International Journal of Mathematical, Engineering and Management Sciences

ISSN: 2455-7749

A Genetic Algorithm Based Hybrid Approach for Reliability-Redundancy Optimization Problem of a Series System with Multiple-Choice

A Genetic Algorithm Based Hybrid Approach for Reliability-Redundancy Optimization Problem of a Series System with Multiple-Choice

Asoke Kumar Bhunia
Department of Mathematics, The University of Burdwan, Burdwan-713104, WB, India.

Avijit Duary
Department of Mathematics, Sir J. C. Bose School of Engineering, SKFGI, Hoogly -712139, WB, India.

Laxminarayan Sahoo
Department of Mathematics, Raniganj Girls Raniganj-713358, West Bengal, India.

DOI https://dx.doi.org/10.33889/IJMEMS.2017.2.3-016

Received on December 10, 2016
Accepted on February 26, 2017


The goal of this paper is to introduce an application of hybrid algorithm in reliability optimization problems for a series system with parallel redundancy and multiple choice constraints to maximize the system reliability subject to system budget and also to minimize the system cost subject to minimum level of system reliability. Both the problems are solved by using penalty function technique for dealing with the constraints and hybrid algorithm. In this algorithm, the well-known real coded Genetic Algorithm is combined with Self-Organizing Migrating Algorithm. As special cases, both the problems are formulated and solved considering single component without redundancy. Finally, the proposed approach is illustrated by some numerical examples and the computational results are discussed.

Keywords- Reliability-redundancy optimization, Multiple-choice constraints, Constrained integer nonlinear optimization, Genetic algorithm, Self-organizing migrating algorithm.


Bhunia, A. K., Duary, A., & Sahoo, L. (2017). A Genetic Algorithm Based Hybrid Approach for Reliability-Redundancy Optimization Problem of a Series System with Multiple-Choice. International Journal of Mathematical, Engineering and Management Sciences, 2(3), 185-212. https://dx.doi.org/10.33889/IJMEMS.2017.2.3-016.

Conflict of Interest


For this research, the first author would like to acknowledge the financial support provided by the Council of Scientific and Industrial Research (CSIR), New Delhi, India.


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 Computation, 216(3), 929-939.

Brindle, A. (1981). Genetic algorithms for function optimization (Doctoral dissertation and Technical Report TR81-2). Edmonton: University of Alberta, Department of Computer Science.

Chelouah, R., & Siarry, P. (2003). Genetic and Nelder–Mead algorithms hybridized for a more accurate global optimization of continuous multiminima functions. European Journal of Operational Research, 148(2), 335-348.

Chern, M. S. (1992). On the computational complexity of reliability redundancy allocation in a series system. Operations Research Letters, 11(5), 309-315.

Coello, C. A. C. (2002). Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. Computer Methods in Applied Mechanics and Engineering, 191(11), 1245-1287.

Deb, K. (2000). An efficient constraint handling method for genetic algorithms. Computer Methods in Applied Mechanics and Engineering, 186, 311–38.

dos Santos Coelho, L. (2009). An efficient particle swarm approach for mixed-integer programming in reliability–redundancy optimization applications. Reliability Engineering and System Safety, 94(4), 830-837.

dos Santos Coelho, L. (2009). Self-organizing migration algorithm applied to machining allocation of clutch assembly. Mathematics and Computers in Simulation, 80(2), 427-435.

dos Santos Coelho, L., & Alotto, P. (2009). Electromagnetic optimization using a cultural self-organizing migrating algorithm approach based on normative knowledge. IEEE Transactions on Magnetics, 45(3), 1446-1449.

dos Santos Coelho, L., & Mariani, V. C. (2010). An efficient cultural self-organizing migrating strategy for economic dispatch optimization with valve-point effect. Energy Conversion and Management, 51(12), 2580-2587.

Fan, S. K. S., Liang, Y. C., & Zahara, E. (2006). A genetic algorithm and a particle swarm optimizer hybridized with Nelder–Mead simplex search. Computers and Industrial Engineering, 50(4), 401-425.

Ghare, P. M., & Taylor, R. E. (1969). Optimal redundancy for reliability in series systems. Operations Research, 17(5), 838-847.

Goldberg, D. E. (1989). Genetic algorithms in search, optimization and machine learning ‘addison-wesley, 1989. Reading, MA.

Goldberg, D., Deb, K., & Korb, B. (1989). Messy genetic algorithms: Motivation, analysis, and first results. Complex systems, (3), 493-530.

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 reliability 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), 24-38.

Holland, J. H. (1975). Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. U Michigan Press.

