On the Traveling Salesman Problem with Hierarchical Objective Function

Abstract

We address a novel variant of the wellknown Traveling Salesman Problem (TSP) called the Traveling Salesman Problem with Hierarchical Objective (TSPHO). In this problem, the customers are divided in to several groups with decreasing priority levels, i.e., the first group is more important than the second one and the second one is more important than the third one, and so on. The difference between TSPHO and the classical TSP lies in the objective function. The Hierarchical Objective does not minimize the total travel cost, but aims to minimize the completion time of the first group then the completion time of the second group, etc. A transformation of the TSPHO into an equivalent Asymmetric TSP is first proposed from which one can use efficient TSP solvers such as Concorde or Lin-Kernighan-Helsgaun (LKH) to solve the problem. A genetic algorithm is also developed as an alternative solution. Computational results show the performance of our methods.