Upper and lower bounding strategies for the generalized minimum spanning tree problem [An article from: European Journal of Operational Research]

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Description:
We address the generalized minimum spanning tree problem (GMST) which requires spanning at least one vertex out of every set of disjoint vertices in a graph. We show that the geometric version of this problem is NP-hard, and we propose two stochastic heuristics. The first one is a very fast randomized greedy search algorithm and the second one being a genetic algorithm. Also, we investigate some existing integer programming formulations and present an new one. A new Lagrangian based lower bound is proposed and implemented to assess the performance of the heuristics. Computational experiments performed on a large set of randomly generated instances with up to 1000 vertices and 10,000 edges provide evidence of the good performance of the proposed heuristics.