Local Search for Integer Quadratic Programming

TL;DR

This paper introduces LS-IQCQP, a novel local search solver for Integer Quadratic Programming that outperforms existing methods and sets new records on benchmark instances.

Contribution

It develops four new local search operators and a two-mode algorithm, advancing the application of local search to IQP problems.

Findings

LS-IQCQP is competitive with Gurobi.

It outperforms other state-of-the-art solvers.

Six new records were established on benchmarks.

Abstract

Integer Quadratic Programming (IQP) is an important problem in operations research. Local search is a powerful method for solving hard problems, but the research on local search algorithms for IQP solving is still on its early stage. This paper develops an efficient local search solver for solving general IQP, called LS-IQCQP. We propose four new local search operators for IQP that can handle quadratic terms in the objective function, constraints or both. Furthermore, a two-mode local search algorithm is introduced, utilizing newly designed scoring functions to enhance the search process. Experiments are conducted on standard IQP benchmarks QPLIB and MINLPLIB, comparing LS-IQCQP with several state-of-the-art IQP solvers. Experimental results demonstrate that LS-IQCQP is competitive with the most powerful commercial solver Gurobi and outperforms other state-of-the-art solvers. Moreover, LS-IQCQP has established 6 new records for QPLIB and MINLPLIB open instances.