Skip to main content
Springer Nature Link
Log in

An improved particle swarm optimization model for solving homogeneous discounted series-parallel redundancy allocation problems

  • Published:
Journal of Intelligent Manufacturing Aims and scope Submit manuscript

Abstract

In this study, we propose an improved particle swarm optimization algorithm (IPSOA) to solve discounted redundancy allocation problems (DRAPs) in series-parallel systems. The system consists of subsystems in series with parallel components in each subsystem. Homogeneous redundant components are used to achieve a desirable system reliability. The components of each subsystem are characterized by their cost, weight, and reliability where the cost is calculated under an all unit discount policy. The goal is to find the optimum combination of the components for each subsystem so that the system reliability is maximized. After formulating the mathematical model, the proposed IPOSA is implemented to achieve the solution. Moreover, an experimental design approach is used to calibrate the algorithm’s parameters. Three numerical problems, each of which considered under several configurations, are discussed to demonstrate the applicability of the proposed procedures. In order to evaluate the accuracy and performance of our IPSOA, all the problems are also solved using two other meta-heuristics, namely, the homogeneous particle swarm optimization algorithm and tabu search. The numerical results show that, when solving DRAPs, IPSOA behaves better than the other two algorithms considered from both a solution quality and a computational viewpoint.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  • Beji, N., Jarboui, B., Eddaly, M., & Chabchoub, H. (2010). A hybrid particle swarm optimization algorithm for the redundancy allocation problem. Journal of Computational Science, 1(3), 159–167.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Coit, D. W., & Konak, A. (2006). Multiple weighted objectives heuristic for the redundancy allocation problem. IEEE Transactions on Reliability, 55(3), 551–558.

    Article  Google Scholar 

  • Coit, D. W., & Smith, A. E. (1996a). Penalty guided genetic search for reliability design optimization. Computers & Industrial Engineering, 30(4), 895–904.

    Article  Google Scholar 

  • Coit, D. W., & Smith, A. E. (1996b). Reliability optimization of series-parallel systems using a genetic algorithm. IEEE Transactions on Reliability, 45(2): 254–260, 266.

  • Crainic, T. G., & Toulouse, M. (2010). Parallel meta-heuristics. In: Gendreau, M., & Potvin, J.-Y. (Eds.), Handbook of Metaheuristics, International Series in Operations Research & Management Science, vol. 146, Springer, pp. 497–541.

  • de Oca, M. A. M., Aydın, D., & Stützle, T. (2011). An incremental particle swarm for large-scale continuous optimization problems: An example of tuning-in-the-loop (re) design of optimization algorithms. Soft Computing, 15(11), 2233–2255.

    Article  Google Scholar 

  • Eberhart, R., & Kennedy, J. (1995). A new optimizer using particle swarm theory. Paper presented at the Micro Machine and Human Science, 1995. In Proceedings of the Sixth International Symposium on MHS’95.

  • Fyffe, D. E., Hines, W. W., & Lee, N. K. (1968). System reliability allocation and a computational algorithm. IEEE Transactions on Reliability, 17(2), 64–69.

    Article  Google Scholar 

  • Garg, H. (2015a). 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.

    Article  Google Scholar 

  • Garg, H. (2015b). An efficient biogeography based optimization algorithm for solving reliability optimization problems. Swarm and Evolutionary Computation, 24, 1–10.

    Article  Google Scholar 

  • Garg, H., Rani, M., & Sharma, S. (2013). An efficient two phase approach for solving reliability-redundancy allocation problem using artificial bee colony technique. Computers & Operations Research, 40(12), 2961–2969.

    Article  Google Scholar 

  • Garg, H., Rani, M., Sharma, S., & Vishwakarma, Y. (2014a). Bi-objective optimization of the reliability-redundancy allocation problem for series-parallel system. Journal of Manufacturing Systems, 33(3), 335–347.

    Article  Google Scholar 

  • Garg, H., Rani, M., Sharma, S., & Vishwakarma, Y. (2014b). Intuitionistic fuzzy optimization technique for solving multi-objective reliability optimization problems in interval environment. Expert Systems with Applications, 41(7), 3157–3167.

