Clique Probing for Mixed-Integer Programs

TL;DR

This paper introduces clique probing, a presolving technique for mixed-integer programming that probes on variable cliques instead of individual variables, leading to more reductions and a 3% performance boost in solvers.

Contribution

It proposes a novel clique probing method for MIP presolving, enhancing reduction efficiency and solver performance by exploiting clique structures.

Findings

Clique probing significantly increases variable reductions.

Integration into SCIP yields a 3% performance improvement.

Experiments on MIPLIB instances confirm effectiveness.

Abstract

Probing is an important presolving technique in mixed-integer programming solvers. It selects binary variables, tentatively fixes them to 0 and 1, and performs propagation to deduce additional variable fixings, bound tightenings, substitutions, and implications. In this work, we propose clique probing instead of probing on individual variables, we select cliques, a set of binary variables of which at most one can be set to one, and systematically probe on all variables of a clique. Experiments with our implementation in the open-source presolve library PaPILO demonstrate that exploiting clique information in this form significantly increases the number of reductions. When integrated into the MIP solver SCIP, we observe a 3% performance improvement on MIPLIB instances containing cliques.