solver:implementing_new_branching_rules

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solver:implementing_new_branching_rules [2021/01/28 17:38] Atharv Bhosekar removed |
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- | ====== Branching on sums of binary variables ====== | ||

- | 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;''// | ||

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- | //My question is then, how can I introduce such a branching rule in GAMS, instead of just using binary branching ?? // | ||

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- | 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)'': | ||

- | <code> | ||

- | delta.prior(s) = 100; | ||

- | sum_delta.prior = 1; | ||

- | mymodel.prioropt=1; | ||

- | solve mymodel min obj using mip; | ||

- | </code> | ||

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- | 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 [[https://www.gams.com/latest/docs/S_CPLEX.html#CPLEXsymmetry|symmetry]]). Preprocessing at the node or aggressive probing might also help (see e.g. Cplex options [[https://www.gams.com/latest/docs/S_CPLEX.html#CPLEXpreslvnd|preslvnd]] and [[https://www.gams.com/latest/docs/S_CPLEX.html#CPLEXprobe|probe]]). |