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Multi-Neighborhood Simulated Annealing-Based Iterated Local Search for Colored Traveling Salesman Problems

A coloring traveling salesman problem (CTSP) generalizes the well-known multiple traveling salesman problem, where colors are used to differentiate salesmen’s the accessibility to individual cities to be visited. As a useful model for a variety of complex scheduling problems, CTSP is computationally challenging. In this paper, we propose a Multi-neighborhood Simulated Annealing-based Iterated Local Search (MSAILS) to solve it. Starting from an initial solution, it iterates through three sequential search procedures: a multi-neighborhood simulated annealing search to find a local optimum, a local search-enhanced edge assembly crossover to find nearby high-quality solutions around a local optimum, and a solution reconstruction procedure to move away from the current search region. Experimental results on two groups of 45 medium and large benchmark instances show that it significantly outperforms state-of-the-art algorithms. In particular, it is able to discover new upper bounds for 29 instances while matching 8 previous best-known upper bounds. Hence, this work greatly advances the field of CTSP.