Preprocessing and Cutting Planes with Conflict Graphs

TL;DR

This paper enhances the CBC solver with conflict graph algorithms, leading to stronger bounds, improved preprocessing, and a higher success rate in solving mixed-integer programs within time limits.

Contribution

Introduces conflict graph-based algorithms and data structures into CBC, including preprocessing, clique cut separators, and odd-cycle cuts, significantly improving solver performance.

Findings

Dual bounds at root node LP relaxation are up to 19.65% stronger.

Number of MIPs solved increased by 23.53%.

Average gap closed improved up to four times.

Abstract

This paper addresses the development of conflict graph-based algorithms and data structures into the COIN-OR Branch-and-Cut (CBC) solver, including: $(i)$ an efficient infrastructure for the construction and manipulation of conflict graphs; $(ii)$ a preprocessing routine based on a clique strengthening scheme that can both reduce the number of constraints and produce stronger formulations; $(iii)$ a clique cut separator capable of obtaining dual bounds at the root node LP relaxation that are $19.65\%$ stronger than those provided by the equivalent cut generator of a state-of-the-art commercial solver, $3.62$ times better than those attained by the clique cut separator of the GLPK solver and $4.22$ times stronger than the dual bounds obtained by the clique separation routine of the COIN-OR Cut Generation Library; and $(iv)$ an odd-cycle cut separator with a new lifting module to produce valid odd-wheel inequalities. The average gap closed by this new version of CBC was up to four times better than its previous version. Moreover, the number of mixed-integer programs solved by CBC in a time limit of three hours was increased by $23.53\%$.