Q: I have implemented a MIP-model in GAMS, which I would like to solve to proven optimality. The problem is degenrate and has a lot optimal solutions, and many solutions very close to the optimum. It is not terminating with the optimal solution, but continuing to examine nodes with a very small gap > 0.00 %.
I have a good idea for a branching rule, which i believe can work around the degeneracy problems. Instead of doing binary branching on fractional binary variables, I intend to branch on the sum of some variables, i.e:
sum(s, delta(s)) =l= k; or
\sum(s, delta(s)) =g= k+1;
My question is then, how can I introduce such a branching rule in GAMS, instead of just using binary branching ??
You could introduce another integer variable
sum_delta =e= sum(s, delta(s)); Now you can use branching priorities to instruct the MIP solver to first branch on the
sum_delta variable and then on the
delta.prior(s) = 100; sum_delta.prior = 1; mymodel.prioropt=1; solve mymodel min obj using mip;
If the multiple close to optimal solutions come from symmetry, you might also want to try a more aggressive level for symmetry braking cuts (see e.g. cplex option symmetry). Preprocessing at the node or aggressive probing might also help (see e.g. Cplex options preslvnd and probe).