Multi-objective grey wolf optimizer approach to the reliability-cost optimization of life support system in space capsule

  • Anuj Kumar
  • Sangeeta Pant
  • Mangey RamEmail author
  • Shshank Chaube
Original Article


The purpose of this paper is to do the reliability-cost optimization of the life support system (LSS) in a space capsule by using a multi-objective gray wolf optimizer algorithm (MOGWO). MOGWO is a population based metaheuristic which mimics the hierarchal & hunting behavior of grey wolves (Canis lupus). An interactive reliability-cost front has been generated by using MOGWO from which decision makers can choose a point of his/her interest. The efficiency of MOGWO in optimizing the reliability-cost of LSS have also been demonstrated by comparing its results with a very popular swarm based optimization technique named multi-objective particle swarm optimization. A framework based upon MOGWO, which is a very new nature inspired metaheuristic, have been presented for reliability-cost optimization of LSS in a space capsule.


Multi-objective optimization Grey wolf optimizer Reliability optimization Space capsule 



  1. Apostolakis GE (1974) Mathematical methods of probabilistic safety analysis. Technical ReportGoogle Scholar
  2. Coello CAC, Pulido GT, Lechuga MS (2004) Handling multiple objectives with particle swarm optimization. IEEE Trans Evol Comput 8(3):256–279Google Scholar
  3. Coit DW, Smith AE (1996) Reliability optimization of series–parallel systems using a genetic algorithm. IEEE Trans Reliab 45:254–260Google Scholar
  4. Fleischer M (2003) The measure of Pareto optima applications to multi-objective metaheuristics. In: Evolutionary multi-criteria optimization, pp 519–533.
  5. Jahromi EA, Feizabadi M (2017) Optimization of multi-objective redundancy allocation problem with non-homogeneous components. Comput Ind Eng 108(2017):111–123Google Scholar
  6. Kishore A, Yadav SP, Kumar S (2009) A multi objective genetic algorithm for reliability optimization problem. Int J Perform Eng 5(3):227–234Google Scholar
  7. Kumar A, Singh SB (2008) Reliability analysis of an n-unit parallel standby system under imperfect switching using copula. Comput Model New Technol 12(1):47–55MathSciNetGoogle Scholar
  8. Kumar A, Pant S, Ram M (2016a) System reliability optimization using grey wolf optimizer algorithm. Qual Reliab Eng Int. Google Scholar
  9. Kumar A, Pant S, Singh SB (2016b) Reliability optimization of complex system by using cuckoos search algorithm. In: Mathematical concepts and applications in mechanical engineering and mechatronics. IGI Global Publisher, pp 95–112Google Scholar
  10. Kumar A, Pant S, Singh SB (2017a) Availability and cost analysis of an engineering system involving subsystems in series configuration. Int J Qual Reliab Manag 34(6):879–894. Google Scholar
  11. Kumar A, Pant S, Ram M, Singh SB (2017b) On solving complex reliability optimization problem using multi-objective particle swarm optimization. In: Ram M, Davim JP (eds) Mathematics applied to engineering. Elsevier, Amsterdam, pp 115–131Google Scholar
  12. Kuo W, Prasad VR (2000) An annotated overview of system-reliability optimization. IEEE Trans Reliab 49:176–187Google Scholar
  13. Marseguerra M, Zio E, Podofillini L (2014) Optimal reliability/availability performance of uncertain systems via multiobjective genetic algorithms: a nuclear application. IEEE Trans Reliab 53(3):424–434Google Scholar
  14. Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61Google Scholar
  15. Mirjalili S, Saremi S, Mirjalili SM, Coelho L (2016) Multi-objective grey wolf optimizer: a novel algorithm for multi-criterion optimization. Expert Syst Appl 47:106–119Google Scholar
  16. Ngatchou P, Zarei A, ElSharkawi M (2005) Pareto multiobjective optimization. In: Proceedings of the 13th international conference on the intelligent systems application to power systemsGoogle Scholar
  17. Pant S, Singh SB (2011) Particle swarm optimization to reliability optimization in complex system. In: IEEE international conference on quality and reliability, Bangkok, pp 211–215Google Scholar
  18. Pant S, Anand D, Kishor A, Singh SB (2015a) A particle swarm algorithm for optimization of complex system reliability. Int J Perform Eng 11(1):33–42Google Scholar
  19. Pant S, Kumar A, Kishor A, Anand D, Singh SB (2015b) Application of a multi-objective particle swarm optimization technique to solve reliability optimization problem. In: The proceeding of IEEE international conference on next generation computing technologies, pp 1004–1007Google Scholar
  20. Pant S, Kumar A, Ram M (2017a) Reliability optimization: a particle swarm approach. In: Ram M, Davim JP (eds) Advances in reliability and system engineering, Springer, Berlin, pp 163–187Google Scholar
  21. Pant S, Kumar A, Ram M (2017b) Flower pollination algorithm development: a state of art review. Int J Syst Assur Eng Manag. 8(Suppl 2):1858. Google Scholar
  22. Pant S, Kumar A, Singh SB, Ram M (2017c) A modified particle swarm optimization algorithm for nonlinear optimization. Nonlinear Stud 24(1):127–138zbMATHGoogle Scholar
  23. Ram M (2013) On system reliability approaches: a brief survey. Int J Syst Assur Eng Manag 4(2):101–117Google Scholar
  24. Rani M, Sharma SP, Garg H (2013) A novel approach for analyzing the behaviour of industrial systems under uncertainty. Int J Perform Eng 9(2):201–210Google Scholar
  25. Ravi V (2004) Optimization of complex system reliability by a modified great deluge algorithm. Asia-Pac J Oper Res 21(4):487–497MathSciNetzbMATHGoogle Scholar
  26. Ravi V, Murty BSN, Reddy J (1997) Nonequilibrium simulated-annealing algorithm applied to reliability optimization of complex systems. IEEE Trans Reliab 46(2):233–239Google Scholar
  27. Shelokar PS, Jayaraman VK, Kulkarni BD (2002) Ant algorithm for single and multiobjective reliability optimization problems. Qual Reliab Eng Int 18(6):497–514Google Scholar
  28. Tillman FA, Hwang CL, Kuo W (1980) Optimization of systems reliability. Marcel Dekker Inc., New YorkzbMATHGoogle Scholar
  29. While L et al (2006) A faster algorithm for calculating hypervolume. IEEE Trans Evol Comput 10(1):29–38Google Scholar
  30. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evolut Comput 1:67–82Google Scholar
  31. Yeh WC (2009) A two-stage discrete particle swarm optimization for the problem of multiple multi-level redundancy allocation in series systems. Expert Syst Appl 36(5):9192–9200Google Scholar
  32. Zamali T, Lazim AM, Osman MTA (2008) An introduction to conflicting bifuzzy set theory, international. J Math Stat 3:86–101MathSciNetzbMATHGoogle Scholar
  33. Zio E, Di Maio F, Martorell S (2008) Fusion of artificial neural networks and genetic algorithms for multi-objective system reliability design optimization. J Risk Reliab 222(2):115–126Google Scholar

Copyright information

© The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Petroleum and Energy StudiesDehradunIndia
  2. 2.Department of Mathematics, Computer Science and EngineeringGraphic Era (Deemed to be University)DehradunIndia

Personalised recommendations