Generic CP-Supported CMSA for Binary Integer Linear Programs

TL;DR

This paper introduces a problem-agnostic CMSA metaheuristic for binary ILPs, utilizing a constraint propagation engine, which matches or outperforms CPLEX on various instances, especially harder ones.

Contribution

The paper develops a generic CMSA framework for binary ILPs, incorporating a constraint propagation component to enhance solution construction.

Findings

Matches CPLEX upper bounds on easy instances

Outperforms CPLEX on hard instances

Constraint propagation aids in difficult problem instances

Abstract

Construct, Merge, Solve and Adapt (CMSA) is a general hybrid metaheuristic for solving combinatorial optimization problems. At each iteration, CMSA (1) constructs feasible solutions to the tackled problem instance in a probabilistic way and (2) solves a reduced problem instance (if possible) to optimality. The construction of feasible solutions is hereby problem-specific, usually involving a fast greedy heuristic. The goal of this paper is to design a problem-agnostic CMSA variant whose exclusive input is an integer linear program (ILP). In order to reduce the complexity of this task, the current study is restricted to binary ILPs. In addition to a basic problem-agnostic CMSA variant, we also present an extended version that makes use of a constraint propagation engine for constructing solutions. The results show that our technique is able to match the upper bounds of the standalone application of CPLEX in the context of rather easy-to-solve instances, while it generally outperforms the standalone application of CPLEX in the context of hard instances. Moreover, the results indicate that the support of the constraint propagation engine is useful in the context of problems for which finding feasible solutions is rather difficult.