Journal of Intelligent Manufacturing

, Volume 25, Issue 3, pp 603–616 | Cite as

Optimizing bi-objective imperfect preventive maintenance model for series-parallel system using established hybrid genetic algorithm



This study establishes a bi-objective imperfect preventive maintenance (BOIPM) model of a series-parallel system. The improvement factor method is used to evaluate the extent to which repairing components can restore the system reliability. The total maintenance cost and mean system reliability are optimized simultaneously through determining the most appropriate maintenance alternative. A bi-objective hybrid genetic algorithm (BOHGA) is established to optimize the BOIPM model. The BOHGA utilizes a Pareto-based technique to determine and retain the superior chromosomes as the GA chromosome evolutions are performed. Additionally, a unit-cost cumulative reliability expectation measure (UCCREM) is developed to evaluate the extent to which maintaining each individual component benefits the total maintenance cost and system reliability over the operational lifetime. This UCCREM is then incorporated into the genetic algorithm to construct a superior initial chromosome population and thereby enhance its solution efficiency. In order to obtain diverse bi-objective solutions as the Pareto-efficient frontier is approached, the closeness metric and diversity metric are employed to evaluate the superiority of the non-dominated solutions. Accordingly, decision makers can easily determine the most appropriate maintenance alternative. Three simulated cases verify the efficacy and practicality of this approach for determining an imperfect preventive maintenance strategy.


Imperfect preventive maintenance Hybrid genetic algorithm Multi-objective optimization Pareto- efficient frontier 


