Open Access   Article

Using Reference Point-Based NSGA-II to System Reliability

H. Kumar1 , S.P. Yadav2

1 Department of Mathematics, I.I.T. Roorkee, Roorkee, India.
2 Department of Mathematics, I.I.T. Roorkee, Roorkee, India.

Correspondence should be addressed to:

Section:Research Paper, Product Type: Journal Paper
Volume-5 , Issue-12 , Page no. 7-14, Dec-2017


Online published on Dec 31, 2017

Copyright © H. Kumar, S.P. Yadav . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

View this paper at   Google Scholar | DPI Digital Library


IEEE Style Citation: H. Kumar, S.P. Yadav, “Using Reference Point-Based NSGA-II to System Reliability”, International Journal of Computer Sciences and Engineering, Vol.5, Issue.12, pp.7-14, 2017.

MLA Style Citation: H. Kumar, S.P. Yadav "Using Reference Point-Based NSGA-II to System Reliability." International Journal of Computer Sciences and Engineering 5.12 (2017): 7-14.

APA Style Citation: H. Kumar, S.P. Yadav, (2017). Using Reference Point-Based NSGA-II to System Reliability. International Journal of Computer Sciences and Engineering, 5(12), 7-14.

309 333 downloads 124 downloads


In principle, a multi-objective optimization problem (MOOP) provides a group of non-dominated solutions (popularly known as Pareto-optimal solutions) for the decision maker (DM). A DM is undecidable to claim one of these solutions to be better than another in the absence of any further information. Due to this reason, a DM needs as many Pareto-optimal solutions as possible. Classical optimization methods are unable to produce multiple solutions at a time because of converting the MOOP to a single-objective optimization problem (SOOP). In the past decades, multi-objective evolutionary algorithms (MOEAs) have been developed to be powerful techniques of identifying a complete picture of the Pareto-optimal solutions space, where a DM can select one out of these solutions according to his/her preference. Moreover, a more efficient MOEA can exploit the search in a better position if the DM provides some general views or ideas about the solution in terms of reference points or weights. Reference point based NSGA-II (R-NSGA-II) is such type of an MOEA where DM’s assigned reference points are used to search the solutions and its diversity is controlled efficiently. This paper presents the applicability of the R-NSGA-II algorithm to the system reliability design problem. The simulation results show the advantage of R-NSGA-II over NSGA-II.

Key-Words / Index Term

Multi-objective optimization problem (MOOP), Multi-objective evolutionary algorithms (MOEAs), Reference points, System reliability, Pareto-optimal front (POF)


[1] K. Deb, “Multi-objective optimization using evolutionary algorithms”, John Wiley & Sons, 2001.
[2] J. Knowles, D. Corne, “The Pareto archived evolution strategy: A new baseline algorithm for multiobjective optimization”, In Proceedings of the 1999 Congress on Evolutionary Computation. Piscataway, NJ: IEEE Press, DOI: 10.1109/CEC.1999.781913, 1999.
[3] N. Srinivas, K. Deb, “Multi-objective optimization using non-dominated sorting in genetic algorithms”, Evol. Comput., Vol. 2, no. 3, pp. 221-248, 1994.
[4] J. Horn, N. Nafploitis, D. Goldberg, “A niched Pareto genetic algorithm for multi-objective optimization”, In Proceedings of the First IEEE Conference on Evolutionary Computation, pp. 82-87, 1994.
[5] E. Zitzler, L. Thiele, “An evolutionary algorithm for multi-objective optimization: The strength Pareto approach”, Technical report 43, Zurich, Switzerland: Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH), 1998.
[6] K. Deb, S. Agarwal, A. Pratap, T. Meyarivan, “A fast and elitist multi-objective genetic algorithm: NSGA-II”, IEEE Trans. Evol. Comput., Vol. 6, pp. 182-197, 2002.
[7] K. Deb, J. Sundar, U.B. Rao, S. Chaudhuri, “Reference Point Based Multi-Objective Optimization Using Evolutionary Algorithms”, International Journal of Computational Intelligence Research, Vol. 2, No. 3, pp. 273-286, 2006.
[8] H. Garg, S.P. Sharma, “Multi-objective reliability-redundancy allocation problem using particle swarm optimization”, Computers & Industrial Engineering, Vol. 64, No. 1, pp. 247-255, 2012.
[9] G.D. Goldberg, “Genetic algorithms for search, optimization, and machine learning”, Reading, MA: Addison-Wesley, 1989.
[10] D. Salazar, C.M. Rocco, B. J. Galvan, “Optimization of constrained multiple objective reliability problems using evolutionary algorithms”, Reliability Engineering and System Safety, 91, pp. 1057-1070, 2006.
[11] A. Kishore, S. P. Yadav, S. Kumar, “Application of a Multi-objective Genetic Algorithm to solve Reliability Optimization Problem”, International Conference on Computational Intelligence and Multimedia Applications, pp. 458-462, DOI: 10.1109/ICCIMA, 2007.
[12] A. Kishore, S. P. Yadav, S. Kumar, “Interactive fuzzy multiobjective optimization using NSGA-II”, OPSEARCH, Vol. 46, No. 2, pp. 214-224, 2009.
[13] Z. Wang, T. Chen, K. Tang., X. Yao, “A Multi-objective Approach to Redundancy Allocation Problem in Parallel-series Systems”, IEEE, pp. 582-589, DOI: 978-1-4244-2959-2/09, 2009.
[14] J. Safari, “Multi-objective reliability optimization of series-parallel systems with a choice of redundancy strategies”, Reliab Eng Syst Saf., 108, pp. 10–20, 2012.
[15] K. Khalili-Damghani, A. R. Abtahi, M. Tavana, “A decision support system for solving multi-objective redundancy allocation problems”, Qual Reliab Eng Int, Vol. 30, No. 8, pp. 1249-1262, 2014.
[16] A. Taboada, F. Baheranwala, D.W. Coit, “Practical solutions for multi-objective optimization: An application to system reliability design problems”, Rel. Engg. Syst. Saft., 92, pp. 314-322, 2007.
[17] K.K. Aggarwal, J.S. Gupta, “On minimizing the cost of reliable systems”, IEEE Transaction on Reliability R-24 (3), pp. 205, 1975.
[18] V. Ravi, B.S.N. Murthy, P.J. Reddy, “Nonequilibrium simulated annealing algorithm applied to reliability optimization of complex systems”, IEEE Trans. On Rel., Vol. 46, No. 2, pp. 233-239, 2000.