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NSGA-II based fuzzy multi-objective reliability analysis

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International Journal of System Assurance Engineering and Management Aims and scope Submit manuscript

Abstract

In many practical situations, we need to reduce the cost of the system and improve its reliability simultaneously. At the same time, all the design data involved in the system design are not precisely known. Incompleteness and unreliability of input information are typical for many practical problems in the multi-objective optimization of system design. In this work, we have analyzed fuzzy multi-objective optimization problem of main characteristics of system design such as reliability and cost simultaneously based on non-dominated sorting genetic algorithm-II (NSGA-II). NSGA-II is one of the multi-objective evolutionary algorithms (MOEAs), provides the decision-maker with a complete picture of the Pareto-optimal solutions space. It finds increasing applications in solving the multi-objective optimization problem (MOOP) because of low computational requirements, elitism, and parameter-less sharing approach. A brief description of NSGA-II and its use for MOOP is given. We have obtained multiple solutions (Pareto-optimal solutions) in a single simulation run. A numerical example of a series system is given to illustrate the proposed approach.

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References

  • Aggarwal KK, Gupta JS (1975) On minimizing the cost of reliable systems. IEEE Trans Reliab 24(3):205

    Article  Google Scholar 

  • Bellman RE, Zadeh LA (1970) Decision making in a fuzzy environment. Manag Sci 17:141–164

    Article  MATH  MathSciNet  Google Scholar 

  • Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, New York

    MATH  Google Scholar 

  • Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197

    Article  Google Scholar 

  • Dhingra AK (1992) Optimal apportionment of reliability and redundancy in series systems under multiple objectives. IEEE Trans Reliab 41(4):576–582

    Article  MATH  Google Scholar 

  • Huang HZ (1997) Fuzzy multi-objective optimization decision-making of reliability of series system. Microelectron Reliab 37(3):447–449

    Article  Google Scholar 

  • Inagaki T, Inoue K, Akashi H (1978) Interactive optimization of system reliability under multiple objectives. IEEE Trans Reliab 27(4):264–267

    Article  MATH  Google Scholar 

  • Kishore A, Yadav SP, Kumar S (2009) A multi-objective genetic algorithm for reliability optimization problem. Int J Perform Eng 5(3):227–234

    Google Scholar 

  • Knowles J, Corne D (1999) The Pareto archived evolution strategy: a new baseline algorithm for multiobjective optimization. In: Proceedings of the 1999 Congress on evolutionary computation. IEEE Press, Piscataway, pp 98–105. doi:10.1109/CEC.1999.781913

  • Kuo W (2007) Recent advances in optimal reliability allocation. IEEE Trans Syst Man Cybern Part A Syst Hum 37(2):143–156

    Article  Google Scholar 

  • Kuo W, Prasad VR, Tillman FA, Hwang CL (2001) Optimal reliability design. Cambridge University Press, Cambridge

    Google Scholar 

  • Mahapatra GS, Roy TK (2006) Fuzzy multi-objective mathematical programming on reliability optimization model. Appl Math Comput 174:643–659

    Article  MATH  MathSciNet  Google Scholar 

  • Park KS (1987) Fuzzy apportionment of system reliability. IEEE Trans Reliab 36:129–132

    Article  MATH  Google Scholar 

  • Ravi V, Reddy PJ, Zimmermann HJ (2000) Fuzzy global optimization of complex system reliability. IEEE Trans Fuzzy Syst 8(3):241–248

    Article  Google Scholar 

  • Sakawa M (1978) Multi-objective optimization by the surrogate worth trade-off method. IEEE Trans Reliab 27:311–314

    Article  MATH  Google Scholar 

  • Salazar D, Rocco CM, Galvan BJ (2006) Optimization of constrained multiple objective reliability problems using evolutionary algorithms. Reliab Eng Syst Saf 91:1057–1070

    Article  Google Scholar 

  • Sharifi M, Guilani PP, Shahriari M (2016) Using NSGA-II algorithm for a three objective redundancy allocation problem with k-out-of-n sub-systems. J Optim Ind Eng 19:87–95

    Google Scholar 

  • Srinivas N, Deb K (1994) Multi-objective optimization using non-dominated sorting in genetic algorithms. Evol Comput 2(3):221–248

    Article  Google Scholar 

  • Vitorino RM, Jorge HM, Neves LP (2015) Multi-objective optimization using NSGA-II for power distribution system reconfiguration. Int Trans Electr Energy Syst 25:38–53

    Article  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353

    Article  MATH  Google Scholar 

  • Zimmermann HJ (1991) Fuzzy set theory and applications, 2nd edn. Kluwer, Boston

    Book  MATH  Google Scholar 

  • Zitzler E, Thiele L (1998) An evolutionary algorithm for multi-objective optimization: the strength Pareto approach, Technical report 43. Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH), Zurich

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Acknowledgement

The first author gratefully acknowledges the financial support given by the Ministry of Human Resource and Development (MHRD), Govt. of India.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, 247667, India

    Hemant Kumar & Shiv Prasad Yadav

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  1. Hemant Kumar
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  2. Shiv Prasad Yadav
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Correspondence to Hemant Kumar.

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Kumar, H., Yadav, S.P. NSGA-II based fuzzy multi-objective reliability analysis. Int J Syst Assur Eng Manag 8, 817–825 (2017). https://doi.org/10.1007/s13198-017-0672-y

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  • DOI: https://doi.org/10.1007/s13198-017-0672-y

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