Self-Organizing Map for the Curvature-Constrained Traveling Salesman Problem

In this paper, we consider a challenging variant of the traveling salesman problem (TSP) where it is requested to determine the shortest closed curvature-constrained path to visit a set of given locations. The problem is called the Dubins traveling salesman problem in literature and its main difficulty arises from the fact that it is necessary to determine the sequence of visits to the locations together with particular headings of the vehicle at the locations. We propose to apply principles of unsupervised learning of the self-organizing map to simultaneously determine the sequence of the visits together with the headings. A feasibility of the proposed approach is supported by an extensive evaluation and comparison to existing solutions. The presented results indicate that the proposed approach provides competitive solutions to existing heuristics, especially in dense problems, where the optimal sequence of the visits cannot be determined as a solution of the Euclidean TSP.