  1. Bai, J.,& Pham, H. (2006). Cost analysis on renewable full-service warranties for multi-component systems. European Journal of Operational Research, 168, 492–508. Google Scholar
  2. Baker, B. M.,& Ayechew, M. A. (2003). A genetic algorithm for the vehicle routing problem. Computers and Operations Research, 30, 787–800.CrossRefGoogle Scholar
  3. Berrichi, A., Amodeo, L., Yalaoui, F., Châtelet, E.,& Mezghiche, M. (2009). Bi-objective optimization algorithms for joint production and maintenance scheduling: Application to the parallel machine problem. Journal of Intelligent Manufacturing, 20, 389–400.Google Scholar
  4. Bris, R., Chatelet, E.,& Yalaoui, F. (2003). New method to minimize the preventive maintenance cost of series-parallel systems. Reliability Engineering& System Safety, 82, 247–255.Google Scholar
  5. Busacca, P., Marseguerra, M.,& Zio, E. (2001). Multi-objective optimization by genetic algorithms: Application to safety systems. Reliability Engineering& System Safety, 72, 59–74.Google Scholar
  6. Castro, I. T. (2009). A model of imperfect preventive maintenance with dependent failure modes. European Journal of Operational Research, 196, 217–224.CrossRefGoogle Scholar
  7. Coello, C. A. C. (1999). A comprehensive survey of evolutionary-based multi-objective optimization techniques. International Journal of Knowledge and Information System, 1(3), 269–308.CrossRefGoogle Scholar
  8. Deb, K., Agrawal, S., Pratap, A.,& Meyarivan, T. (2002). A fast and elitist multi-objective genetic algorithm: NSGAII. IEEE Transactions on Evolutionary Computation, 6, 182–197.Google Scholar
  9. Deb, K. (2001). Multi-objective optimization using evolutionary algorithms. MA: Wiley.Google Scholar
  10. Elsayed, A. (1996). Reliability engineering. MA: Wiley.Google Scholar
  11. Fonseca, C. M.,& Fleming, P. J. (1998). Multi-objective optimization and multiple constraint handling with evolutionary algorithms—part I: A unified formulation. IEEE Transactions on SMC—Part A: System and Humans, 28(1), 26–37.Google Scholar
  12. Fonseca, C. M.,& Fleming, P. J. (1997). Multi-objective optimization. NY: Oxford (Handbook of Evolutionary Computation).Google Scholar
  13. Gen, M.,& Cheng, R. (1997). Genetic algorithms and engineering design (pp. 133–172). MA: Wiley.Google Scholar
  14. Harrington, E. (1965). The desirability function. Industrial Quality Control, 21(10), 494–498.Google Scholar
  15. Hsieh, Y. C., Chen, T. C.,& Bricker, D. L. (1998). Genetic algorithms for reliability design problems. Microelectronics Reliability, 38, 1599–1605.Google Scholar
  16. Khatab, A., Rezg, N.,& Ait-Kadi, D. (2011). Optimum block replacement policy over a random time horizon. Journal of Intelligent Manufacturing, 22(6), 885–889.Google Scholar
  17. Konak, A., Coit, D. W.,& Smith, A. E. (2006). Multi-objective optimization using genetic algorithms: A tutorial. Reliability Engineering& System Safety, 91, 992–1007.Google Scholar
  18. Levitin, G.,& Lisnianski, A. (2000). Optimization of imperfect preventive maintenance for multi-state systems. Reliability Engineering& System Safety, 67, 193–203.CrossRefGoogle Scholar
  19. Liao, W., Pan, E.,& Xi, L. (2010). Preventive maintenance scheduling for repairable system with deterioration. Journal of Intelligent Manufacturing, 21(6), 875–884.Google Scholar
  20. Lin, T. W.,& Wang, C. H. (2012). A hybrid genetic algorithm to minimize the periodic preventive maintenance cost in a series-parallel system. Journal of Intelligent Manufacturing, 23(4), 1225–1236 .Google Scholar
  21. Montgomery, D. C. (2005). Design and analysis of experiments (6th ed.). NY: Wiley.Google Scholar
  22. Moradi, E., Fatemi Ghomi, S. M. T.,& Zandieh, M. (2011). Bi-objective optimization research on integrated fixed time interval preventive maintenance and production for scheduling flexible job-shop problem. Expert Systems with Applications, 38(6), 7169–7178.Google Scholar
  23. Nahas, N., Khatab, A., Ait-Kadi, D.,& Nourelfath, M. (2008). Extended great deluge algorithm for the imperfect preventive maintenance optimization of multi-state systems. Reliability Engineering& System Safety, 93, 1658–1672.Google Scholar
  24. Nakagawa, T. (2005). Maintenance theory of reliability. London: Springer.Google Scholar
  25. Nosoohi, I.,& Hejazi, S. R. (2011). A multi-objective approach to simultaneous determination of spare part numbers and preventive replacement times. Applied Mathematical Modelling, 35, 1157–1166.CrossRefGoogle Scholar
  26. Osyczka, A.,& Kundu, S. (1996). A modified distance method for multi-criteria optimization, using genetic algorithms. Computers& Industrial Engineering, 30, 871–882.CrossRefGoogle Scholar
  27. Park, D. H., Jung, G. M.,& Yum, J. K. (2000). Cost minimization for periodic maintenance policy of a system subject to slow degradation. Reliability Engineering& System Safety, 68, 105–112.Google Scholar
  28. Pham, H.,& Wang, H. Z. (1996). Imperfect maintenance. European Journal of Operational Research, 94, 425–438.CrossRefGoogle Scholar
  29. Quan, G., Greenwood, G. W., Donglin, L.,& Sharon, H. (2007). Searching for multi-objective preventive maintenance schedules: Combining preferences with evolutionary algorithms. European Journal of Operational Research, 177, 1969–1984.Google Scholar
  30. Rudolph, G. (2001). Evolutionary search under partially ordered fitness sets. In Proceedings of the international symposium on information science innovations in engineering of natural and artificial intelligent systems, pp. 818–822.Google Scholar
  31. Sachdeva, A., Kumar, D.,& Kumar, P. (2008). Planning and optimizing the maintenance of paper production systems in a paper plant. Computers and Industrial Engineering, 55, 817–829.Google Scholar
  32. Schutz, J., Rezg, N.,& Léger, J.-B. (2011). An integrated strategy for efficient business plan and maintenance plan for systems with a dynamic failure distribution. Journal of Intelligent Manufacturing. doi:10.1007/s10845-011-0543-3.
  33. Soro, I. W., Nourelfath, M.,& Aıt-Kadi, D. (2010). Performance evaluation of multi-state degraded systems with minimal repairs and imperfect preventive maintenance. Reliability Engineering& System Safety, 95, 65–69.Google Scholar
  34. Srinivas, N.,& Deb, K. (1994). Multi-objective optimization using non-dominated sorting in genetic algorithms. Evolutionary Computation, 2(3), 221–248.Google Scholar
  35. 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, 550–556.Google Scholar
  36. Tian, Z., Lin, D.,& Wu, B. (2012). Condition based maintenance optimization considering multiple objectives. Journal of Intelligent Manufacturing, 23(2), 333–340.Google Scholar
  37. Tsai, Y. T., Wang, K. S.,& Teng, H. Y. (2001). Optimizing preventive maintenance for mechanical components using genetic algorithms. Reliability Engineering& System Safety, 74, 89–97.Google Scholar
  38. Tsai, Y. T., Wang, K. S.,& Tsai, L. C. (2004). A study of availability-centered preventive maintenance for multi-component systems. Reliability Engineering& System Safety, 261–270.Google Scholar
  39. Wang, H. Z. (2002). A survey of maintenance policies of deteriorating systems. European Journal of Operational Research, 139, 469–489.CrossRefGoogle Scholar
  40. Wang, C. H.,& Li, C. H. (2011). Optimization of an established multi-objective delivering problem by an improved hybrid algorithm. Expert Systems with Applications, 38, 4361–4367.CrossRefGoogle Scholar
  41. Wang, C. H., Lu, J. Z.,& Wu, C. J. (2009). Optimization of a multi-objective transportation model during War for military. The Journal of Chung Cheng Institute of Technology, 37(2), 10–29.Google Scholar
  42. Yamachi, H., Tsujimura, Y., Kambayashi, Y.,& Yamamoto, H. (2006). Multi-objective genetic algorithm for solving N-version program design problem. Reliability Engineering& System Safety, 91, 1083–1094.Google Scholar
  43. Zequeira, R. I.,& Bérenguer, C. (2006). Periodic imperfect preventive maintenance with two categories of competing failure modes. Reliability Engineering& System Safety, 91, 460–468.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Department of Power Vehicle and Systems EngineeringChung Cheng Institute of Technology, National Defense UniversityTauyuan CountyTaiwan (R.O.C)

Personalised recommendations