Originally posted by: SystemAdmin

Dear all,

I try to solve a complicated MILP problem, but the optimal result returned by CPLEX is obvious not correct, the MILP slack bound error is huge as

Display which part of the solution: quality
Incumbent solution:
MILP objective 7.8200000000e+002
MILP solution norm |x| (Total, Max) 2.00074e+007 5.00000e+006
MILP solution error (Ax=b) (Total, Max) 7.70900e-011 7.66249e-011
MILP x bound error (Total, Max) 2.59597e-013 1.92624e-014
MILP x integrality error (Total, Max) 6.12999e-017 7.66249e-018
MILP slack bound error (Total, Max) 1.95000e+003 4.50000e+002

Some slacks for less and equal constraints are negative and far away from 0, so the solution breaks these constraints at all.

Any ideas about this problem.

Thanks a lot.
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: SystemAdmin

Have you tried to turn on numerical emphasis:

CPLEX> set emphasis numerical y

What is the output of

CPLEX> display problem statistics

#CPLEXOptimizers
#DecisionOptimization

Originally posted by: SystemAdmin

I didn't turn on numerical emphasis and the output of stats is

Display which problem characteristic: stats
Problem name: vnpromodel4.lp
Variables : 2383 Nneg: 1985, Binary: 398
Objective nonzeros : 25
Linear constraints : 2783 Less: 1383, Equal: 1400
Nonzeros : 9494
RHS nonzeros : 1187

Variables : Min LB: 0.0000000 Max UB: 1.000000
Objective nonzeros : Min : 1.000000 Max : 1.000000
Linear constraints :
Nonzeros : Min : 1.000000 Max : 1.000000e+007
RHS nonzeros : Min : 1.000000 Max : 150.0000
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: SystemAdmin

I would suggest that you do one or both of the following:

(a) turn on numerical emphasis (per Daniel's question/suggestion);
(b) use 'set mip strategy kappastats' to collect basis condition number information (setting = 2) and then, after solving, display the kappa statistics (I think that is under 'display solution quality kappa' but I won't swear to it).

Paul

Mathematicians are like Frenchmen: whenever you say something to them, they translate it into their own language, and at once it is something entirely different. (Goethe)
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: SystemAdmin

Hi Paul,

I turn on the numerical emphasis and set mip strategy kappastats to collect basis condition number information setting to 2.
The result is same, but the processing time decreased a lot...

Display which part of the solution: qua
Incumbent solution:
MILP objective 9.3500000000e+002
MILP solution norm |x| (Total, Max) 6.00049e+007 4.99993e+006
MILP solution error (Ax=b) (Total, Max) 2.79130e-013 2.84217e-014
MILP x bound error (Total, Max) 3.84060e-013 2.40728e-014
MILP x integrality error (Total, Max) 6.42079e-017 3.21039e-017
MILP slack bound error (Total, Max) 1.80000e+003 4.50000e+002

Branch-and-cut subproblem optimization:
Max condition number: 7.9997e+023
Percentage (number) of stable bases: 2.24% (20165)
Percentage (number) of suspicious bases: 64.07% (576540)
Percentage (number) of unstable bases: 16.04% (144345)
Percentage (number) of ill-posed bases: 17.65% (158785)
Attention level: 0.230991
CPLEX encountered numerical difficulties while solving this model.

Thanks a lot
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: SystemAdmin

Both the last message and the kappa statistics tell the same story: your model has substantial numerical stability problems. There are multiple possible causes; bad scaling is one possibility. Your constraint coefficients span seven orders of magnitude. I've seen worse, but that might contribute to the instability. You might consider whether you can shrink the ratio of largest to smallest coefficient magnitude. Beyond that, I cannot offer much specific advice. Searching "instability" or "stability" on this forum should turn up posts from other people with unstable models; maybe you'll find something helpful in one of those threads.

Paul

Mathematicians are like Frenchmen: whenever you say something to them, they translate it into their own language, and at once it is something entirely different. (Goethe)
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: SystemAdmin

Thanks a lot.
Some coefficients in the model are extremely large, that may cause the problem.
I think I will modify the model and try again later.
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: SystemAdmin

Hi, I google the numerical emphasis and found you. Would you tell me how to turn on the numerical emphasis with c++? Thanks so much.
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: SystemAdmin

CPLEX > Parameters of CPLEX > Parameters Reference Manual > List of CPLEX parameters > numerical precision emphasis

Paul

Mathematicians are like Frenchmen: whenever you say something to them, they translate it into their own language, and at once it is something entirely different. (Goethe)
#CPLEXOptimizers
#DecisionOptimization