Originally posted by: basvdm

Hi there!

I'm currently working on a MILP to be solved with CPLEX in MATLAB.

The MILP concerns two objectives which are defined by means of weighted sum with respect to each other. So, objective A has a weight alpha, and objective B has a weight beta= 1-alpha.

The number of decision variables related to A equals around 500 whereas the number of decision variables related to B is around 540. Both types of decision variables are binary states.

Now, for some reason when I try to find the optimal solution in MATLAB it takes me about 2 minutes to have the mip gap converged to 0.0001 for alpha being 0.99. For the opposite case, alpha equals 0.01, the mip gap converges very slowly (read: mip gap is still 27% after 7 hours..). 

Does anyone know how I can solve such issue? 

Thanks in advance!

This is not unexpected. In one case you are basically solving a model with objective A, in the other case you are solving a model with objective B. It can well be that solving for A is a lot easier than solving for B (or vice versa). Could you export the two problem instances to SAV files and post them here? Or at least attach log files for the two solves?

You may want to try playing with the MIP emphasis parameter for the case that solves too slowly.