The Traveling Salesman Problem with flexible coloring

This paper introduces a new generalized version of the Traveling Salesman Problem (TSP)(TSP) in which nodes belong to various color classes and each color class must be visited as an entity. We distinguish the cases of the problem for which the colors are either pre-assigned or can be selected from a given subset of colors. We establish computational complexity and provide concise formulations for the problems that lend themselves to derive tight lower bounds. Exact solutions for special cases and a two-phase heuristic for the general case are provided. Worst case performance and asymptotic performance of the heuristic are analyzed and the effectiveness of the proposed heuristic in solving large industrial size problems is empirically demonstrated.