solver:implementing_new_branching_rules

This shows you the differences between two versions of the page.

Both sides previous revision Previous revision Next revision | Previous revision | ||

solver:implementing_new_branching_rules [2020/05/26 12:45] Frederik Fiand |
— (current) | ||
---|---|---|---|

Line 1: | Line 1: | ||

- | ====== 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;''// | ||

- | |||

- | //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(s)'': | ||

- | <code> | ||

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

- | sum_delta.prior = 1; | ||

- | mymodel.prioropt=1; | ||

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

- | </code> | ||

- | |||

- | 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]]). |

IMPRESSUM / LEGAL NOTICE
PRIVACY POLICY
solver/implementing_new_branching_rules.1590489929.txt.gz ยท Last modified: 2020/05/26 12:45 by Frederik Fiand