A new hybrid optimization algorithm to solve path selection

This paper introduces an enhanced Hybrid Optimized Path Selection (HOPS) algorithm developed to tackle the Traveling Salesman Problem (TSP). Unlike traditional greedy algorithms and the Hungarian method, HOPS incorporates simulated annealing with temperature scheduling, entropy regularization, row-column constraints, and gradient-driven optimization techniques. These integrated mechanisms effectively help escape local optima and improve the quality of the generated routes.Experimental tests were conducted on TSP instances with 50, 100, and 1000 cities. The results show that HOPS consistently yields shorter path lengths compared to benchmark methods. In the 50-city scenario, HOPS achieved a path length of 6.88, outperforming both the greedy algorithm (8.52) and the Hungarian algorithm (8.35). For the 100-city case, HOPS obtained a path length of 9.47, which is slightly better than the greedy algorithm’s 9.96 and notably lower than the Hungarian algorithm’s 11.18. These experiments confirm that the HOPS algorithm exhibits higher optimization performance and computational efficiency in solving TSP.