This article addresses the system reliability optimization problem as reliability–redundancy allocation problem, aiming to maximize the system reliability through a trade-off between redundancy levels and the reliability of the components. In this study, cold-standby strategy has been considered for the redundant components, and a population-based meta-heuristic algorithm, called stochastic fractal search, is applied to solve different benchmark problems. Using the proposed stochastic fractal search algorithm, all the benchmark problems are improved and new structures with higher reliability values have been found. The experimental results reveal the superiority of the proposed stochastic fractal search algorithm in terms of quality and robustness of the solutions in cold-standby redundancy case compared to all previous studies.
ElsayedEA.Reliability engineering. Hoboken, NJ: John Wiley & Sons, 2012.
2.
KuoWPrasadVR.An annotated overview of system-reliability optimization. IEEE Trans Reliab2000; 49: 176–187.
3.
LevitinGXingLDaiY.Optimal sequencing of warm standby elements. Comput Ind Eng2013; 65: 570–576.
4.
CoitDW.Maximization of system reliability with a choice of redundancy strategies. IIE Trans2003; 35: 535–543.
5.
HaCKuoW.Reliability redundancy allocation: an improved realization for nonconvex nonlinear programming problems. Eur J Oper Res2006; 171: 24–38.
6.
ChernM-S.On the computational complexity of reliability redundancy allocation in a series system. Oper Res Lett1992; 11: 309–315.
7.
Tavakkoli-MoghaddamRSafariJSassaniF.Reliability optimization of series-parallel systems with a choice of redundancy strategies using a genetic algorithm. Reliab Eng Syst Saf2008; 93: 550–556.
8.
CoitDW.Cold-standby redundancy optimization for nonrepairable systems. IIE Trans2001; 33: 471–478.
9.
WangWXiongJXieM.A study of interval analysis for cold-standby system reliability optimization under parameter uncertainty. Comput Ind Eng2016; 97: 93–100.
10.
ValaeiMRBehnamianJ.Allocation and sequencing in 1-out-of-N heterogeneous cold-standby systems: multi-objective harmony search with dynamic parameters tuning. Reliab Eng Syst Saf2017; 157: 78–86.
11.
KuoWLinH-HXuZ, et al. Reliability optimization with the Lagrange-multiplier and branch-and-bound technique. IEEE Trans Reliab1987; 36: 624–630.
12.
ZiaLCoitDW.Redundancy allocation for series-parallel systems using a column generation approach. IEEE Trans Reliab2010; 59: 706–717.
13.
ArdakanMAHamadaniAZ.Reliability–redundancy allocation problem with cold-standby redundancy strategy. Simul Model Pract Theory2014; 42: 107–118.
14.
KuoWWanR.Recent advances in optimal reliability allocation. In: LevitinG (ed.) Computational intelligence in reliability engineering. Berlin: Springer, 2007, pp.1–36.
15.
HookeRJeevesTA.“Direct search” solution of numerical and statistical problems. J ACM1961; 8: 212–229.
16.
TillmanFAHwangC-LKuoW.Determining component reliability and redundancy for optimum system reliability. IEEE Trans Reliab1977; 26: 162–165.
17.
GopalKAggarwalKKGuptaJS.An improved algorithm for reliability optimization. IEEE Trans Reliab1978; 27: 325–328.
18.
SharmaJVenkateswaranKV.A direct method for maximizing the system reliability. IEEE Trans Reliab1971; 20: 256–259.
19.
ArdakanMARezvanMT.Multi-objective optimization of reliability–redundancy allocation problem with cold-standby strategy using NSGA-II. Reliab Eng Syst Saf2018; 172: 225–238.
20.
KimHKimP.Reliability–redundancy allocation problem considering optimal redundancy strategy using parallel genetic algorithm. Reliab Eng Syst Saf2017; 159: 153–160.
21.
KhorshidiHAGunawanIIbrahimMY.A value-driven approach for optimizing reliability-redundancy allocation problem in multi-state weighted k-out-of-n system. J Manuf Syst2016; 40: 54–62.
22.
HsiehY-CChenT-CBrickerDL.Genetic algorithms for reliability design problems. Microelectron Reliab1998; 38: 1599–1605.
23.
Dos Santos CoelhoL. An efficient particle swarm approach for mixed-integer programming in reliability–redundancy optimization applications. Reliab Eng Syst Saf2009; 94: 830–837.
24.
ZhangEWuYChenQ.A practical approach for solving multi-objective reliability redundancy allocation problems using extended bare-bones particle swarm optimization. Reliab Eng Syst Saf2014; 127: 65–76.
25.
GargHRaniMSharmaSP, et al. Bi-objective optimization of the reliability-redundancy allocation problem for series-parallel system. J Manuf Syst2014; 33: 335–347.
26.
HuangC-L.A particle-based simplified swarm optimization algorithm for reliability redundancy allocation problems. Reliab Eng Syst Saf2015; 142: 221–230.
27.
HeQHuXRenH, et al. A novel artificial fish swarm algorithm for solving large-scale reliability–redundancy application problem. ISA Trans2015; 59: 105–113.
28.
YehW-C.A novel boundary swarm optimization method for reliability redundancy allocation problems. Reliab Eng Syst Saf. Epub ahead of print 5 February 2018. DOI: 10.1016/j.ress.2018.02.002.
29.
