  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. In the case where the weights of
the OWA are strictly decreasing, we then propose a mixed integer programming
formulation, and provide dedicated optimality conditions yielding an important
reduction of the size of the program. Next, we present two bounds that can be
used to prune subspaces of solutions either in a shaving phase or in a branch
and bound procedure. The validity of these bounds does not depend on specific
properties of the weights (apart from non-negativity). All these exact
resolution algorithms are compared on the basis of numerical experiments,
according to their respective validity scopes.
