The multiobjective traveling salesman problem: A survey and a new approach

Abstract

The traveling salesman problem (TSP) is a challenging problem in combinatorial optimization. In this paper we consider the multiobjective TSP for which the aim is to obtain or to approximate the set of efficient solutions. In a first step, we classify and describe briefly the existing works, that are essentially based on the use of metaheuristics. In a second step, we propose a new method, called two-phase Pareto local search. In the first phase of this method, an initial population composed of an approximation to the extreme supported efficient solutions is generated. The second phase is a Pareto local search applied to all solutions of the initial population. The method does not use any numerical parameter. We show that using the combination of these two techniques-good initial population generation and Pareto local search-gives, on the majority of the instances tested, better results than state-of-the-art algorithms. © 2010 Springer-Verlag Berlin Heidelberg.