Solving Colored Traveling Salesman Problem via Multi-neighborhood Simulated Annealing Search

A colored traveling salesman problem (CTSP) is an important variant of the well-known multiple traveling salesman problem, which uses colors to differentiate salesmen’s accessibility to individual cities to be visited. As a highly useful model for some complex scheduling problems, CTSP is NP-hard. A Multi-neighborhood Simulated Annealing Search (MSAS) approach is proposed to solve it in this paper. Starting from an initial solution, it iterates through two complementary neighborhoods: intra-route and inter-route neighborhoods. Experiments on three groups of 60 widely-used benchmark instances show that it achieves highly competitive performance compared to state-of-the-art algorithms. Moreover, MSAS can be integrated into other search methods to further improve performance, which is demonstrated by using a recently proposed iterated two-phase local search.