Interactive Search for Compromise Solutions in Multicriteria Graph Problems

In this paper, the purpose is to adapt classical interactive methods to multicriteria combinatorial problems in order to explore the non-dominated solutions set. We propose an interactive procedure alternating a calculation stage determining the current best compromise solution and a dialogue stage allowing decision maker to specify his/her preferences. For the calculation stage, we propose an efficient procedure which relies on algorithms providing k-best solutions of a scalarized version of the problem. Moreover, we show how to exploit previous iterations to speed-up the interactive process. We provide numerical experiments of our method on multicriteria shortest path and spanning tree problems.