Parametric Disjunctive Cuts for Sequences of Mixed Integer Linear Optimization Problems

TL;DR

This paper introduces parametric disjunctive inequalities (PDIs) that reuse previous optimality proofs to generate cuts, significantly improving the efficiency of solving sequences of related mixed-integer linear programs.

Contribution

The paper presents a novel class of cuts called PDIs, which leverage prior solutions to enhance solving sequences of related MILPs, balancing computational cost and cut strength.

Findings

PDIs support the disjunctive hull under certain conditions

Augmenting branch-and-cut with PDIs reduces solve times on challenging instances

PDIs improve performance on perturbed MIPLIB 2017 instances

Abstract

Many applications require solving sequences of related mixed-integer linear programs. We introduce a class of parametric disjunctive inequalities (PDIs), obtained by reusing the disjunctive proofs of optimality from prior solves to construct cuts valid for perturbed instances. We describe several methods of generating such cuts that navigate the tradeoff between computational expense and strength. We provide sufficient conditions under which PDIs support the disjunctive hull and a tightening step that guarantees support when needed. On perturbed instances from MIPLIB 2017, augmenting branch-and-cut with PDIs substantially improves performance, reducing total solve times on the majority of challenging cases.