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Soft Computing

, Volume 20, Issue 6, pp 2281–2307 | Cite as

An improved fruit fly optimization algorithm to solve the homogeneous fuzzy series–parallel redundancy allocation problem under discount strategies

  • Seyed Mohsen MousaviEmail author
  • Najmeh Alikar
  • Seyed Taghi Akhavan Niaki
Methodologies and Application

Abstract

In this paper, a mathematical formulation is first derived for a homogenous fuzzy series–parallel redundancy allocation problem, where both the system and its subsystems can only take two states of complete perfect and complete failure. Identical redundant components are included in order to achieve desirable system reliability. The components of each subsystem characterized by their cost, weight, and reliability, are purchased from the market under all-unit discount and incremental quantity discount strategies. The goal is to find the optimum combination of the number of components for each subsystem that maximizes the system reliability under total fuzzy cost and weight constraints. An improved fruit fly optimization algorithm (IFOA) is proposed to solve the problem, where a particle swarm optimization, a genetic algorithm, and a Tabu search algorithm are utilized to validate the results obtained. These algorithms are the most common ones in the literature to solve series–parallel redundancy allocation problems. Moreover, design of experiments using the Taguchi approach is employed to calibrate the parameters of the algorithms. At the end, some numerical examples are solved to demonstrate the applicability of the proposed methodology. The results are generally in favor IFOA.

Keywords

Fuzzy redundancy allocation problem  Series–parallel systems Discount strategies  Meta-heuristic approaches Taguchi method 

Notes

Acknowledgments

The authors thank the Bright Sparks unit (University of Malaya) for additional financial support. The authors are also thankful for constructive comments of respected anonymous reviewers. Taking care of the comments certainly improved the presentation.

