Improved heuristics for the bounded-diameter minimum spanning tree problem

Authors:
Alok Singh;Ashok K. Gupta
Affiliations:
University of Allahabad, J. K. Institute of Applied Physics and Technology, Faculty of Science, 211002, Allahabad, UP, India;University of Allahabad, J. K. Institute of Applied Physics and Technology, Faculty of Science, 211002, Allahabad, UP, India
Venue:
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Year:
2007

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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.