For example, to branch on the sum of some variables as in the following constraints:

```
sum(s, delta(s)) =l= k; or \sum(s, delta(s)) =g= k+1;
```

Another integer variable can be introduced

```
sum_delta =e= sum(s, delta(s));
```

Branching priorities can then be set to instruct the MIP solver to first branch on the sum_delta variable and then on the delta(s):

```
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).