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Evolutionary Algorithm on General Cover with Theoretically Guaranteed Approximation Ratio

Author

Listed:
  • Yaoyao Zhang

    (College of Mathematics and System Science, Xinjiang University, Urumqi, Xinjiang 830046, China)

  • Chaojie Zhu

    (School of Mathematical Sciences, Zhejiang Normal University, Jinhua, Zhejiang 321004, China)

  • Shaojie Tang

    (Naveen Jindal School of Management, University of Texas at Dallas, Richardson, Texas 75080)

  • Yingli Ran

    (School of Mathematical Sciences, Zhejiang Normal University, Jinhua, Zhejiang 321004, China)

  • Ding-Zhu Du

    (Department of Computer Science, University of Texas at Dallas, Richardson, Texas 75080)

  • Zhao Zhang

    (School of Mathematical Sciences, Zhejiang Normal University, Jinhua, Zhejiang 321004, China)

Abstract

Theoretical studies on evolutionary algorithms have developed vigorously in recent years. Many such algorithms have theoretical guarantees in both running time and approximation ratio. Some approximation mechanism seems to be inherently embedded in many evolutionary algorithms. In this paper, we identify such a relation by proposing a unified analysis framework for a global simple multiobjective evolutionary algorithm (GSEMO) and apply it on a minimum weight general cover problem, which is general enough to subsume many important problems including the minimum submodular cover problem in which the submodular function is real-valued, and the minimum connected dominating set problem for which the potential function is nonsubmodular. We show that GSEMO yields theoretically guaranteed approximation ratios matching those achievable by a greedy algorithm in expected polynomial time when the potential function g is polynomial in the input size and the minimum gap between different g -values is a constant.

Suggested Citation

  • Yaoyao Zhang & Chaojie Zhu & Shaojie Tang & Yingli Ran & Ding-Zhu Du & Zhao Zhang, 2024. "Evolutionary Algorithm on General Cover with Theoretically Guaranteed Approximation Ratio," INFORMS Journal on Computing, INFORMS, vol. 36(2), pages 510-525, March.
    • Handle: RePEc:inm:orijoc:v:36:y:2024:i:2:p:510-525
    DOI: 10.1287/ijoc.2022.0327
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    References listed on IDEAS

    as
    1. Jiao Zhou & Zhao Zhang & Weili Wu & Kai Xing, 2014. "A greedy algorithm for the fault-tolerant connected dominating set in a general graph," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 310-319, July.
    2. Ding-Zhu Du & Ker-I Ko & Xiaodong Hu, 2012. "Design and Analysis of Approximation Algorithms," Springer Optimization and Its Applications, Springer, number 978-1-4614-1701-9, June.
    Full references (including those not matched with items on IDEAS)

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