A novel local search for unicost set covering problem using hyperedge configuration checking and weight diversity

基于超边配置检测和权值多样化策略的局部搜索改进算法求解集合覆盖问题

Science China Information Sciences volume 60, Article number: 062103 (2017) Cite this article

Abstract

The unicost version of well-known set covering problem (SCP) is central to a wide variety of practical applications for which finding an optimal solution quickly is crucial. In this paper, we propose a new local searchbased algorithm for the unicost SCP which follows the general framework of the popular stochastic local search with a particular focus on the hyperedge selection strategy and weight diversity strategy. Specifically, a strategy as called hyperedge configuration checking strategy is proposed here to avoid the search trajectory which leads to local optima. Additionally, a new weight diversity strategy is proposed for the diversification of search results, by changing the weight of both covered and uncovered vertices in the current solution. The experimental results show that our algorithm significantly outperforms the state-of-the-art heuristic algorithm by one to two orders of magnitudes on the 85 classical instances. Also, our algorithm improves the current optimal solutions of 11 instances.

创新点

本文提出了一个基于随机局部搜索求解集合覆盖的算法. 在本文中, 提出一种超边配置检测策略用来避免陷入局部最优. 更重要地, 通过改变未覆盖和覆盖顶点的权值,本文设计了一种权值多样化策略用来得到更多地不同的解. 在经典的85个测试用例上, 实验结果给出本文设计的局部搜索算法比目前最好的启发式算法,能够使用更短的时间找到更好的候选解.

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Acknowledgments

This work was supported in part by National Natural Science Foundation of China (Grant Nos. 61272208, 61370156, 61402196, 61503074, 61672261), Natural Science Foundation of Zhejiang Province (LY16F020004), and Program for New Century Excellent Talents in University (Grant No. NCET-13-0724). The authors of this paper express sincere gratitude to all the anonymous reviewers for their hard work.

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Affiliations

  1. Symbol Computation and Knowledge Engineer of Ministry of Education, Jilin University, Changchun, 130012, China

    Yiyuan Wang, Dantong Ouyang, Liming Zhang & Minghao Yin

  2. College of Computer Science and Technology, Jilin University, Changchun, 130012, China

    Yiyuan Wang, Dantong Ouyang & Liming Zhang

  3. School of Computer Science and Information Technology, Northeast Normal University, Changchun, 130117, China

    Minghao Yin

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  1. Yiyuan Wang
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  2. Dantong Ouyang
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  3. Liming Zhang
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  4. Minghao Yin
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Correspondence to Minghao Yin.

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Wang, Y., Ouyang, D., Zhang, L. et al. A novel local search for unicost set covering problem using hyperedge configuration checking and weight diversity. Sci. China Inf. Sci. 60, 062103 (2017). https://doi.org/10.1007/s11432-015-5377-8

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Keywords

  • unicost set covering problem
  • hyperedge configuration checking
  • local search
  • weight diversity strategy
  • hyperedge selection strategy

关键词

  • 集合覆盖问题
  • 超边配置检测
  • 局部搜索
  • 权值多样化策略
  • 超边选择策略