### Citations

118 |
Normal-Boundary Intersection: A new method for generating the Pareto surface in nonlinear multi-criteria optimization problems”,
- Das, Dennis
- 1998
(Show Context)
Citation Context ... approaches based on whether the solutions found are on the Pareto frontier. Two commonly used deterministic approximate methods are Normal Boundary Intersection (NBI) [34] and Normal Constraint (NC) =-=[35]-=- methods. While these methods are shown to be effective for solving large multi-objective optimization problems, they are not suitable for solving the subsystems’ sub-problems in the decomposition bas... |

52 | Genetic algorithms in optimization of system reliability”, - Painton, Campbell - 1995 |

47 |
Pratap A, Agarwal S, Meyarivan T. A fast and elitist multiobjective genetic algorithm: NSGA-II
- Deb
(Show Context)
Citation Context ...AP as a tri-objective problem (i.e., maximize reliability, minimize cost and weight) and solved this problem using the Nondominated Sorting Genetic Algorithm (NSGA2) originally proposed by Deb et al. =-=[27]-=-. In [24], the same authors from [23] presented an improved version of NSGA2 called MOMS-GA to solve the tri-objective redundancy allocation problem in multi-state systems. Authors of [25] employed a ... |

21 | Multiobjective optimization by genetic algorithms: Application to safety systems. Reliability Engineering and System Safety, - Giuggioli, Marseguerra, et al. - 2001 |

15 |
Optimization of constrained multiple-objective reliability problems using evolutionary algorithms. Reliability Engineering and System Safety
- Salazar, Rocco, et al.
- 2006
(Show Context)
Citation Context ... allocation problem in multi-state systems. Authors of [25] employed a Tabu search and Monte-Carlo simulation method to solve the bi-objective (reliability and cost) redundancy allocation problem. In =-=[26]-=-, authors employed a problem-specific evolutionary algorithm to solve the continuous reliability optimization problems where the decision variables are the reliabilities of the components. The meta-he... |

13 | An efficient algorithm to solve integer-programming problems arising in system-reliability design. - Misra, Sharma - 1991 |

11 |
A new approach to solving problems of multi‐state system reliability optimization. Quality and reliability engineering international,
- Levitin, Lisnianski
- 2001
(Show Context)
Citation Context ...oposed method over metaheuristic methods on a numerical example taken from the literature. & 2012 Elsevier Ltd. All rights reserved. RAP) is a well-known erature. It has a broad ctrical power systems =-=[2]-=-, and telecommunim can be increased by s, but this can also been used to solve such formulations, including dynamic programming [4–6], integer programming [7–9], mixed integer and nonlinear programmin... |

10 | Dynamic programming and the reliability of multicomponent devices. - Bellman, Dreyfus - 1958 |

8 |
A Multiobjective Genetic Algorithm Approach to the Optimization of the Technical Specifications of a Nuclear Safety System. Reliability Engineering and System Safety
- Marseguerra, Zio, et al.
- 2004
(Show Context)
Citation Context ...nnealing algorithm based optimization approach. Studies [20–22] used multi-criteria formulations with genetic algorithm (GA). The approach in [21] was based on GA and Monte Carlo simulation; while in =-=[22]-=- GA and physical programming were combined to 0951-8320/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ress.2012.09.013 n Corresponding author. Tel.: þ1 313... |

8 |
Multi-objective integer programming: a general approach for generating all non-dominated solutions,”
- Ozlen, Azizoglu
- 2009
(Show Context)
Citation Context ...set of non-dominated solutions, but it is generally computationally impractical for large problems. To improve the computational efficiency of the A-constraint method, an adaptive A-constraint method =-=[29]-=- was proposed for multiobjective combinatorial optimization problems and requires integral objective function values. While this method is more efficient than the traditional A-constraint method, it i... |

7 | Reliability optimization of series-parallel systems using a genetic algorithm - DW, AE - 1996 |

