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An Ant Colony Optimization Algorithm for the Minimum Weight Vertex Cover Problem

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  • Shyong Shyu
  • Peng-Yeng Yin
  • Bertrand Lin

Abstract

Given an undirected graph and a weighting function defined on the vertex set, the minimum weight vertex cover problem is to find a vertex subset whose total weight is minimum subject to the premise that the selected vertices cover all edges in the graph. In this paper, we introduce a meta-heuristic based upon the Ant Colony Optimization (ACO) approach, to find approximate solutions to the minimum weight vertex cover problem. In the literature, the ACO approach has been successfully applied to several well-known combinatorial optimization problems whose solutions might be in the form of paths on the associated graphs. A solution to the minimum weight vertex cover problem however needs not to constitute a path. The ACO algorithm proposed in this paper incorporates several new features so as to select vertices out of the vertex set whereas the total weight can be minimized as much as possible. Computational experiments are designed and conducted to study the performance of our proposed approach. Numerical results evince that the ACO algorithm demonstrates significant effectiveness and robustness in solving the minimum weight vertex cover problem. Copyright Kluwer Academic Publishers 2004

Suggested Citation

  • Shyong Shyu & Peng-Yeng Yin & Bertrand Lin, 2004. "An Ant Colony Optimization Algorithm for the Minimum Weight Vertex Cover Problem," Annals of Operations Research, Springer, vol. 131(1), pages 283-304, October.
    • Handle: RePEc:spr:annopr:v:131:y:2004:i:1:p:283-304:10.1023/b:anor.0000039523.95673.33
    DOI: 10.1023/B:ANOR.0000039523.95673.33
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    Citations

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    Cited by:

    1. Lin Chen & Jin Peng & Bo Zhang & Shengguo Li, 2017. "Uncertain programming model for uncertain minimum weight vertex covering problem," Journal of Intelligent Manufacturing, Springer, vol. 28(3), pages 625-632, March.
    2. Raka Jovanovic & Antonio P. Sanfilippo & Stefan Voß, 2022. "Fixed set search applied to the multi-objective minimum weighted vertex cover problem," Journal of Heuristics, Springer, vol. 28(4), pages 481-508, August.
    3. Luzhi Wang & Shuli Hu & Mingyang Li & Junping Zhou, 2019. "An Exact Algorithm for Minimum Vertex Cover Problem," Mathematics, MDPI, vol. 7(7), pages 1-8, July.
    4. Taoqing Zhou & Zhipeng Lü & Yang Wang & Junwen Ding & Bo Peng, 2016. "Multi-start iterated tabu search for the minimum weight vertex cover problem," Journal of Combinatorial Optimization, Springer, vol. 32(2), pages 368-384, August.
    5. Pedro Pinacho-Davidson & Christian Blum, 2020. "Barrakuda : A Hybrid Evolutionary Algorithm for Minimum Capacitated Dominating Set Problem," Mathematics, MDPI, vol. 8(11), pages 1-26, October.
    6. Lin, B.M.T. & Lu, C.Y. & Shyu, S.J. & Tsai, C.Y., 2008. "Development of new features of ant colony optimization for flowshop scheduling," International Journal of Production Economics, Elsevier, vol. 112(2), pages 742-755, April.
    7. Stefan Voßs & Andreas Fink & Cees Duin, 2005. "Looking Ahead with the Pilot Method," Annals of Operations Research, Springer, vol. 136(1), pages 285-302, April.
    8. Shuli Hu & Xiaoli Wu & Huan Liu & Yiyuan Wang & Ruizhi Li & Minghao Yin, 2019. "Multi-Objective Neighborhood Search Algorithm Based on Decomposition for Multi-Objective Minimum Weighted Vertex Cover Problem," Sustainability, MDPI, vol. 11(13), pages 1-21, July.
    9. Luciano Ferreira Cruz & Flavia Bernardo Pinto & Lucas Camilotti & Angelo Marcio Oliveira Santanna & Roberto Zanetti Freire & Leandro Santos Coelho, 2022. "Improved multiobjective differential evolution with spherical pruning algorithm for optimizing 3D printing technology parametrization process," Annals of Operations Research, Springer, vol. 319(2), pages 1565-1587, December.
    10. Zhang, Wenjie & Tu, Jianhua & Wu, Lidong, 2019. "A multi-start iterated greedy algorithm for the minimum weight vertex cover P3 problem," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 359-366.

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