A multiobjective non-dominated sorting genetic algorithm (NSGA-II) for the Multiple Traveling Salesman Problem

This paper considers a multi-objective version of the Multiple Traveling Salesman Problem (MOmTSP). In particular, two objectives are considered: the minimization of the total traveled distance and the balance of the working times of the traveling salesmen. The problem is formulated as an integer multi-objective optimization model. A non-dominated sorting genetic algorithm (NSGA-II) is proposed to solve the MOmTSP. The solution scheme allows one to find a set of ordered solutions in Pareto fronts by considering the concept of dominance. Tests on real world instances and instances adapted from the literature show the effectiveness of the proposed algorithm