The matching relaxation for a class of generalized set partitioning problems

TL;DR

This paper proposes a novel discrete relaxation technique for set partitioning problems with packing constraints, improving bounds and solution methods, demonstrated through maritime logistics benchmarks.

Contribution

Introduces a new combinatorial relaxation based on maximum weighted matchings for set partitioning problems with packing constraints.

Findings

Provides effective dual bounds for the problems

Enhances variable reduction techniques and heuristics

Achieves promising computational results on benchmarks

Abstract

This paper introduces a discrete relaxation for the class of combinatorial optimization problems which can be described by a set partitioning formulation under packing constraints. We present two combinatorial relaxations based on computing maximum weighted matchings in suitable graphs. Besides providing dual bounds, the relaxations are also used on a variable reduction technique and a matheuristic. We show how that general method can be tailored to sample applications, and also perform a successful computational evaluation with benchmark instances of a problem in maritime logistics.