    Article  Google Scholar 

  • Garg, H., & Sharma, S. (2013). Multi-objective reliability-redundancy allocation problem using particle swarm optimization. Computers & Industrial Engineering, 64(1), 247–255.

    Article  Google Scholar 

  • Glover, F., & Martí, R. (2006). Tabu search. In: Alba, E., & Martí, R. (Eds.), Metaheuristic procedures for training neutral networks, Operations Research/Computer Science Interfaces Series, vol. 36. Springer, pp. 53–69.

  • 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.

    Article  Google Scholar 

  • Jarboui, B., Damak, N., Siarry, P., & Rebai, A. (2008a). A combinatorial particle swarm optimization for solving multi-mode resource-constrained project scheduling problems. Applied Mathematics and Computation, 195(1), 299–308.

    Article  Google Scholar 

  • Jarboui, B., Ibrahim, S., Siarry, P., & Rebai, A. (2008b). A combinatorial particle swarm optimisation for solving permutation flowshop problems. Computers & Industrial Engineering, 54(3), 526–538.

    Article  Google Scholar 

  • Kulturel-Konak, S., Smith, A. E., & Coit, D. W. (2003). Efficiently solving the redundancy allocation problem using tabu search. IIE Transactions, 35(6), 515–526.

    Article  Google Scholar 

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

  • Kuo, W., & Prasad, V. R. (2000). An annotated overview of system-reliability optimization. IEEE Transactions on Reliability, 49(2), 176–187.

    Article  Google Scholar 

  • Levitin, G., Lisnianski, A., Ben-Haim, H., & Elmakis, D. (1998). Redundancy optimization for series-parallel multi-state systems. IEEE Transactions on Reliability, 47(2), 165–172.

    Article  Google Scholar 

  • Liang, Y.-C., & Chen, Y.-C. (2007). Redundancy allocation of series-parallel systems using a variable neighborhood search algorithm. Reliability Engineering & System Safety, 92(3), 323–331.

    Article  Google Scholar 

  • Liang, Y.-C., & Smith, A. E. (2004). An ant colony optimization algorithm for the redundancy allocation problem (RAP). IEEE Transactions on Reliability, 53(3), 417–423.

    Article  Google Scholar 

  • Mariano, C. H., & Kuri-Morales, A. F. (2012). Complex componential approach for redundancy allocation problem solved by simulation-optimization framework. Journal of Intelligent Manufacturing: 1–20.

  • Massim, Y., Yalaoui, F., Châtelet, E., Yalaoui, A., & Zeblah, A. (2012). Efficient immune algorithm for optimal allocations in series-parallel continuous manufacturing systems. Journal of Intelligent Manufacturing, 23(5), 1603–1619.

    Article  Google Scholar 

  • Mousavi, S. M., Hajipour, V., Niaki, S. T. A., & Aalikar, N. (2013). A multi-product multi-period inventory control problem under inflation and discount: A parameter-tuned particle swarm optimization algorithm. The International Journal of Advanced Manufacturing Technology, 70(9), 1739–1756.

    Google Scholar 

  • Mousavi, S. M., Bahreininejad, A., Musa, S. N., & Yusof, F. (2014a). A modified particle swarm optimization for solving the integrated location and inventory control problems in a two-echelon supply chain network. Journal of Intelligent Manufacturing, 28(1), 191–206.

    Article  Google Scholar 

  • Mousavi, S. M., Niaki, S. T. A., Bahreininejad, A., & Musa, S. N. (2014b). Multi-Item Multiperiodic Inventory Control Problem with Variable Demand and Discounts: A Particle Swarm Optimization Algorithm. The Scientific World Journal, 2014, 1–16.

  • Mousavi, S. M., Alikar, N., & Niaki, S. T. A. (2015a). An improved fruit fly optimization algorithm to solve the homogeneous fuzzy series–parallel redundancy allocation problem under discount strategies. Soft Computing, 20(6), 2281–2307.

