Efficient Local and Tabu Search Strategies for Large-Scale Quadratic Integer Programming

TL;DR

This paper introduces efficient local and tabu search algorithms for large-scale quadratic integer programming, achieving high-quality solutions faster than existing solvers and addressing a gap in non-convex problem research.

Contribution

It presents a novel closed-form formula for single-variable changes and develops tailored local and tabu search strategies for large-scale QIP problems.

Findings

Strategies outperform Gurobi 11.0.2 in solution quality and speed

Effective for instances with up to 8000 variables

Provides new necessary and sufficient conditions for local improvement

Abstract

This study investigates the area of general quadratic integer programming (QIP), encompassing both unconstrained (UQIP) and constrained (CQIP) variants. These NP-hard problems have far-reaching applications, yet the non-convex cases have received limited attention in the literature. To address this gap, we introduce a closed-form formula for single-variable changes, establishing novel necessary and sufficient conditions for 1-Opt local improvement in UQIP and CQIP. We develop a simple local and sophisticated tabu search with an oscillation strategy tailored for large-scale problems. Experimental results on instances with up to 8000 variables demonstrate the efficiency of these strategies, producing high-quality solutions within a short time. Our approaches significantly outperform the Gurobi 11.0.2 solver.