References

  1. Abouei Ardakan M, Zeinal Hamadani A (2014) Reliability–redundancy allocation problem with cold-standby redundancy strategy. Simul Model Pract Theory 42:107–118Google Scholar
  2. Agarwal M, Sharma VK (2010) Ant colony approach to constrained redundancy optimization in binary systems. Appl Math Model 34:992–1003MathSciNetCrossRefzbMATHGoogle Scholar
  3. Beji N, Jarboui B, Eddaly M, Chabchoub H (2010) A hybrid particle swarm optimization algorithm for the redundancy allocation problem. J Comput Sci 1:159–167CrossRefGoogle Scholar
  4. Chern M-S (1992) On the computational complexity of reliability redundancy allocation in a series system. Oper Res Lett 11:309–315MathSciNetCrossRefzbMATHGoogle Scholar
  5. Chiou J-S, Tsai S-H, Liu M-T (2012) A PSO-based adaptive fuzzy PID-controllers. Simul Model Pract Theory 26:49–59Google Scholar
  6. Coit DW, Smith AE (1996a) Reliability optimization of series-parallel systems using a genetic algorithm. IEEE Trans Reliab 45:254–260, 266Google Scholar
  7. Coit DW, Smith AE (1996b) Penalty guided genetic search for reliability design optimization. Comput Ind Eng 30:895–904Google Scholar
  8. Dai H, Zhao G, Lu J, Dai S (2012) Comment and improvement on “A new fruit fly optimization algorithm: taking the financial distress model as an example”. Knowl Based Syst 26:69–74CrossRefGoogle Scholar
  9. Dai H, Liu A, Lu J, Dai S, Wu X, Sun Y (2014) Optimization about the layout of IMUs in large ship based on fruit fly optimization algorithm. Opt Int J Light Electron Opt. doi: 10.1016/j.ijleo.2014.08.037
  10. Garg H, Sharma S (2013) Multi-objective reliability–redundancy allocation problem using particle swarm optimization. Comput Ind Eng 64:247–255CrossRefGoogle Scholar
  11. Garg H, Rani M, Sharma S, Vishwakarma Y (2014) Bi-objective optimization of the reliability–redundancy allocation problem for series–parallel system. J Manuf Syst 33:335–347CrossRefGoogle Scholar
  12. Ha C, Kuo W (2006) Reliability redundancy allocation: an improved realization for nonconvex nonlinear programming problems. Eur J Oper Res 171:24–38MathSciNetCrossRefzbMATHGoogle Scholar
  13. Hu P, Cao G-Y, Zhu X-J, Li J (2010) Modeling of a proton exchange membrane fuel cell based on the hybrid particle swarm optimization with Levenberg–Marquardt neural network. Simul Model Pract Theory 18:574–588CrossRefGoogle Scholar
  14. Jarboui B, Ibrahim S, Siarry P, Rebai A (2008a) A combinatorial particle swarm optimisation for solving permutation flowshop problems. Comput Ind Eng 54:526–538Google Scholar
  15. Jarboui B, Damak N, Siarry P, Rebai A (2008b) A combinatorial particle swarm optimization for solving multi-mode resource-constrained project scheduling problems. Appl Math Comput 195:299–308Google Scholar
  16. Kanagaraj G, Ponnambalam S, Jawahar N (2013) A hybrid cuckoo search and genetic algorithm for reliability–redundancy allocation problems. Comput Ind Eng 66:1115–1124CrossRefGoogle Scholar
  17. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of IEEE international conference on neural networks, Perth, Australia, pp 1942–1948Google Scholar
  18. Khalili-Damghani K, Amiri M (2012) Solving binary-state multi-objective reliability redundancy allocation series–parallel problem using efficient epsilon-constraint, multi-start partial bound enumeration algorithm, and DEA. Reliab Eng Syst Saf 103:35–44Google Scholar
  19. Kulturel-Konak S, Smith AE, Coit DW (2003) Efficiently solving the redundancy allocation problem using Tabu search. IIE Trans 35:515–526CrossRefGoogle Scholar
  20. Kuo W (2001) Optimal reliability design: fundamentals and applications. Cambridge University Press, CambridgeGoogle Scholar
  21. Kuo W, Prasad VR (2000) An annotated overview of system-reliability optimization. IEEE Trans Reliab 49:176–187CrossRefGoogle Scholar
  22. Levitin G, Lisnianski A, Ben-Haim H, Elmakis D (1998) Redundancy optimization for series–parallel multi-state systems. IEEE Trans Reliab 47:165–172CrossRefGoogle Scholar
  23. Li H-Z, Guo S, Li C-J, Sun J-Q (2013) A hybrid annual power load forecasting model based on generalized regression neural network with fruit fly optimization algorithm. Knowl Based Syst 37:378–387CrossRefGoogle Scholar
  24. Li J-Q, Pan Q-K, Mao K, Suganthan P (2014) Solving the steelmaking casting problem using an effective fruit fly optimisation algorithm. Knowl Based Syst 72:28–36CrossRefGoogle Scholar
  25. Liang Y-C, Smith AE (2004) An ant colony optimization algorithm for the redundancy allocation problem (RAP). IEEE Trans Reliab 53:417–423CrossRefGoogle Scholar
  26. Liang Y-C, Chen Y-C (2007) Redundancy allocation of series–parallel systems using a variable neighborhood search algorithm. Reliab Eng Syst Saf 92:323–331CrossRefGoogle Scholar
