“…The traveling salesman problem (TSP) is a typical non-deterministic polynomial (NP)hard problem with the goal of designing the shortest route for a traveler to visit each city without repetition, followed by returning to the starting city. In production and life, TSP has been widely used as a model in many fields, such as vehicle path planning [1,2,3], machine learning [4], temporal graphs [5], word sense disambiguation [6], green logistics [7], fuel efficiency management [8], wireless charging [9], and so on. Hence, solving the TSP is of great significance for household, civil, and military applications.…”