Jabeen, S. D., & Bhunia, A. K. (2006). Real-coded genetic algorithm with variable rates of cross-over and mutation: a basis of global optimization for multi-modal functions via interval technique. International Journal of Computer Mathematics, 83(12), 853-866.

Koziel, S., & Michalewicz, Z. (1999). Evolutionary algorithms, homomorphous mappings, and constrained parameter optimization. Evolutionary computation, 7(1), 19-44.

Kuo, W. (2001). Optimal reliability design: fundamentals and applications. Cambridge University Press.

Michalewicz, Z. (1996). Genetic algorithms data structures evolution programs. Springer, Berlin.

Michalewicz, Z., & Schoenauer, M. (1996). Evolutionary algorithms for constrained parameter optimization problems. Evolutionary Computation, 4(1), 1-32.

Nahas, N., & Nourelfath, M. (2005). Ant system for reliability optimization of a series system with multiple-choice and budget constraints. Reliability Engineering & System Safety, 87(1), 1-12.

Nakagawa, Y., Nakashima, K., & Hattori, Y. (1978). Optimal reliability allocation by branch-and-bound technique. IEEE Transactions on Reliability, 1, 31-38.

Nauss, R. M. (1978). The 0–1 knapsack problem with multiple choice constraints. European Journal of Operational Research, 2(2), 125-131.

Nolle, L., Zelinka, I., Hopgood, A. A., & Goodyear, A. (2005). Comparison of a self-organizing migration algorithm with simulated annealing and differential evolution for automated waveform tuning. Advances in Engineering Software, 36(10), 645-653.

Nourelfath, M., & Nahas, N. (2003). Quantized hopfield networks for reliability optimization. Reliability Engineering & System Safety, 81(2), 191-196.

Pedamallu, C. S., & Ozdamar, L. (2008). Investigating a hybrid simulated annealing and local search algorithm for constrained optimization. European Journal of Operational Research, 185(3), 1230-1245.

Renders, J. M., & Flasse, S. P. (1996). Hybrid methods using genetic algorithms for global optimization. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 26(2), 243-258.

Sahoo, L., Bhunia, A. K., & Kapur, P. K. (2012). Genetic algorithm based multi-objective reliability optimization in interval environment. Computers and Industrial Engineering, 62(1), 152-160.

Sakawa, M., & Kato, K. (2002). An interactive fuzzy satisficing method for general multiobjective 0–1 programming problems through genetic algorithms with double strings based on a reference solution. Fuzzy Sets and Systems, 125(3), 289-300.

Salhi, S., & Queen, N. M. (2004). A hybrid algorithm for identifying global and local minima when optimizing functions with many minima. European Journal of Operational Research, 155(1), 51-67.

Senkerik, R., Zelinka, I., Davendra, D., & Oplatkova, Z. (2010). Utilization of SOMA and differential evolution for robust stabilization of chaotic Logistic equation. Computers and Mathematics with Applications, 60(4), 1026-1037.

Sinha, P., & Zoltners, A. A. (1979). The multiple-choice knapsack problem. Operations Research, 27(3), 503-515.

Sun, X. L., & Li, D. (2002). Optimality condition and branch and bound algorithm for constrained redundancy optimization in series systems. Optimization and Engineering, 3(1), 53-65.

Sung, C. S., & Cho, Y. K. (2000). Reliability optimization of a series system with multiple-choice and budget constraints. European Journal of Operational Research, 127(1), 159-171.

Sung, C. S., & Lee, H. K. (1994). A branch-and-bound approach for spare unit allocation in a series system. European journal of operational research, 75(1), 217-232.

Tillman, F. A., Hwang, C. L., & Kuo, W. (1977). Optimization Techniques for System Reliability with RedundancyߞA Review. IEEE Transactions on Reliability, 26(3), 148-155.

Tillman, F. A., Hwang, C. L., & Kuo, W. (1980). Optimization of systems reliability (Vol. 4). Marcel Dekker Inc.

Zelinka, I, & Lampinen, J. (2000). SOMA – self-organizing migrating algorithm. Proceedings of the 6th international Mendel conference on soft computing, Brno, Czech Republic; 177–187.

Zelinka, I. (2004). SOMA—self-organizing migrating algorithm. In New optimization techniques in engineering (pp. 167-217). Springer Berlin Heidelberg.

Zelinka, I., Lampinen, J., & Nolle, L. (2001). On the theoretical proof of convergence for a class of SOMA search algorithms, In: Proceedings of the 7th International MENDEL Conference on Soft Computing., pp. 103-110. ISBN 0802141894X.