GargH.An approach for solving constrained reliability-redundancy allocation problems using cuckoo search algorithm. Beni-suef Univ J Basic Appl Sci2015; 4: 14–25.
30.
GargH.An efficient biogeography based optimization algorithm for solving reliability optimization problems. Swarm Evol Comput2015; 24: 1–10.
31.
ChenT-C.IAs based approach for reliability redundancy allocation problems. Appl Math Comput2006; 182: 1556–1567.
32.
ZouDGaoLLiS, et al. An effective global harmony search algorithm for reliability problems. Expert Syst Appl2011; 38: 4642–4648.
33.
MellalMAZioE.A penalty guided stochastic fractal search approach for system reliability optimization. Reliab Eng Syst Saf2016; 152: 213–227.
34.
MisraKBLjubojevicMD.Optimal reliability design of a system: a new look. IEEE Trans Reliab1973; 22: 255–258.
35.
HikitaMNakagawaYNakashimaK, et al. Reliability optimization of systems by a surrogate-constraints algorithm. IEEE Trans Reliab1992; 41: 473–480.
36.
NakagawaYNakashimaK.A heuristic method for determining optimal reliability allocation. IEEE Trans Reliab1977; 26: 156–161.
37.
KohdaTInoueK.A reliability optimization method for complex systems with the criterion of local optimality. IEEE Trans Reliab1982; 31: 109–111.
38.
SamroutMYalaouiFChâteletE, et al. New methods to minimize the preventive maintenance cost of series–parallel systems using ant colony optimization. Reliab Eng Syst Saf2005; 89: 346–354.
39.
NahasNNourelfathM.Ant system for reliability optimization of a series system with multiple-choice and budget constraints. Reliab Eng Syst Saf2005; 87: 1–12.
40.
ValianETavakoliSMohannaS, et al. Improved cuckoo search for reliability optimization problems. Comput Ind Eng2013; 64: 459–468.
41.
ValianEValianE.A cuckoo search algorithm by Lévy flights for solving reliability redundancy allocation problems. Eng Optim2013; 45: 1273–1286.
42.
HsiehY-CYouP-S.An effective immune based two-phase approach for the optimal reliability–redundancy allocation problem. Appl Math Comput2011; 218: 1297–1307.
43.
WangLLiL.A coevolutionary differential evolution with harmony search for reliability–redundancy optimization. Expert Syst Appl2012; 39: 5271–5278.
44.
YehW-CHsiehT-J.Solving reliability redundancy allocation problems using an artificial bee colony algorithm. Comput Oper Res2011; 38: 1465–1473.
45.
AfonsoLDMarianiVCdos Santos CoelhoL.Modified imperialist competitive algorithm based on attraction and repulsion concepts for reliability-redundancy optimization. Expert Syst Appl2013; 40: 3794–3802.
46.
SoltaniR.Reliability optimization of binary state non-repairable systems: a state of the art survey. Int J Ind Eng Comput2014; 5: 339–364.
47.
RabbaniMBosjinSYazdanparastR, et al. A stochastic time-dependent green capacitated vehicle routing and scheduling problem with time window, resiliency and reliability: a case study. Decis Sci Lett2018; 7: 381–394.
48.
ShekharCJainMRainaA, et al. Sensitivity analysis of repairable redundant system with switching failure and geometric reneging. Decis Sci Lett2017; 6: 337–350.
49.
GunjiBDeepakBBahubalendruniM, et al. Hybridized genetic-immune based strategy to obtain optimal feasible assembly sequences. Int J Ind Eng Comput2017; 8: 333–346.
WuPGaoLZouD, et al. An improved particle swarm optimization algorithm for reliability problems. ISA Trans2011; 50: 71–81.
52.
SunCWeiZ-QZhouC-J, et al. Stochastic fractal search algorithm for 3D protein structure prediction. Destech Trans Comput Sci Eng2016; 1: 156–160.
53.
RahmanTAZ. Parameters optimization of an SVM-classifier using stochastic fractal search algorithm for monitoring an aerospace structure. Int J Fluids Heat Transf2016; 1: 68–78.
54.
SahaDSaikiaLC.Impact of phase-locked loop on system dynamics of a CCGT incorporated diverse source system employed with AC/DC interconnection. J Renew Sustain Energy2017; 9: 045506.
55.
MosbahHEl-HawaryME.Optimization of neural network parameters by Stochastic Fractal Search for dynamic state estimation under communication failure. Electr Power Syst Res2017; 147: 288–301.
56.
MosaviMRKhisheMHatam KhaniY, et al. Training radial basis function neural network using stochastic fractal search algorithm to classify sonar dataset. Iran J Electr Electron Eng2017; 13: 100–111.
57.
Mezura-MontesECoelloCAC. Constraint-handling in nature-inspired numerical optimization: past, present and future. Swarm Evol Comput2011; 1: 173–194.
58.
JiaXChenHChengZ, et al. A comparison between two switching policies for two-unit standby system. Reliab Eng Syst Saf2016; 148: 109–118.
59.
KimH.Maximization of system reliability with the consideration of component sequencing. Reliab Eng Syst Saf2018; 170: 64–72.
60.
ArdakanMAHamadaniAZ.Reliability optimization of series–parallel systems with mixed redundancy strategy in subsystems. Reliab Eng Syst Saf2014; 130: 132–139.
