A new approach for the multiobjective minimum spanning tree

This paper presents a new algorithm for the multiobjective minimum spanning tree problem that can be used with any number of criteria. It is based on a labelling algorithm for the multiobjective shortest path problem in a transformed network. Some restrictions are added to the paths (minimal paths) in order to obtain a one-to-one correspondence between trees in the original network and minimal paths in the transformed one. The correctness of the algorithm is proved as well as the presentation of a short example. Finally, some computational experiments were reported showing the proposed method outperforms the others in the literature. A deep study is also done about the number of nondominated solutions and a statistical model is presented to predict its variation in the number of nodes and criteria. All the test instances used are available through the web page http://www.mat.uc.pt/~zeluis/INVESTIG/MOMST/momst.htm.