A swarm intelligence-based hybrid metaheuristic with tabu search for the quadratic assignment problem

Abstract

The Grey Wolf Optimizer (GWO), inspired by the hunting behavior of grey wolves, is an effective swarm intelligence-based algorithm increasingly recognized for solving NP-hard problems. The Quadratic Assignment Problem (QAP), known for its complexity and widespread industrial applications, presents a significant challenge in combinatorial optimization. This paper introduces a novel discrete variant of GWO for QAP, the Hybrid Grey Wolf Optimizer (HGWO), which integrates an enhanced Tabu Search (TS) to improve GWO’s effectiveness in solving the QAP. This enhanced TS is employed to refine the exploitation phase by focusing on promising areas identified by GWO. Due to the combinatorial nature of QAP, the outcomes of classical GWO are transformed into discrete values using the largest real value mapping technique. In our computational experiments across all 134 QAPLIB benchmark instances, HGWO achieved the best-known solutions for 110 instances. It maintains an impressively low average deviation of 0.20%, demonstrating high accuracy and robustness. Comparative analysis with established algorithms like Genetic Algorithm, Bat Algorithm, and Whale Optimization Algorithm demonstrates that HGWO surpasses most competing methods. Rigorous statistical tests, including the Friedman nonparametric test and the Wilcoxon signed-rank test, validate these results, underscoring HGWO’s potential as a powerful tool for QAP and indicating fruitful directions for future research in combinatorial optimization strategies.