Abstract: We consider a variant of the classic problem of  the traveling salesman problem (TSP) in combinatorial optimization problem: 
 the close enough traveling salesman problem (CETSP).  Firstly, we comprehensively introduce the history, solving methods, and algorithms for both TSP and CETSP, including exact algorithms (such as branch and bound method, linear programming) and heuristic algorithms (such as particle swarm optimization, greedy algorithms, etc.). The TSP requires finding the shortest path to visit each city  once and return to the starting point given a list of cities and distances. CETSP is a generalization of TSP, allowing the visiting point for each target to be chosen from within a specified neighborhood, rather than  exact location. It is  suitable for practical applications that can  tolerate errors, such as logistics distribution, intelligent transportation, and wireless sensor networks, etc. CETSP has higher flexibility and adaptability, which can significantly reduce computational resources and time consumption, particularly for large-scale problems with greater advantages. Secondly, we introduce  the potential  of CETSP in practical applications, especially in logistics, industrial manufacturing, traffic planning, information and communication, offering effective solutions for improving efficiency, reducing costs, and promoting intelligent decision-making. Finally, we have identified some future research directions for CETSP.

Key words:  , close enough traveling salesman problem, heuristic algorithm, path planning, model application