An interactive approach to identify the best compromise solution for two objective shortest path problems

Abstract

In recent years there has been a growing interest in multiobjective path problems. Although efficient algorithms exist for solving single objective shortest path problems, the same is not true for generating the noninferior solution set for multiobjective problems, as the number of noninferior solutions may grow exponentially with the number of nodes. Hansen (1980) [ Lecture Notes in Economics and Mathematical Systems 177 (Edited by M. Beckmann and H.P. Kunzi),pp. 109–127. Springer, Berlin], Climaco and Martins (1982) [ Eur. J. Opl Res. 11, 399–404], Martins (1984) [ Eur. J. Opl. Res. 16, 236–245], and Henig (1985) [ Eur. J. Opl. Res. 25, 281–291] present exact algorithms for generating the entire noninferior solution set for a two objective shortest path problem. All of the above authors acknowledge the computational complexity of the problem and consequently, with the exception of Martins (1984), propose algorithms to generate an approximation of the noninferior solution set. None of these authors, however, recommend direct interaction with the decision makers. In this article, we propose an interactive method to generate an approximation of the noninferior solution set for two objective shortest path problems. The goal of this approach is to assist the decision maker in selecting the preferred or best compromise solution from among the noninferior solutions.