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

Abstract : 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).