Shortest path problems with partial information: Models and algorithms for detecting dominance

Abstract

In this work we focus on partial information models for the well-known shortest path problem, where we consider multiple instances of values for the parameters that determine the cost of each arc. This allows coping with the uncertainty about the future, the imprecision of data, the arbitrariness of some options, the evolving values of the decision makers (DMs) and/or the multiplicity of DMs (in group decision making). This paper proves some results and presents detailed algorithms to identify the set of non dominated paths, a concept from decision theory under partial information. We first address problems with a finite set of instances, then problems with a general (eventually not discrete) set of instances and finally we study a particular case of the latter, which complies with a condition that may hold in some situations. To deal with these partial information problems we propose a new use for existing multicriteria algorithms based on the ranking of shortest paths.