Abstract
The Euclidean Bounded Diameter Minimum Spanning Tree (BDMST) Problem aims to find the spanning tree with the lowest cost, or weight, under the constraint that the diameter does not exceed a given integer D, and where the weight of an edge is the Euclidean distance between its two end points (vertices). Several well-known heuristic approaches have been applied to this problem. The bi-objective version of this problem aims to minimize two conflicting objectives, weight (or cost), and diameter. Several heuristics for the BDMST problem have been recast for the bi-objective BDMST problem (or BOMST problem) and their performance studied on the entire range of possible diameter values. While some of the extant heuristics are seen to dominate other heuristics over certain portions of the Pareto front of solutions, no single heuristic performs well over the entire range. This paper presents a hybrid tree construction heuristic that combines a greedy approach with a heuristic strategy for constructing effective tree “backbones”. The performance of the proposed heuristic is shown to be consistently superior to the other extant heuristics on a standard benchmark suite of dense Euclidean graphs widely used in the literature.
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Prakash, V.P., Patvardhan, C., Srivastav, A. (2018). Effective Heuristics for the Bi-objective Euclidean Bounded Diameter Minimum Spanning Tree Problem. In: Bhattacharyya, P., Sastry, H., Marriboyina, V., Sharma, R. (eds) Smart and Innovative Trends in Next Generation Computing Technologies. NGCT 2017. Communications in Computer and Information Science, vol 827. Springer, Singapore. https://doi.org/10.1007/978-981-10-8657-1_44
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