erwin\Documents>..\Downloads\cbc output.mps -solve -solution stdout Welcome to the CBC MILP Solver Version: 2.7.5 Build Date: Nov 10 2011 Revision Number: 1759 command line - ..\Downloads\cbc output.mps -solve -solution stdout (default strategy 1) At line 1 NAME          MODEL At line 2 ROWS At line 5 COLUMNS At line 9 RHS At line 11 BOUNDS At line 12 ENDATA Problem MODEL has 1 rows, 1 columns and 1 elements Coin0008I MODEL read with 0 errors Continuous objective value is -1 - 0.00 seconds Cgl0004I processed model has 0 rows, 0 columns (0 integer) and 0 elements Cbc3007W No integer variables - nothing to do Cuts at root node changed objective from -1 to -1.79769e+308 Probing was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds) Gomory was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds) Knapsack was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds) Clique was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds) MixedIntegerRounding2 was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds) FlowCover was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds) TwoMirCuts was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds) Result - Optimal solution found Objective value:                -1.00000000 Enumerated nodes:               0 Total iterations:               0 Time (CPU seconds):             0.01 Time (Wallclock seconds):       0.01 Optimal - objective value -1.00000000       0 x                      1                     -1 Total time (CPU seconds):       0.02   (Wallclock seconds):       0.02 C:\Users\erwin\Documents>

The output is a little bit confusing, but indeed x assumes the value 1. This confirms x is binary.