Abstract
The traveling salesman problem (TSP) remains challenging for metaheuristic algorithms, especially as the number of cities increases. This study proposes the particle-guided adaptive grey wolf optimizer (PMGHWO), which combines grey wolf optimizer (GWO)-based leadership guidance with crossover, particle-guided perturbation, and adaptive local refinement. PMGHWO was evaluated on ten TSPLIB instances and compared with grey wolf optimizer (GWO), genetic algorithms (GA), particle swarm optimization (PSO), whale optimization algorithm (WOA), and Harris Hawks optimization (HHO) under the same experimental conditions. The proposed method achieved shorter average tours on all tested instances, with reductions of 18.75% compared with GWO, 19.77% with HHO, 23.30% with GA, 39.08% with WOA, and 57.51% with PSO. Friedman and Wilcoxon tests confirmed significant differences between PMGHWO and the compared methods. The ablation study showed that adaptive refinement had the strongest effect on solution quality, while the influence of particle-guided perturbation and crossover varied across the benchmark instances. Although PMGHWO required more computation than the original GWO, its runtime remained competitive with several of the other methods. Overall, the results show that PMGHWO is a promising approach for TSP optimization and warrants further evaluation on larger and more complex combinatorial problems.