Department of Mathematics, Raniganj Girls College, Raniganj-713358, West Bengal, India.
This paper presents the use of genetic algorithm to solve reliability redundancy allocation problem of complicated system in fuzzy environment. Generally, this problem has been formulated as single objective integer non-linear programming problem with several resource constraints. In this paper, the reliability of each component as well as other parameters related to the problem is considered to be fuzzy valued. In this work, the corresponding constrained optimization problem has been transformed to crisp constrained optimization problem using defuzzification of fuzzy number. Here, widely known Yager ranking Index has been used for defuzzification of fuzzy number. The Big-M penalty function technique has been used to transform the constrained optimization problem into an unconstrained optimization problem. The converted problem has been solved with the help of real coded genetic algorithm. To illustrate the proposed methodology, a numerical example has been considered and solved. To study the performance of the proposed genetic algorithm, sensitivity analyses have been done graphically.
Keywords- Redundancy allocation problem, Genetic algorithm, Fuzzy number, Defuzzification technique, Yager Index.
Sahoo, L. (2017). Genetic Algorithm Based Approach for Reliability Redundancy Allocation Problems in Fuzzy Environment. International Journal of Mathematical, Engineering and Management Sciences, 2(4), 259-272. https://dx.doi.org/10.33889/IJMEMS.2017.2.4-020.
Conflict of Interest
Aggarwal, K. K., & Gupta, J. S. (2005). Penalty function approach in heuristic algorithms for constrained. IEEE Transactions on Reliability, 54(3), 549-558.
Bhunia, A. K., Sahoo, L., & Roy, D. (2010). Reliability stochastic optimization for a series system with interval component reliability via genetic algorithm. Applied Mathematics and Computations, 216(3), 929-939.
El-Sharkawi, L. (2008). Modern heuristic optimization techniques (1st ed.). Wiley Inter Science, New Jersey, USA.
Gen, M., & Cheng, R. (1997). Genetic algorithm and engineering design (1st ed.). USA, John Wiley & Sons, New York, NY.
Goldberg, D. E. (1989). Genetic algorithms in search, optimization and machine learning reading. MA: Addison-Wesley, USA.
Gupta, R. K, Bhunia, A. K., & Roy, D. (2009). A GA Based penalty function technique for solving constrained redundancy allocation problem of series system with interval valued reliabilities of components. Journal of Computational and Applied Mathematics, 232(2), 275-284.
Ha, C., & Kuo, W. (2006). Reliability redundancy allocation: An improved realization for nonconvex nonlinear programming problems. European Journal of Operational Research, 171(1), 124-138.
Hikita, M., Nakagawa, K., Nakashima, K., & Narihisa, H. (1992). Reliability optimization of systems by a surrogate-constraints algorithm. IEEE Transactions on Reliability, 41(3), 473-480.
Hwang, C. L., Tillman, F. A., & Kuo, W. (1979). Reliability optimization by generalized lagrangian-function based and reduced-gradient methods. IEEE Transactions on Reliability, 28(4), 316-319.
Kim, J. H., & Yum, B. J. (1993). A heuristic method for solving redundancy optimization problems in complex systems. IEEE Transactions on Reliability, 42(4), 572-578.
Kuo, W., & Prasad, V. R. (2001). An annoted overview of system-reliability optimization. IEEE Transactions on Reliability, 49,176-187.
Kuo, W., Lin, H., Xu, Z. & Zhang, W. (1987), Reliability optimization with the Lagrange-multiplier and branch-and-bound technique, IEEE Transactions on Reliability, 36(5), 624-630.
Misra, K. B., & Sharma, U. (1991). An efficient algorithm to solve integer- programming problems arising in system-reliability design. IEEE Transactions on Reliability, 40(1), 81-91.
Nakagawa, Y., & Miyazaki, S. (1981). Surrogate constraints algorithm for reliability optimization problems with two constraints. IEEE Transactions on Reliability, 30(2), 175-180.
Nakagawa, Y., & Nakashima, K. (1977). A heuristic method for determining optimal reliability allocation. IEEE Transactions on Reliability, 26(3), 156-161.
Sahoo, L., Bhunia, A. K., & Kapur, P. K. (2012). Genetic algorithm based multi-objective reliability optimization in interval environment. Computer Industrial Engineering, 62(1), 152-160.
Sun, X. L., & Li, D. (2002). Optimization condition and branch and bound algorithm for constrained redundancy optimization in series system. Optimization and Engineering, 3(1), 53-65.
Sung, C. S. & Cho, Y. K. (1999). Branch and bound redundancy optimization for a series system with multiple-choice constraints. IEEE Transactions on Reliability, 48(2), 108-117.
Tillman, F. A., Hwang, C. L., & Kuo, W. (1977). Optimization technique for system reliability with redundancy: A Review. IEEE Transactions on Reliability, 26(3), 148-155.
Yager, R. R. (1981). A procedure for ordering fuzzy subsets of the unit interval. Information Sciences, 24(2), 143-161.
Yager, R. R., & Filev, D. P. (1993). On the issue of defuzzification and selection based on a fuzzy set. Fuzzy Sets and Systems, 55(3), 255-271.
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338-352.