Review of Traveling Salesman Problem Solution Methods

The Traveling Salesman Problem (TSP) is a key focus in the fields of computer science and operations research, widely applied in areas such as data collection, search and rescue, robot task allocation and scheduling, etc. This paper, by reviewing recent literature, first introduces the definition and mathematical model of the TSP, followed by an exposition of the concepts of classical TSP. Subsequently, an analysis of solving algorithms for the classical Traveling Salesman Problem is conducted, categorizing them into exact algorithms, heuristic algorithms, and learning-based algorithms. The paper then provides an assessment of the advantages and disadvantages associated with these three categories of algorithms, accompanied by an elaborate overview of the research advancements made in recent years. Future research on TSP will focus on exploring undeveloped algorithms and integrating stable ones to address larger-scale problems, enhance solution quality, avoid local optima, and improve solution efficiency. Breakthroughs are anticipated in the application of learning-based methods for solving the Traveling Salesman Problem (TSP).