*sum(s, delta(s)) =l= k;*or

*sum(s, delta(s)) =g= k+1;*

How can I introduce such a branching rule in GAMS, instead of just using binary branching ?

**Moderator:** aileen

Please ask questions in the other sub-forums

I have implemented a MIP-model in GAMS, which I would like to solve to proven optimality. The problem is degenerate 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;*

How can I introduce such a branching rule in GAMS, instead of just using binary branching ?

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(s)*:

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).

Code: Select all

```
delta.prior(s) = 100;
sum_delta.prior = 1;
mymodel.prioropt=1;
solve mymodel min obj using mip;
```