Linguistic Based Pareto Guided Fuzzy Multi-Objective Optimization

Hemant Kumar¹ , Narendra Swami²

Section:Research Paper, Product Type: Journal-Paper
Vol.8 , Issue.3 , pp.6-10, Sep-2021

Online published on Sep 30, 2021

Copyright © Hemant Kumar, Narendra Swami . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In principle, a problem consists of mutually conflicting objectives in an engineering system design generates multiple solutions instead of a single solution. A set of solutions is required to satisfy such types of problems. These solutions are popularly known as Pareto-optimal solutions. An engineer always interests in reducing the cost and improving the reliability of the system simultaneously. This paper proposes linguistic fuzzy multi-objective models where reliability and cost are involved in the system design. Such types of formulations give an idea to find out the best compromise solution as per the demand of the decision-maker. At the same time, it removes the uncertainty confronted by a system design engineer in formulating the system design at the initial stage. The Pareto-optimal solutions are obtained by an efficient multi-objective evolutionary technique, namely NSGA-II. A designer finds the guided Pareto-optimal solutions as per the formulated models of the problem in linguistic forms. The best compromise solution is found by the decision-maker while analyzing the different cases of fuzzy models. The proposed approach is shown by taking a numerical example.

Key-Words / Index Term :
Reliability, Fuzzy multi-objective optimization problem (FMOOP), Linguistic hedges, NSGA-II

References :
[1] K. Deb, “Multi-objective optimization using evolutionary algorithms”, John Wiley & Sons, USA, pp. 1-9, 2001.
[2] H. Kumar, S. P. Yadav, “NSGA-II based decision-making in fuzzy multi-objective optimization of system reliability”. In: Deep K, Jain M, Salhi S (eds) Decision science in action. Asset analytics (performance and safety management). Springer, pp. 105–117, 2019.
[3] K. Deb, S. Agarwal, A. Pratap, T. Meyarivan, “A fast and elitist multi-objective genetic algorithm: NSGA-II”, IEEE Trans. Evol. Comput., Vol. 6, pp. 182-197, 2002.
[4] H. Garg, S.P. Sharma, “Multi-objective reliability-redundancy allocation problem using particle swarm optimization”, Computers & Industrial Engineering, Vol. 64, No. 1, pp. 247-255, 2012.
[5] H. Kumar, S. P. Yadav, “NSGA-II based fuzzy multi-objective reliability analysis”, International Journal of System Assurance Engineering and Management, Vol. 8, pp. 817-825, 2017.
[6] H. Kumar, “Using Reference Point-Based NSGA-II to System Reliability”, International Journal of Computer Science and Engineering, Vol. 5, Issue.12, pp. 7-14, 2017.
[7] H. Kumar, A. P. Singh, S. P. Yadav, “NSGA-II Based Analysis of Fuzzy Multi-objective Reliability-Redundancy Allocation Problem Using Various Membership functions”, INAE Letters, Vol. 4, pp. 191-206, 2019.
[8] H. Z. Huang, “Fuzzy multi-objective optimization decision-making of reliability of series system”, Microelectronics Reliability, Vol. 37, pp. 447-449, 1997.
[9] H. J. Zimmermann, “Fuzzy set theory and its applications”, Kluwer, Boston, ISBN 0-7923-9624-3, USA, pp. 1-10, 1996.
[10] A. K. Dhingra, H. Moskowitz, “Application of fuzzy theories to multiple objective decision-making in system design”, European Journal of Operational Research, Vol. 53, pp. 348-361, 1991.
[11] H. Kumar, S. P. Yadav, “Fuzzy rule-based reliability analysis using NSGA-II”, International Journal of System Assurance Engineering and Management, Vol. 10, pp. 953-972, 2019.