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Improved heuristics for the bounded-diameter minimum spanning tree problem

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Abstract

Given an undirected, connected, weighted graph and a positive integer k, the bounded-diameter minimum spanning tree (BDMST) problem seeks a spanning tree of the graph with smallest weight, among all spanning trees of the graph, which contain no path with more than k edges. In general, this problem is NP-Hard for 4 ≤  k <  n − 1, where n is the number of vertices in the graph. This work is an improvement over two existing greedy heuristics, called randomized greedy heuristic (RGH) and centre-based tree construction heuristic (CBTC), and a permutation-coded evolutionary algorithm for the BDMST problem. We have proposed two improvements in RGH/CBTC. The first improvement iteratively tries to modify the bounded-diameter spanning tree obtained by RGH/CBTC so as to reduce its cost, whereas the second improves the speed. We have modified the crossover and mutation operators and the decoder used in permutation-coded evolutionary algorithm so as to improve its performance. Computational results show the effectiveness of our approaches. Our approaches obtained better quality solutions in a much shorter time on all test problem instances considered.

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Authors and Affiliations

  1. J. K. Institute of Applied Physics and Technology, Faculty of Science, University of Allahabad, Allahabad, 211002, UP, India

    Alok Singh & Ashok K. Gupta

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  1. Alok Singh
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  2. Ashok K. Gupta
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Correspondence to Alok Singh.

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Singh, A., Gupta, A.K. Improved heuristics for the bounded-diameter minimum spanning tree problem. Soft Comput 11, 911–921 (2007). https://doi.org/10.1007/s00500-006-0142-y

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  • DOI: https://doi.org/10.1007/s00500-006-0142-y

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