Neighborhood Search for the Bounded Diameter Minimum Spaning Tree

Many optimization problems including the network design problem of finding the bounded diameter minimum spanning tree are computationally intractable. Therefore, a practical approach for solving such problems is to employ heuristic algorithms that can find solution close to the optimal one within a reasonable amount of time. Neighborhood search algorithms are a wide class of algorithms where at each iteration an improved solution is found by searching the “neighborhood” of the current solution. A critical issue in the design of a neighborhood search algorithm is the choice of the neighborhood structure. Literature reveals that the larger the neighborhood, the better is the quality of the locally optimal solutions and the greater is the accuracy of the final solution obtained. At the same time, the larger the neighborhood search, the longer it takes to search the neighborhood for optimum. For this reason, an efficient search strategy is required to produce an effective heuristic in large neighborhoods. This paper focus on two known neighborhood structures for the BDMST problem. Both types of neighborhoods are large in the sense that they contain exponentially large number of candidate solutions. A novel intelligent neighborhood search technique (INST) is introduced and compared with the previously published local search techniques. Keywords-Bounded Diameter Minimum spanning tree, Local search, Heuristics.