    Article  Google Scholar 

  • Mousavi, S. M., Alikar, N., Niaki, S. T. A., & Bahreininejad, A. (2015b). Two tuned multi-objective meta-heuristic algorithms for solving a fuzzy multi-state redundancy allocation problem under discount strategies. Applied Mathematical Modelling, 39(22), 6968–6989.

  • Nahas, N., Nourelfath, M., & Ait-Kadi, D. (2007). Coupling ant colony and the degraded ceiling algorithm for the redundancy allocation problem of series-parallel systems. Reliability Engineering & System Safety, 92(2), 211–222.

    Article  Google Scholar 

  • Naka, S., Genji, T., Yura, T., & Fukuyama, Y. (2001). Practical distribution state estimation using hybrid particle swarm optimization. Paper presented at the Power Engineering Society Winter Meeting, 2001.

  • Nannen, V., & Eiben, A. E. (2007). Efficient relevance estimation and value calibration of evolutionary algorithm parameters. In: IEEE Congress on Evolutionary Computation, 2007. CEC 2007, pp. 103–110.

  • Ouzineb, M., Nourelfath, M., & Gendreau, M. (2008). Tabu search for the redundancy allocation problem of homogenous series-parallel multi-state systems. Reliability Engineering & System Safety, 93(8), 1257–1272.

    Article  Google Scholar 

  • Sha, D., & Hsu, C.-Y. (2008). A new particle swarm optimization for the open shop scheduling problem. Computers & Operations Research, 35(10), 3243–3261.

    Article  Google Scholar 

  • Shi, Y., & Eberhart, R. C. (1999). Empirical study of particle swarm optimization. Paper presented at the Evolutionary Computation, 1999. CEC 99. Proceedings of the 1999 Congress on.

  • Smit, S. K., & Eiben, A. E. (2009). Comparing parameter tuning methods for evolutionary algorithms. In: IEEE Congress on Evolutionary Computation, 2009. CEC 2009, pp. 399–406

  • Tavakkoli-Moghaddam, R., Safari, J., & Sassani, F. (2008). Reliability optimization of series-parallel systems with a choice of redundancy strategies using a genetic algorithm. Reliability Engineering & System Safety, 93(4), 550–556.

    Article  Google Scholar 

  • Tillman, F. A., Hwang, C.-L., & Kuo, W. (1977). Optimization techniques for system reliability with redundancy—A review. IEEE Transactions on Reliability, 26(3), 148–155.

    Article  Google Scholar 

  • Zhang, H., Tam, C., & Li, H. (2006). Multimode project scheduling based on particle swarm optimization. Computer-Aided Civil and Infrastructure Engineering, 21(2), 93–103.

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the anonymous reviewers and the editor for their insightful comments and suggestions.

Author information

Authors and Affiliations

  1. Department of Industrial Engineering Shiraz Branch, Islamic Azad University, Shiraz, Iran

    Seyed Mohsen Mousavi

  2. Department of Mechanical Engineering, Faculty of Engineering, University of Malaya, Kuala Lumpur, Malaysia

    Najmeh Alikar

  3. Business Systems and Analytics Department, Distinguished Chair of Business Analytics, La Salle University, Philadelphia, PA, 19141, USA

    Madjid Tavana

  4. Business Information Systems Department, Faculty of Business Administration and Economics, University of Paderborn, 33098, Paderborn, Germany

    Madjid Tavana

  5. Department of Mathematics and Statistics, York University, Toronto, Canada

    Debora Di Caprio

  6. Polo Tecnologico IISS G. Galilei, Via Cadorna 14, 39100, Bolzano, Italy

    Debora Di Caprio

Authors
  1. Seyed Mohsen Mousavi
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Najmeh Alikar
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Madjid Tavana
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Debora Di Caprio
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Madjid Tavana.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mousavi, S.M., Alikar, N., Tavana, M. et al. An improved particle swarm optimization model for solving homogeneous discounted series-parallel redundancy allocation problems. J Intell Manuf 30, 1175–1194 (2019). https://doi.org/10.1007/s10845-017-1311-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10845-017-1311-9

Keywords