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Multi-objective hierarchical genetic algorithms for multilevel redundancy allocation optimization

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  • Kumar, Ranjan
  • Izui, Kazuhiro
  • Yoshimura, Masataka
  • Nishiwaki, Shinji

Abstract

Multilevel redundancy allocation optimization problems (MRAOPs) occur frequently when attempting to maximize the system reliability of a hierarchical system, and almost all complex engineering systems are hierarchical. Despite their practical significance, limited research has been done concerning the solving of simple MRAOPs. These problems are not only NP hard but also involve hierarchical design variables. Genetic algorithms (GAs) have been applied in solving MRAOPs, since they are computationally efficient in solving such problems, unlike exact methods, but their applications has been confined to single-objective formulation of MRAOPs. This paper proposes a multi-objective formulation of MRAOPs and a methodology for solving such problems. In this methodology, a hierarchical GA framework for multi-objective optimization is proposed by introducing hierarchical genotype encoding for design variables. In addition, we implement the proposed approach by integrating the hierarchical genotype encoding scheme with two popular multi-objective genetic algorithms (MOGAs)—the strength Pareto evolutionary genetic algorithm (SPEA2) and the non-dominated sorting genetic algorithm (NSGA-II). In the provided numerical examples, the proposed multi-objective hierarchical approach is applied to solve two hierarchical MRAOPs, a 4- and a 3-level problems. The proposed method is compared with a single-objective optimization method that uses a hierarchical genetic algorithm (HGA), also applied to solve the 3- and 4-level problems. The results show that a multi-objective hierarchical GA (MOHGA) that includes elitism and mechanism for diversity preserving performed better than a single-objective GA that only uses elitism, when solving large-scale MRAOPs. Additionally, the experimental results show that the proposed method with NSGA-II outperformed the proposed method with SPEA2 in finding useful Pareto optimal solution sets.

Suggested Citation

  • Kumar, Ranjan & Izui, Kazuhiro & Yoshimura, Masataka & Nishiwaki, Shinji, 2009. "Multi-objective hierarchical genetic algorithms for multilevel redundancy allocation optimization," Reliability Engineering and System Safety, Elsevier, vol. 94(4), pages 891-904.
    • Handle: RePEc:eee:reensy:v:94:y:2009:i:4:p:891-904
    DOI: 10.1016/j.ress.2008.10.002
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    References listed on IDEAS

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    1. Konak, Abdullah & Coit, David W. & Smith, Alice E., 2006. "Multi-objective optimization using genetic algorithms: A tutorial," Reliability Engineering and System Safety, Elsevier, vol. 91(9), pages 992-1007.
    2. Yun, Won Young & Song, Young Man & Kim, Ho-Gyun, 2007. "Multiple multi-level redundancy allocation in series systems," Reliability Engineering and System Safety, Elsevier, vol. 92(3), pages 308-313.
    3. Sarker, Ruhul & Liang, Ko-Hsin & Newton, Charles, 2002. "A new multiobjective evolutionary algorithm," European Journal of Operational Research, Elsevier, vol. 140(1), pages 12-23, July.
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    Cited by:

    1. Ye, Zhisheng & Li, Zhizhong & Xie, Min, 2010. "Some improvements on adaptive genetic algorithms for reliability-related applications," Reliability Engineering and System Safety, Elsevier, vol. 95(2), pages 120-126.
    2. Ding, Yi & Hu, Yishuang & Li, Daqing, 2021. "Redundancy Optimization for Multi-Performance Multi-State Series-Parallel Systems Considering Reliability Requirements," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    3. Abdullah Konak & Alice E. Smith, 2011. "Efficient Optimization of Reliable Two-Node Connected Networks: A Biobjective Approach," INFORMS Journal on Computing, INFORMS, vol. 23(3), pages 430-445, August.
    4. Faghih-Roohi, Shahrzad & Xie, Min & Ng, Kien Ming & Yam, Richard C.M., 2014. "Dynamic availability assessment and optimal component design of multi-state weighted k-out-of-n systems," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 57-62.
    5. Milia Habib & Farouk Yalaoui & Hicham Chehade & Iman Jarkass & Nazir Chebbo, 2017. "Multi-objective design optimisation of repairable -out-of- subsystems in series with redundant dependency," International Journal of Production Research, Taylor & Francis Journals, vol. 55(23), pages 7000-7021, December.
    6. Khalili-Damghani, Kaveh & Amiri, Maghsoud, 2012. "Solving binary-state multi-objective reliability redundancy allocation series-parallel problem using efficient epsilon-constraint, multi-start partial bound enumeration algorithm, and DEA," Reliability Engineering and System Safety, Elsevier, vol. 103(C), pages 35-44.
    7. Li, Zhaojun & Liao, Haitao & Coit, David W., 2009. "A two-stage approach for multi-objective decision making with applications to system reliability optimization," Reliability Engineering and System Safety, Elsevier, vol. 94(10), pages 1585-1592.
    8. Andrés Cacereño & David Greiner & Blas J. Galván, 2021. "Multi-Objective Optimum Design and Maintenance of Safety Systems: An In-Depth Comparison Study Including Encoding and Scheduling Aspects with NSGA-II," Mathematics, MDPI, vol. 9(15), pages 1-39, July.

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