A bicriteria Traveling Salesman Problem with sequence priorities

Abstract

This paper introduces a bicriteria version of the classical Traveling Salesman Problem (TSP) which is motivated by various applications in the context of service delivery. The additional objective allows to take priorities among locations into account while minimizing the costs of traveling. For this, cities in the input are given in a strict ordering, e.g., due to arrival times of delivery requests. The goal is to compute the set of efficient solutions when both objectives are optimized simultaneously. To the best of our knowledge, this variation of TSP has not been studied before. After making the notion of priorities precise, we present a local-search algorithm to approximate the set of non-dominated solutions. While still being conceptionally easy, our algorithm employs different means of intensification and diversification in a way we call breadth-first local search. We maintain one candidate solution for each possible value of the additional objective in a polynomially-sized archive, and try to improve this set towards the Pareto front. Experimental results with test data from TSPLIB show that this is a reasonable approach to attack the problem. © Springer-Verlag Berlin Heidelberg 2009.