An interactive bi-objective shortest path approach: searching for unsupported nondominated solutions

Abstract

In many network routing problems several conflicting objectives must be considered. Even for the bi-objective shortest path problem, generating and presenting the whole set of nondominated solutions (paths) to a decision maker, in general, is not effective because the number of these paths can be very large. Interactive procedures are adequate to overcome these drawbacks. Current et al. [1] proposed an interactive approach based on a NISE-like procedure to search for nondominated supported solutions and using auxiliar constrained shortest path problems to carry out the search inside the duality gaps. In this paper we propose a new interactive approach to search for unsupported nondominated solutions (lying inside duality gaps) based on a k-shortest path procedure. Both approaches are compared. Scope and purpose Network routing problems are generally multidimensional in nature, and in many cases the explicit consideration of multiple objectives is adequate. Objectives related to cost, time, accessibility, environmental impact, reliability and risk are appropriated for selecting the most satisfactory (“best compromise”) route in many problems. In general there is no single optimal solution in a multiobjective problem but rather, a set of nondominated solutions from which the decision maker must select the most satisfactory. However, generating and presenting the whole set of nondominated paths to a decision maker, in general, is not effective because the number of these paths can be very large. Interactive procedures are adequate to overcome these drawbacks. This paper introduces an interactive procedure to assist the decision maker in identifying the “best compromise” solution for the bi-objective shortest path problem. The procedure incorporates an efficient k-shortest path algorithm to identify nondominated solutions lying inside duality gaps. Test problem results indicate that the procedure can be readily executed on a PC for large-scale instances of problems.