An Evolutionary Algorithm with Path Relinking for a Bi-objective Multiple Traveling Salesman Problem with Profits

Nacima Labadie (1) , Jan Melechovský (2) , Christian Prins (1)

1 LOSI - Laboratoire d'Optimisation des Systèmes Industriels
2 VSE - Prague University of Economics and Business

This chapter deals with a bi-objective multiple traveling salesman problem with profits (BOMTSPP), generalizing the classical TSP with profits (TSPP). The TSPP is in fact a generic name for TSP problems taking into account the length of the tour and profits collected at customers. However, all these problems are not really bi-objective: the two criteria are aggregated into a single objective or one of them is replaced by a constraint. Our BOMTSPP aims at building m cycles covering a subset of potential customers so that the total collected profit is maximized and the overall traveling distance is minimized. This new problem generalizes the TSPP in two directions: a true bi-objective treatment and the construction of multiple tours. The proposed solution method is an effective evolutionary algorithm, reinforced by a post-optimization procedure based on path-relinking (PR).

Mots clés: Multiple traveling salesman problem; Traveling salesman problem with profits; Multi-objective optimization; Evolutionary algorithm; Path-relinking

Domaines: Recherche opérationnelle [math.OC]

Nacima Labadie, Jan Melechovský, Christian Prins. An Evolutionary Algorithm with Path Relinking for a Bi-objective Multiple Traveling Salesman Problem with Profits. Applications of Multi-Criteria and Game Theory Approaches, pp.195-223, 2014, Springer Series in Advanced Manufacturing, 978-1-4471-5295-8. ⟨10.1007/978-1-4471-5295-8_10⟩. ⟨hal-02490543⟩