  27. Lins ID, Droguett EL (2011) Redundancy allocation problems considering systems with imperfect repairs using multi-objective genetic algorithms and discrete event simulation. Simul Model Pract Theory 19:362–381CrossRefGoogle Scholar
  28. Mahapatra G, Roy T (2011) Optimal redundancy allocation in series–parallel system using generalized fuzzy number. Tamsui Oxf J Inf Math Sci 27:1–20MathSciNetzbMATHGoogle Scholar
  29. Mousavi SM, Hajipour V, Niaki STA, Aalikar N (2013a) A multi-product multi-period inventory control problem under inflation and discount: a parameter-tuned particle swarm optimization algorithm. Int J Adv Manuf Technol 70:1739–1756Google Scholar
  30. Mousavi SM, Hajipour V, Niaki STA, Alikar N (2013b) Optimizing multi-item multi-period inventory control system with discounted cash flow and inflation: two calibrated meta-heuristic algorithms. Appl Math Model 37:2241–2256Google Scholar
  31. Mousavi SM, Bahreininejad A, Musa SN, Yusof F (2014a) A modified particle swarm optimization for solving the integrated location and inventory control problems in a two-echelon supply chain network. J Intell Manuf. doi: 10.1007/s10845-014-0970-z
  32. Mousavi SM, Sadeghi J, Niaki STA, Alikar N, Bahreininejad A, Metselaar HSC (2014b) Two parameter-tuned meta-heuristics for a discounted inventory control problem in a fuzzy environment. Inf Sci 276:42–62Google Scholar
  33. 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. Reliab Eng Syst Saf 92:211–222CrossRefGoogle Scholar
  34. Naka S, Genji T, Yura T, Fukuyama Y (2001) Practical distribution state estimation using hybrid particle swarm optimization. In: Power engineering society winter meeting, 2001. IEEE, pp 815–820Google Scholar
  35. Ouzineb M, Nourelfath M, Gendreau M (2008) Tabu search for the redundancy allocation problem of homogenous series-parallel multi-state systems. Reliab Eng Syst Saf 93:1257–1272CrossRefGoogle Scholar
  36. Pan W-T (2012) A new fruit fly optimization algorithm: taking the financial distress model as an example. Knowl Based Syst 26:69–74CrossRefGoogle Scholar
  37. Pan Q-K, Sang H-Y, Duan J-H, Gao L (2014) An improved fruit fly optimization algorithm for continuous function optimization problems. Knowl Based Syst 62:69–83CrossRefGoogle Scholar
  38. Sadeghi J, Mousavi SM, Niaki STA, Sadeghi S (2013) Optimizing a multi-vendor multi-retailer vendor managed inventory problem: two tuned meta-heuristic algorithms. Knowl Based Syst 50:159–170Google Scholar
  39. Sha D, Hsu C-Y (2008) A new particle swarm optimization for the open shop scheduling problem. Comput Oper Res 35:3243–3261CrossRefzbMATHGoogle Scholar
  40. Shi Y, Eberhart RC (1999) Empirical study of particle swarm optimization. In: Proceedings of the 1999 Congress on evolutionary computation, 1999. CEC 99. IEEEGoogle Scholar
  41. Tavakkoli-Moghaddam R, Safari J, Sassani F (2008) Reliability optimization of series–parallel systems with a choice of redundancy strategies using a genetic algorithm. Reliab Eng Syst Saf 93:550–556CrossRefGoogle Scholar
  42. Tillman FA, Hwang C-L, Kuo W (1977) Optimization techniques for system reliability with redundancy? A review. IEEE Trans. Reliab 26:148–155MathSciNetCrossRefzbMATHGoogle Scholar
  43. Wang S, Watada J (2009) Modelling redundancy allocation for a fuzzy random parallel–series system. J Comput Appl Math 232:539–557CrossRefzbMATHGoogle Scholar
  44. Wang L, Zheng X-L, Wang S-Y (2013) A novel binary fruit fly optimization algorithm for solving the multidimensional knapsack problem. Knowl Based Syst 48:17–23CrossRefGoogle Scholar
  45. Wei LS, Wu X, Niu MQ, Chen ZY (2014) FOA based PID controller for human balance keeping. Appl Mech Mater 494:1072–1075CrossRefGoogle Scholar
  46. Yuan X, Dai X, Zhao J, He Q (2014) On a novel multi-swarm fruit fly optimization algorithm and its application. Appl Math Comput 233:260–271MathSciNetzbMATHGoogle Scholar
  47. Zhang H, Tam C, Li H (2006) Multimode project scheduling based on particle swarm optimization. Comput Aided Civil Infrastruct Eng 21:93–103CrossRefGoogle Scholar
  48. Zheng X-L, Wang L, Wang S-Y (2014) A novel fruit fly optimization algorithm for the semiconductor final testing scheduling problem. Knowl Based Syst 57:95–103CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Seyed Mohsen Mousavi
    • 1
    Email author
  • Najmeh Alikar
    • 2
  • Seyed Taghi Akhavan Niaki
    • 3
  1. 1.Young Researchers and Elite Club, Qazvin BranchIslamic Azad UniversityQazvinIran
  2. 2.Centre for Product Development and Manufacture, Department of Mechanical Engineering, Faculty of EngineeringUniversity of MalayaKuala LumpurMalaysia
  3. 3.Department of Industrial EngineeringSharif University of TechnologyTehranIran

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