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Practical solutions for multi-objective optimization: An application to system reliability design problems

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  • Taboada, Heidi A.
  • Baheranwala, Fatema
  • Coit, David W.
  • Wattanapongsakorn, Naruemon

Abstract

For multiple-objective optimization problems, a common solution methodology is to determine a Pareto optimal set. Unfortunately, these sets are often large and can become difficult to comprehend and consider. Two methods are presented as practical approaches to reduce the size of the Pareto optimal set for multiple-objective system reliability design problems. The first method is a pseudo-ranking scheme that helps the decision maker select solutions that reflect his/her objective function priorities. In the second approach, we used data mining clustering techniques to group the data by using the k-means algorithm to find clusters of similar solutions. This provides the decision maker with just k general solutions to choose from. With this second method, from the clustered Pareto optimal set, we attempted to find solutions which are likely to be more relevant to the decision maker. These are solutions where a small improvement in one objective would lead to a large deterioration in at least one other objective. To demonstrate how these methods work, the well-known redundancy allocation problem was solved as a multiple objective problem by using the NSGA genetic algorithm to initially find the Pareto optimal solutions, and then, the two proposed methods are applied to prune the Pareto set.

Suggested Citation

  • Taboada, Heidi A. & Baheranwala, Fatema & Coit, David W. & Wattanapongsakorn, Naruemon, 2007. "Practical solutions for multi-objective optimization: An application to system reliability design problems," Reliability Engineering and System Safety, Elsevier, vol. 92(3), pages 314-322.
  • Handle: RePEc:eee:reensy:v:92:y:2007:i:3:p:314-322
    DOI: 10.1016/j.ress.2006.04.014
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    Cited by:

    1. Sanath Kahagalage & Hasan Hüseyin Turan & Fatemeh Jalalvand & Sondoss El Sawah, 2023. "A novel graph-theoretical clustering approach to find a reduced set with extreme solutions of Pareto optimal solutions for multi-objective optimization problems," Journal of Global Optimization, Springer, vol. 86(2), pages 467-494, June.
    2. Nahar F. Alshammari & Mohamed Mahmoud Samy & Shimaa Barakat, 2023. "Comprehensive Analysis of Multi-Objective Optimization Algorithms for Sustainable Hybrid Electric Vehicle Charging Systems," Mathematics, MDPI, vol. 11(7), pages 1-31, April.
    3. Cao, Dingzhou & Murat, Alper & Chinnam, Ratna Babu, 2013. "Efficient exact optimization of multi-objective redundancy allocation problems in series-parallel systems," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 154-163.
    4. Juan Li & Bin Xin & Panos M. Pardalos & Jie Chen, 2021. "Solving bi-objective uncertain stochastic resource allocation problems by the CVaR-based risk measure and decomposition-based multi-objective evolutionary algorithms," Annals of Operations Research, Springer, vol. 296(1), pages 639-666, January.
    5. Kayedpour, Farjam & Amiri, Maghsoud & Rafizadeh, Mahmoud & Shahryari Nia, Arash, 2017. "Multi-objective redundancy allocation problem for a system with repairable components considering instantaneous availability and strategy selection," Reliability Engineering and System Safety, Elsevier, vol. 160(C), pages 11-20.
    6. Safari, Jalal, 2012. "Multi-objective reliability optimization of series-parallel systems with a choice of redundancy strategies," Reliability Engineering and System Safety, Elsevier, vol. 108(C), pages 10-20.
    7. Hemant Kumar & Shiv Prasad Yadav, 2019. "Fuzzy rule-based reliability analysis using NSGA-II," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(5), pages 953-972, October.
    8. 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.
    9. Fiondella, Lance & Lin, Yi-Kuei & Pham, Hoang & Chang, Ping-Chen & Li, Chendong, 2017. "A confidence-based approach to reliability design considering correlated failures," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 102-114.
    10. Khalili-Damghani, Kaveh & Abtahi, Amir-Reza & Tavana, Madjid, 2013. "A new multi-objective particle swarm optimization method for solving reliability redundancy allocation problems," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 58-75.
    11. Zhu, Xiaoyan & Wang, Jun & Yuan, Tao, 2019. "Design and maintenance for the data storage system considering system rebuilding process," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    12. 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.
    13. Lins, Isis Didier & Rêgo, Leandro Chaves & Moura, Márcio das Chagas & Droguett, Enrique López, 2013. "Selection of security system design via games of imperfect information and multi-objective genetic algorithm," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 59-66.
    14. 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.
    15. H A Taboada & J F Espiritu & D W Coit, 2008. "Design allocation of multistate series-parallel systems for power systems planning: A multiple objective evolutionary approach," Journal of Risk and Reliability, , vol. 222(3), pages 381-391, September.
    16. Cao, Ran & Coit, David W. & Hou, Wei & Yang, Yushu, 2020. "Game theory based solution selection for multi-objective redundancy allocation in interval-valued problem parameters," Reliability Engineering and System Safety, Elsevier, vol. 199(C).
    17. Petchrompo, Sanyapong & Wannakrairot, Anupong & Parlikad, Ajith Kumar, 2022. "Pruning Pareto optimal solutions for multi-objective portfolio asset management," European Journal of Operational Research, Elsevier, vol. 297(1), pages 203-220.
    18. Shan, Songqing & Wang, G. Gary, 2008. "Reliable design space and complete single-loop reliability-based design optimization," Reliability Engineering and System Safety, Elsevier, vol. 93(8), pages 1218-1230.
    19. Zhang, Enze & Wu, Yifei & Chen, Qingwei, 2014. "A practical approach for solving multi-objective reliability redundancy allocation problems using extended bare-bones particle swarm optimization," Reliability Engineering and System Safety, Elsevier, vol. 127(C), pages 65-76.
    20. Dolatshahi-Zand, Ali & Khalili-Damghani, Kaveh, 2015. "Design of SCADA water resource management control center by a bi-objective redundancy allocation problem and particle swarm optimization," Reliability Engineering and System Safety, Elsevier, vol. 133(C), pages 11-21.
    21. Selçuklu, Saltuk Buğra & Coit, David W. & Felder, Frank A., 2020. "Pareto uncertainty index for evaluating and comparing solutions for stochastic multiple objective problems," European Journal of Operational Research, Elsevier, vol. 284(2), pages 644-659.
    22. Mlakar, Miha & Petelin, Dejan & Tušar, Tea & Filipič, Bogdan, 2015. "GP-DEMO: Differential Evolution for Multiobjective Optimization based on Gaussian Process models," European Journal of Operational Research, Elsevier, vol. 243(2), pages 347-361.
    23. Jorge Salas & Víctor Yepes, 2019. "VisualUVAM: A Decision Support System Addressing the Curse of Dimensionality for the Multi-Scale Assessment of Urban Vulnerability in Spain," Sustainability, MDPI, vol. 11(8), pages 1-17, April.

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