Potential Bug Inquiry of GLPK

[Andrew Makhorin]

> Hi,
>  
> I am using the latest version of GLPK to solve the attached MIP
> problem (seed.mps), and I am getting the following result:
>  
> Solver: GLPK_CMD
> Status: Optimal
> Objective: 4450.011933000001
> x0 = 18, x1 = -24, x2 = -37, x3 = 9, x4 = -3, x5 = -48, x6 = 16, x7 =
> 9, x8 = -13.3293, x9 = 23.8585
>  
> While all the other solvers I have tried (including CBC, SCIP, HiGHS
> and Gurobi) return the same result as following:
>  
> Solver: CBC, SCIP, HiGHS, Gurobi
> Status: Optimal
> Objective: 4485.181539630002
> x0 = 18, x1 = -24, x2 = -37, x3 = 9, x4 = -4, x5 = -48, x6 = 16, x7 =
> 9, x8 = -13.575019, x9 = 23.694121
>  
> Is this result expected for GLPK? I'm not sure if this difference of
> the answer is due to a different algorithm used by GLPK or it’s an
> implementation issue. Any response or suggestions are appreciated!
>  
> Thanks for your time!
>  
> Best wishes,
> Xintong Zhou
> Cheriton School of Computer Science
> University of Waterloo
>  


Thank you for your report.


CBC, SCIP, HiGHS, and Gurobi report correct solution.  

Solving your instance with glpk I found that some constraints in the
optimal solution are slightly violated, e.g. row _C756 has lower bound 
83.06 while in the solution its activity is 83.0599.  So the glpk
solution is not buggy but has low precision.  I think this effect can
be eliminated by reformulating your model; in particular, using integer 
variables with large bounds (-200 .. 200) seems to me not a good idea.


Andrew Makhorin