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Dual Neighborhoods Search for Solving The Minimum Dominating Tree Problem
Version 1
: Received: 11 August 2023 / Approved: 11 August 2023 / Online: 14 August 2023 (09:13:05 CEST)
A peer-reviewed article of this Preprint also exists.
Pan, Z.; Wu, X.; Xiong, C. Dual-Neighborhood Search for Solving the Minimum Dominating Tree Problem. Mathematics 2023, 11, 4214. Pan, Z.; Wu, X.; Xiong, C. Dual-Neighborhood Search for Solving the Minimum Dominating Tree Problem. Mathematics 2023, 11, 4214.
Abstract
The minimum dominating tree (MDT) problem consists of finding a minimum weight sub-graph from an undirected graph, such that each vertex not in this sub-graph is adjacent to at least one of the vertices in it, and the sub-graph is connected without any ring structures. This paper presents a Dual Neighborhoods Search (DNS) algorithm for solving the MDT problem, which integrates several distinguishing features, such as two neighborhoods collaboratively working for optimizing the objective function, a fast neighborhood evaluation method to boost the searching effectiveness, and several diversification techniques to help the searching process jump out of the local optimum trap thus obtaining better solutions. DNS improves the previous best-known results for 4 public benchmark instances while providing competitive results for the remaining ones. Several ingredients of DNS are investigated to demonstrate the importance of the proposed ideas and techniques.
Keywords
Meta-heuristic ; Dominating tree; Dual neighborhoods; Fast neighborhood evaluation; Optimization
Subject
Computer Science and Mathematics, Data Structures, Algorithms and Complexity
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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