An Efficient Method for Solving the Traveling Salesman Problem Using Modern Optimization Algorithms

Metaheuristic algorithms have demonstrated strong effectiveness in solving complex real-world optimization problems. This paper presents two discrete metaheuristic approaches for the Travelling Salesman Problem (TSP): the Discrete Spotted Hyena Optimizer (SHO) and the Grey Wolf Optimizer (GWO). The SHO draws inspiration from the cooperative hunting behaviour of spotted hyenas, and the GWO models the leadership hierarchy and hunting strategies of grey wolves. A hybrid method, MSHOSA (Modified SHO with Simulated Annealing initialization), is proposed to enhance performance further. MSHOSA integrates simulated annealing during the initialization phase to refine starting solutions and applies adaptive swap-sequence operators to balance exploration and exploitation throughout the search. Experiments on over 50 TSPLIB benchmark instances demonstrate that MSHOSA achieves competitive and often improved performance compared with several baseline algorithms, particularly on small- and medium-scale instances. The results highlight the potential of SA-based hybridization to enhance the quality of solutions and mitigate premature convergence in TSP optimization.