On Investigation of Crisp Bi-Objective Formulations for Fuzzy Traveling Salesman Problem and Fuzzy p-Median Problem

Abstract

Abstract We consider two classic problems: the Traveling Salesman Problem and the p-Median Problem. In both problems the total traveling cost (in some sense) is minimized, assuming that all traveling times are known. In most real-word applications the input data are uncertain, and this fact should be taken into account when a solution is constructed. In this paper we investigate bi-objective versions of the problems, where the total cost and fuzzy uncertainty associated with the traveling times (membership function) are optimized. A greedy approximation algorithm is proposed and experimentally tested on instances from TSPLIB library.