A Hybrid Fire Fly and Differential Evolution Algorithm for Optimization of a Mixed Repairable and Non-Repairable System Reliability Problem

Document Type: Research Paper

Authors

1 Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

2 Industrial Engineering Department, University of Science and Technology, Tehran, Iran

Abstract

In this paper, a hybrid meta-heuristic approach is proposed to optimize the mathematical model of a system with mixed repairable and non-repairable components. In this system, repairable and non-repairable components are connected in series. Redundant components and preventive maintenance strategies are applied for non-repairable and repairable components, respectively. The problem is formulated as a bi-objective mathematical programming model aiming to reach a tradeoff between system reliability and cost. By hybridizing a standard multi-objective fire fly (MOFA) and differential evolution (DE) algorithms, a powerful and efficient approach called MOF-DE algorithm which has inherited the advantages of the two algorithms is introduced to solve this problem. In order to achieve the best performance of MOF-DE, response surface methodology (RSM) is used to set proper values for the algorithm parameters. To evaluate the performance of the proposed algorithm, various numerical examples are tested and results are compared with methods like NSGA-II, MOPSO and standard MOFA. From the experiments, it is concluded that the performance of the MOF-DE algorithm is better than other methods at finding promising solutions. Finally, sensitivity analysis is carried out to investigate behavior of the proposed algorithm.

Keywords

Main Subjects


Gandomi, A., Yang, X., & Alavi, A. (2011). Mixed variable structural optimization using Firefly Algorithm. Computers and Structures, 89, 2325-2336.

Amirabadi, H., Khalili, K., Foorginejad, A., & Ashoori, J. (2013). Modeling of abrasive water-jet cutting of glass using artificial neural network and optimization of surface roughness using firefly algorithm. Modares Mechanical Engineering, 13, 123-134.

Azaron, A., Katagiri, H., Kato, K., & Sakawa, M. (2005). Reliability evaluation and optimization of dissimilar-component cold-standby redundant systems. Journal of the Operations Research Society of Japan, 48(1), 71-88.

Chai-ead, N., Aungkulanon, P., & Luangpaiboon, P. (2011). Bees and Firefly Algorithms for Noisy Non-Linear Optimisation Problems. International MultiConference of Engineers and Computer Scientist. Hong Kong.

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

Coit, D. (2001). Cold-standby redundancy optimization for nonrepairable systems. Iie Transactions,, 33(6), 471-478.

Das, S., & Nagaratnam Suganthan, P. (2011). Differential Evolution: A Survey of the State of the Art. IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION, 15, 4-31.

De Castro, H., & Cavalca, K. (2006). Maintenance resources optimization applied to a manufacturing system. Reliability Engineering & System Safety, 91(4), 413-420.

Dieter, A., Pickard, K., & Bertsche, B. (2010). Periodic renewal of spare parts using Weibull. Quality and Reliability Engineering International, 26(3), 193-198.

Gandomi, A., Yang, X., & Alavi, A. (2011). Mixed variable structural optimization using Firefly Algorithm. Computers and Structures, 89, 2325-2336.

Amirabadi, H., Khalili, K., Foorginejad, A., & Ashoori, J. (2013). Modeling of abrasive water-jet cutting of glass using artificial neural network and optimization of surface roughness using firefly algorithm. Modares Mechanical Engineering, 13, 123-134.

Azaron, A., Katagiri, H., Kato, K., & Sakawa, M. (2005). Reliability evaluation and optimization of dissimilar-component cold-standby redundant systems. Journal of the Operations Research Society of Japan, 48(1), 71-88.

Chai-ead, N., Aungkulanon, P., & Luangpaiboon, P. (2011). Bees and Firefly Algorithms for Noisy Non-Linear Optimisation Problems. International MultiConference of Engineers and Computer Scientist. Hong Kong.

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

Coit, D. (2001). Cold-standby redundancy optimization for nonrepairable systems. Iie Transactions,, 33(6), 471-478.

Das, S., & Nagaratnam Suganthan, P. (2011). Differential Evolution: A Survey of the State of the Art. IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION, 15, 4-31.

De Castro, H., & Cavalca, K. (2006). Maintenance resources optimization applied to a manufacturing system. Reliability Engineering & System Safety, 91(4), 413-420.

Dieter, A., Pickard, K., & Bertsche, B. (2010). Periodic renewal of spare parts using Weibull. Quality and Reliability Engineering International, 26(3), 193-198.

Dos Santos Coelho, L., de Andrade Bernert, D. L., & Mariani, V. C. (2011). A Chaotic Firefly Algorithm Applied to Reliability-Redundancy Optimization. IEEE Congress on Evolutionary Computation (CEC). New Orleans, LA.

Garg, H. (2015). An approach for solving constrained reliability-redundancy allocation problems using cuckoo search algorithm. Beni-Suef University Journal of Basic and Applied Sciences, 4(1), 14-25.

Goel, N., Gupta, D., & Goel, S. (2013). Performance of Firefly and Bat Algorithm for Unconstrained Optimization Problems. International Journal of Advanced Research in Computer Science and Software Engineering, 31, 1405-1409.

He, Q., Hu, X., Ren, H., & Zhang, H. (2015). A novel artificial fish swarm algorithm for solving large-scale reliability–redundancy application problem. ISA transactions, 59, 105-113.

