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Multi-Objective Neighborhood Search Algorithm Based on Decomposition for Multi-Objective Minimum Weighted Vertex Cover Problem

Author

Listed:
  • Shuli Hu

    (School of Computer Science and Information Technology, Northeast Normal University, Changchun 130117, China)

  • Xiaoli Wu

    (School of Computer Science and Information Technology, Northeast Normal University, Changchun 130117, China)

  • Huan Liu

    (School of Computer Science and Information Technology, Northeast Normal University, Changchun 130117, China)

  • Yiyuan Wang

    (School of Computer Science and Information Technology, Northeast Normal University, Changchun 130117, China)

  • Ruizhi Li

    (School of Management Science and Information Engineering, Jilin University of Finance and Economics, Changchun 130117, China)

  • Minghao Yin

    (School of Computer Science and Information Technology, Northeast Normal University, Changchun 130117, China
    Key Laboratory of Applied Statistics of MOE, Northeast Normal University, Changchun 130024, China)

Abstract

The multi-objective minimum weighted vertex cover problem aims to minimize the sum of different single type weights simultaneously. In this paper, we focus on the bi-objective minimum weighted vertex cover and propose a multi-objective algorithm integrating iterated neighborhood search with decomposition technique to solve this problem. Initially, we adopt the decomposition method to divide the multi-objective problem into several scalar optimization sub-problems. Meanwhile, to find more possible optimal solutions, we design a mixed score function according to the problem feature, which is applied in initializing procedure and neighborhood search. During the neighborhood search, three operators ( A d d , D e l e t e , S w a p ) explore the search space effectively. We performed numerical experiments on many instances, and the results show the effectiveness of our new algorithm (combining decomposition and neighborhood search with mixed score) on several experimental metrics. We compared our experimental results with the classical multi-objective algorithm non-dominated sorting genetic algorithm II. It was obviously shown that our algorithm can provide much better results than the comparative algorithm considering the different metrics.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jsusta:v:11:y:2019:i:13:p:3634-:d:244959
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. 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.

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