A new relaxation method for the generalized minimum spanning tree problem

We consider a generalization of the minimum spanning tree problem, called the generalized minimum spanning tree problem, denoted by GMST. It is known that the GMST problem is NPNP-hard. We present several mixed integer programming formulations of the problem. Based on a new formulation of the problem we give a new solution procedure that finds the optimal solution of the GMST problem for graphs with nodes up to 240. We discuss the advantages of our approach in comparison with earlier methods.