Heungseob, K., & Pansoo, K. (2017). Reliability models for a nonrepairable system with heterogeneous components having a phase-type time-to-failure distribution. Reliability models for a nonrepairable system with heteroReliability Engineering & System Safety, 37-46.

Huang, H.-Z., Qu, J., & Zuo, M. J. (2009). Genetic-algorithm-based optimal apportionment of reliability and redundancy under multiple objective. IIE Transactions, 41, 287–298.

Jardine, A., & Buzacott, J. (1985). Equipment reliability and maintenance. European Journal of Operational Research, 19(3), 285-296.

Khalili-Damghani, K., Abtahi, A.-R., & Tavana, M. (2013). A new multi-objective particle swarm optimization method for solving reliability redundancy allocation problems. Reliability Engineering & System Safety, 111, 58-75.

Kumar, R., Izui, K., Yoshimura, M., & Nishiwaki, S. (2009). Multi-objective hierarchical genetic algorithms for multilevel redundancy allocation optimization. Reliability Engineering and System Safety, 94, 891-904.

Li, H., & Ye, C. (2012). Firefly Algorithm on Multi-Objective Optimization of Production Scheduling System. Advances in Mechanical Engineering and its Applications, 3, 258-262.

Li, Z., Liao, H., & Coit, D. (2009). A two-stage approach for multi-objective decision making with applications to system reliability optimization. Reliability Engineering and System Safety, 94, 1585-1592.

Liang, Y.-C., & Lo, M.-H. (2010). Multi-objective redundancy allocation optimization using a variable neighborhood search algorithm. Journal of Heuristics, 16, 511–535.

Marichelvam, M., Prabaharan, T., & Yang, X. (2014). A Discrete Firefly Algorithm for the Multi-objective Hybrid Flowshop Scheduling Problems. IEEE TRANSCATIONS ON EVOLUTIONARY COMPUTATION, 18, 301 - 305.

MohammadZadeh Dogahe, S., & Sadjadi, S. (2015). A New Biobjective Model to Optimize Integrated Redundancy Allocation and Reliability-Centered Maintenance Problems in a System Using Metaheuristics. Mathematical Problems in Engineering.

Najafi, A., Akhavan Niaki, S., & Shahsavar, M. (2009). A parameter-tuned genetic algorithm for the resource investment problem with discounted cash flows and generalized precedence relations. Computers &OperationsResearch, 36, 2994-3001.

Rebaiaia, M. L., Ait-Kadi, D., Rahimi, S. A., & Jamshidi, A. (2016). Numerical comparative analysis between age and block maintenance strategies in the presence of probability distributions with increasing failure rate. International Federation of Automatic Control, (pp. 1904-1909).

Rigdon, S. (2008). Reliability Optimization. In Encyclopedia of Statistics in Quality and Reliability (pp. 1599-1604). John Wiley & Sons.

Ruiz-Vanoye, J., & Díaz-Parra, O. (2011). Similarities between meta-heuristics algorithms and the science of life. Central European Journal of Operations Research, 19, 445-66.

Safari, J. (2012). Multi-objective reliability optimization of series-parallel systems with a choice of redundancy strategies. Reliability Engineering & System Safety, 108, 10-20.

Salmasnia, A., Ameri, E., & Niaki, S. (2016). A robust loss function approach for a multi-objective redundancy allocation problem. Applied Mathematical Modelling, 40(1), 635-645.

Sayadi, M., Hafezalkotob, A., & Jalali Naini, S. (2013). Firefly-inspired algorithm for discrete optimization problems: An application to manufacturing cell formation. Journal of Manufacturing Systems, 32, 78-84.

Soltani, R., Safari, J., & Sadjadi, S. (2015). Robust counterpart optimization for the redundancy allocation problem in series-parallel systems with component mixing under uncertainty. Applied Mathematics and Computation, 80-88.

Suman, B. (2003). Simulated annealing-based multiobjective algorithms and their application for system reliability. Engineering Optimization, 35, 391–416.

Taboadaa, H., Baheranwalaa, F., & Coit, D. (2007). Practical solutions for multi-objective optimization: An application to system reliability design problems. Reliability Engineering and System Safety, 92, 314-322.

Weibull, W. (1951). A Statistical Distribution Function of Wide Applicability. Journal of applied mechanics.

Yang, X. (2010). Nature-inspired metaheuristic algorithm. Luniver Press.

Yang, X. (2013). Multiobjective Firefly Algorithm for Continuous Optimization. Engineering with Computers, 29, 175-184.

Yang, X.-S., & He, X. (2013). Firefly Algorithm: Recent Advances and Applications. Journal of Swarm Intelligence, 1, 36-50.

Yu, X., & Gen, M. (2010). Introduction to evolutionary algorithms. Springer.

Zhao, J.-H., Liu, Z., & Dao, M.-T. (2007). Reliability optimization using multiobjective ant colony system approaches. Reliability Engineering and System Safety, 92, 109-120.

Zoulfaghari, H., Hamadani, A., & Abouei Ardakan, M. (2014). Bi-objective redundancy allocation problem for a system with mixed repairable and non-repairable components. ISA Transactions, 53, 17-24.