Exact algorithms for OWA-optimization in multiobjective spanning tree problems

This paper deals with the multiobjective version of the optimal spanning tree problem. More precisely, we are interested in determining the optimal spanning tree according to an Ordered Weighted Average (OWA) of its objective values. We first show that the problem is weakly NP-hard. We then propose different mixed integer programming formulations, according to different subclasses of OWA functions. Furthermore, we provide various preprocessing procedures, the validity scopes of which depends again on the considered subclass of OWA functions. For designing such procedures, we propose generalized optimality conditions and efficiently computable bounds. These procedures enable to reduce the size of the instances before launching an off-the-shelf software for solving the mixed integer program. Their impact on the resolution time is evaluated on the basis of numerical experiments.