Originally posted by: Anjikum

Hello,

I am solving a LP problem with around 4 Million columns and used Barrier as LP method for solving the same and also used Primal crossover. Convergence of Primal and Dual obj happened in 122 secs and Cross over took around 2605 Secs.  I have attached log for reference.

I tried the same with dual crossover and observed behaviour to be same and haven't used any convergence tolerance parameters.
Following are my clarification(s) with respect to following problem:
a) Many of my variable objective costs are same , Does that pose problem for Barrier method/its crossover? If so, does Numerical Emphasis parameter helps?
b) The same problem, I have converted variable type to Integer type and solved,  for which am finding difficult to get a feasible solution in an Hour.

Thanks in Advance.

Originally posted by: BoJensen

Some problems are better suited for barrier and other for simplex. On your problem barrier converges quickly, but then crossover struggles. When the cross over phase is finished, the found basis may not always be optimal and an extra call to the simplex optimizer is needed. Simplex seems to take a relative long time in this last call. It could be that simplex is just slow in general to this particular type of problem. You can try several settings :

• Check the kappa value of the final basis, if it's relative high then try to raise markowitz tolerance CPX_PARAM_EPMRK. This may help cross over to produce a better start basis.
• The log indicates the simplex optimizer makes little progress, this could be due to degeneracy. Try to switch on CPX_PARAM_PERIND or maybe even CPX_PARAM_EPPER.
• Force barrier to take more iterations and higher precision in the barrier solution CPX_PARAM_BAREPCOMP, may avoid the simplex step (if lucky).

Try also to solve the problem with primal and dual simplex to see if simplex in general struggles with this instance.

Originally posted by: Anjikum

Hello, 

Hello,

Thanks a lot for your answer.

I tried with Perturbation ON and attached is the log obtained.

After perturbation started, there is a huge value of Dual objective. Does that signify any problem with respect to degeneracy?. As you suggested, tried with Simplex and Dual, No much significant improvement with respect to in solving time and convergence.

Thank in Advance.

Originally posted by: BoJensen

Is it possible you can share your model with me ? If yes, please send to bo.jensen (at) dk (dot) ibm (dot) com.