A Discrete Hybrid Grey Wolf Optimizer Algorithm to solve QuadraticAssignment Problem

Abstract

Grey Wolf Optimizer (GWO) is one of the popular swarm intelligence-based algorithms inspired bythe hunting behavior of wolves which is emerging as a robust candidate for addressing NP-hard problems.The Quadratic Assignment Problem (QAP) is a complex combinatorial optimization problem with signif-icant research interest due to its diverse real-world and industrial applications. This paper attempts tosolve QAP using GWO and proposes a novel discrete Hybrid Grey Wolf Optimizer (HGWO) that combinesGWO with Tabu Search (TS) to address the QAP. TS is used to enhance the exploitation by searching themost promising regions located by GWO. As QAP is a combinatorial optimization problem, the continu-ous values obtained from the classical GWO are converted to discrete values using the largest real valuemapping. In HGWO, the position of each individual is first updated by GWO and further improved byTS. The performance of HGWO is evaluated through computational experiments on 100 QAP benchmarkinstances, where it achieves optimal or near-optimal solutions for most cases. The numerical results arefurther compared with other well-known algorithms from the literature, such as Genetic Algorithm, BatAlgorithm, Whale Optimization Algorithm and others, where it has shown impressive performance andoutperformed most of the algorithms. Also, statistical tests such as the Friedman non-parametric test andthe Wilcoxon signed rank test are conducted for an unbiased and rigorous comparison. The analysis of thenumerical results obtained demonstrated that HGWO has merit in solving QAP, indicating directions forfuture research in combinatorial optimization strategies