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Dual-Neighborhood Search for Solving the Minimum Dominating Tree Problem

Author

Listed:
  • Ze Pan

    (School of Computer Science, Hubei University of Technology, Wuhan 430068, China)

  • Xinyun Wu

    (School of Computer Science, Hubei University of Technology, Wuhan 430068, China)

  • Caiquan Xiong

    (School of Computer Science, Hubei University of Technology, Wuhan 430068, China)

Abstract

The minimum dominating tree (MDT) problem consists of finding a minimum weight subgraph from an undirected graph, such that each vertex not in this subgraph is adjacent to at least one of the vertices in it, and the subgraph is connected without any ring structures. This paper presents a dual-neighborhood 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 four 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.

Suggested Citation

  • Ze Pan & Xinyun Wu & Caiquan Xiong, 2023. "Dual-Neighborhood Search for Solving the Minimum Dominating Tree Problem," Mathematics, MDPI, vol. 11(19), pages 1-20, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4214-:d:1256247
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    References listed on IDEAS

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    1. Shuli Hu & Huan Liu & Xiaoli Wu & Ruizhi Li & Junping Zhou & Jianan Wang, 2019. "A Hybrid Framework Combining Genetic Algorithm with Iterated Local Search for the Dominating Tree Problem," Mathematics, MDPI, vol. 7(4), pages 1-14, April.
    2. S. Lin & B. W. Kernighan, 1973. "An Effective Heuristic Algorithm for the Traveling-Salesman Problem," Operations Research, INFORMS, vol. 21(2), pages 498-516, April.
    3. Pop, Petrică C. & Matei, Oliviu & Sabo, Cosmin & Petrovan, Adrian, 2018. "A two-level solution approach for solving the generalized minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 265(2), pages 478-487.
    4. F. Carrabs & R. Cerulli & R. Pentangelo & A. Raiconi, 2018. "A two-level metaheuristic for the all colors shortest path problem," Computational Optimization and Applications, Springer, vol. 71(2), pages 525-551, November.
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