Abstract
The objective of this chapter is to develop and solve the reliability optimization problems of series-parallel, parallel-series and complicated system considering the reliability of each component as interval valued number. For optimization of system reliability and system cost separately under resource constraints, the corresponding problems have been formulated as constrained integer/mixed integer programming problems with interval objectives with the help of interval arithmetic and interval order relations. Then the problems have been converted into unconstrained optimization problems by two different penalty function techniques. To solve these problems, two different real coded genetic algorithms (GAs) for interval valued fitness function with tournament selection, whole arithmetical crossover and non-uniform mutation for floating point variables, uniform crossover and uniform mutation for integer variables and elitism with size one have been developed. To illustrate the models, some numerical examples have been solved and the results have been compared. As a special case, taking lower and upper bounds of the interval valued reliabilities of component as same the corresponding problems have been solved and the results have been compared with the results available in the existing literature. Finally, to study the stability of the proposed GAs with respect to the different GA parameters (like, population size, crossover and mutation rates), sensitivity analyses have been shown graphically.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Ha, C., Kuo, W.: Reliability redundancy allocation: An improved realization for nonconvex nonlinear programming problems. European Journal of Operational Research 171, 124–138 (2006)
Coelho, L.S.: An efficient particle swarm approach for mixed-integer programming in reliability redundancy optimization applications. Reliability Engineering and System Safety 94, 830–837 (2009)
Tillman, F.A., Hwuang, C.L., Kuo, W.: Optimization technique for system reliability with redundancy: A Review. IEEE Trans. Reliability 26, 148–155 (1977)
Kuo, W., Prasad, V.R., Tillman, F.A., Hwuang, C.L.: Optimal Reliability Design Fundamentals and application. Cambridge University Press, Cambridge (2001)
Misra, K.B., Sharama, U.: An efficient algorithm to solve integer-programming problems arising in system reliability design. IEEE Trans. Reliability 40, 81–91 (1991)
Nakagawa, Y., Nakashima, K., Hattori, Y.: Optimal reliability allocation by branch-and-bounded technique. IEEE Trans. Reliability 27, 31–38 (1978)
Ohtagaki, H., Nakagawa, Y., Iwasaki, A., Narihisa, H.: Smart greedy procedure for solving a nonlinear knapsacclass of reliability optimization problems. Mathl. Comput. Modeling 22, 261–272 (1995)
Sun, X., Duan, L.: Optimal Condition and Branch and Bound Algorithm for Constrained Redundancy Optimization in Series System. Optimization and Engineering 3, 53–65 (2002)
Sun, X.L., Mckinnon, K.I.M., Li, D.: A convexification method for a class of global optimization problems with applications to reliability optimization. Journal of Global Optimization 21, 185–199 (2001)
Gen, M., Yun, Y.: Soft computing approach for reliability optimization. Reliability Engineering and System Safety 91, 1008–1026 (2006)
Chern, M.S.: On the computational complexity of reliability redundancy allocation in a series system. Operations Research Letter 11, 309–315 (1992)
Martorell, S., Sanchez, A., Carlos, S., Serradell, V.: Alternatives and challenges in optimizing industrial safety using genetic algorithms. Reliability Engineering and System Safety 86, 25–38 (2004)
Zhao, J., Liu, Z., Dao, M.: Reliability optimization using multiobjective ant colony system approaches. Reliability Engineering and system safety 92, 109–120 (2007)
Zio, E.: Reliability engineering: Old problems and new challanges. Reliability Engineering and System Safety 94, 125–141 (2009)
Coolen, F.P.A., Newby, M.J.: Bayesian reliability analysis with imprecise prior probabilities. Reliability Engineering and System Safety 43, 75–85 (1994)
Utkin, L.V., Gurov, S.V.: Imprecise reliability of general structures. Knowledge and Information Systems 1(4), 459–480 (1999)
Utkin, L.V., Gurov, S.V.: New reliability models based on imprecise probabilities. In: Hsu, C. (ed.) Advanced Signal Processing Technology, pp. 110–139. World Scientific, Singapore (2001)
Gupta, R.K., Bhunia, A.K., Roy, D.: A GA based penalty function technique for solving constrained redundancy allocation problem of series system with interval valued reliability of components. Journal of Computational and Applied Mathematics 232, 275–284 (2009)
Bhunia, A.K., Sahoo, L., Roy, D.: Reliability stochastic optimization for a series system with interval component reliability via genetic algorithm. Applied Mathematics and Computation 216, 929–939 (2010)
Mahato, S.K., Bhunia, A.K.: Interval-Arithmetic-Oriented Interval Computing Technique for Global Optimization. In: Applied Mathematics Research eXpress 2006, pp. 1–19 (2006)
Ishibuchi, H., Tanaka, H.: Multiobjective programming in optimization of the interval objective function. European Journal of Operational Research 48, 219–225 (1990)
Chanas, S., Kuchta, D.: Multiobjective programming in the optimization of interval objective functions-A generalized approach. European journal of Operational Research 94, 594–598 (1996)
Goldberg, D.E.: Genetic Algorithms: Search, Optimization and Machine Learning. Addison-Wesley, Reading (1989)
Gen, M., Cheng, R.: Genetic algorithms and engineering optimization. John Wiley and Sons Inc., Chichester (2000)
Michalawich, Z.: Genetic Algorithms + Data structure = Evaluation Programs. Springer, Berlin (1996)
Sakawa, M.: Genetic Algorithms and fuzzy multiobjective optimization. Kluwer Academic Publishers, Dordrecht (2002)
Levitin, G.: Genetic algorithms in reliability engineering. Reliability Engineering and System Safety 91, 9751–9976 (2006)
Villanueva, J.F., Sanchez, A.I., Carlos, S., Martorell, S.: Genetic algorithm-based optimization of testing and maintenance under uncertain unavailability and cost estimation: A survey of strategies for harmonizing evoluation and accuracy. Reliability Engineering and System Safety 93, 1830–1841 (2008)
Ye, Z., Li, Z., Xie, M.: Some improvements on adaptive genetic algorithms for reliability-related applications. Reliability Engineering and System Safety 95, 120–126 (2010)
Deb, K.: An efficient constraint handling method for genetic algorithms. Computer Methods in Applied Mechanics and Engineering 186, 311–338 (2000)
Aggarwal, K.K., Gupta, J.S.: Penalty function approach in heuristic algorithms for constrained. IEEE Transactions on Reliability 54(3), 549–558 (2005)
Miettinen, K., Makela, M.M., Toivanen, J.: Numerical comparison of some Penalty-Based Constraint Handling Techniques in Genetic Algorithms. Journal of Global Optimization 2, 427–446 (2003)
Hansen, E., Walster, G.W.: Global optimization using interval analysis. Marcel Dekker Inc., New York (2004)
Karmakar, S., Mahato, S., Bhunia, A.K.: Interval oriented multi-section techniques for global optimization. Journal of Computation and Applied Mathematics 224, 476–491 (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Bhunia, A.K., Sahoo, L. (2011). Genetic Algorithm Based Reliability Optimization in Interval Environment. In: Nedjah, N., dos Santos Coelho, L., Mariani, V.C., de Macedo Mourelle, L. (eds) Innovative Computing Methods and Their Applications to Engineering Problems. Studies in Computational Intelligence, vol 357. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20958-1_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-20958-1_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-20957-4
Online ISBN: 978-3-642-20958-1
eBook Packages: EngineeringEngineering (R0)