Restricted dynamic programming based neighborhoods for the hop‐constrained minimum spanning tree problem

In this paper we develop, study and test new neighborhood structures for the Hop‐constrained Minimum Spanning Tree Problem (HMSTP). These neighborhoods are defined by restricted versions of a new dynamic programming formulation for the problem and provide a systematic way of searching neighborhood structures based on node‐level exchanges. We have also developed several local search methods that are based on the new neighborhoods. Computational experiments for a set of benchmark instances with up to 80 nodes show that the more elaborate methods produce in a quite fast way, heuristic solutions that are, for all cases, within 2% of the optimum.