Comparison of Heuristics for the Colorful Traveling Salesman Problem

In the Colorful Traveling Salesman Problem (CTSP), given a graph G with a (not necessarily distinct) label (color) assigned to each edge, a Hamiltonian tour with the minimum number of different labels is sought. The problem is a variant of the well-known Hamiltonian Cycle problem and has potential applications in telecommunication networks, optical networks, and multimodal transportation networks, in which one aims to ensure connectivity or other properties by means of a limited number of connection types. We propose two new heuristics based on the deconstruction of a Hamiltonian tour into subpaths and their reconstruction into a new tour, as well as an adaptation of an existing approach. Extensive experimentation shows the effectiveness of the proposed approaches.