Multi-criteria optimization with the Choquet integral in shortest path problems

The Multi-Criteria Decision Aid (MCDA) research field focuses on building a preference model that helps the Decision Maker (DM) choosing a preferred solution among the set of efficient solutions. The Multi-Objective Combinatorial Optimization (MOCO) research field focuses on algorithms to find a set of efficient solutions. The straightforward approach to integrate preferences in a MOCO algorithm is first to compute a complete set of efficient solutions with a MOCO algorithm and then to use a MCDA preference model. This approach allows to work on these two research fields independently but algorithms computing a complete set of efficient solutions have in general exponential execution times. The aim of our work is to use the preference model during the search of solutions to reduce the computation time