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

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.