6 | Pruned pareto-optimal sets for the system redundancy allocation problem based on multiple prioritized objectives
- Kulturel-Konak, Coit, et al.
- 2008
(Show Context)
Citation Context ... Deb et al. [27]. In [24], the same authors from [23] presented an improved version of NSGA2 called MOMS-GA to solve the tri-objective redundancy allocation problem in multi-state systems. Authors of =-=[25]-=- employed a Tabu search and Monte-Carlo simulation method to solve the bi-objective (reliability and cost) redundancy allocation problem. In [26], authors employed a problem-specific evolutionary algo... |

4 |
A new multiple objective evolutionary algorithm for reliability optimization of series-parallel systems
- Taboada, DW
(Show Context)
Citation Context ...bout 39%. 3. Case study example In this section, we experimentally compare the proposed me with the popular meta-heuristic based approach NSGA2 o series-parallel RAP example taken from the literature =-=[30]-=-. series-parallel system consists of three subsystems (s3), wit option of five, four and five types of components in each subsys (m1 5, m2 4, m3 5) respectively. The maximum numbe components is... |

3 | An ant colony optimization algorithm for the redundancy allocation problem (RAP - LY, AE |

2 | System reliability allocation and a computation algorithm - DE, WW, et al. |

2 | Redundancy allocation for series-parallel systems using integer linear programming - Billionnet |

2 | Murty BSN, Reddy PJ. Nonequilibrium simulated annealing algorithm applied to reliability optimization of complex systems - Ravi - 1997 |

2 | A heuristic for solving the redundancy allocation problem for multi-state series–parallel systems. Reliability Engineering and System Safety; 83(3):341–9 - JE, DW - 2004 |

2 | Redundancy allocation for series-parallel systems using a column generation approach
- Zia, DW
(Show Context)
Citation Context ...ed by s, but this can also been used to solve such formulations, including dynamic programming [4–6], integer programming [7–9], mixed integer and nonlinear programming [16], column generation method =-=[17]-=-, and meta-heuristics [10–15]. These single-objective optimization techniques have their own advantages. However, in practical applications, multiple considerations must be taken into account when det... |

2 |
Dialynas EN. Reliability and cost optimization of electronic devices considering the component failure rate uncertainty. Reliability Engineering & System Safety 2004;84:271–84
- EP
(Show Context)
Citation Context ...ystem first set of methods treat the RAP as a single objective optimization constraints. Various single-objective optimization approaches have teger ained hms. timedependent reliability. The study in =-=[19]-=- provided an efficient electronic devices by using a single or a multi-objective simulated Contents lists available at SciVerse ScienceDirect .e Reliability Engineering Reliability Engineering and Sys... |

2 |
Coit DW, Wattanapongsakorn N. Practical solutions for multi-objective optimization: an application to system reliability design problems. Reliability Engineering & System Safety 2007;92(3):314–22
- Taboada, Baheranwala
(Show Context)
Citation Context ...2013) 154–163 155single-objective optimization problem, multi-objective optimization problems usually have a set of solutions called Pareto-optimal (i.e., non-dominated) solutions (e.g., [23–26]). In =-=[23]-=-, the authors formulated the RAP as a tri-objective problem (i.e., maximize reliability, minimize cost and weight) and solved this problem using the Nondominated Sorting Genetic Algorithm (NSGA2) orig... |

2 |
MOMS-GA: A multi-objective multi-state genetic algorithm for system reliability optimization design problems
- HA, JF, et al.
(Show Context)
Citation Context ...ri-objective problem (i.e., maximize reliability, minimize cost and weight) and solved this problem using the Nondominated Sorting Genetic Algorithm (NSGA2) originally proposed by Deb et al. [27]. In =-=[24]-=-, the same authors from [23] presented an improved version of NSGA2 called MOMS-GA to solve the tri-objective redundancy allocation problem in multi-state systems. Authors of [25] employed a Tabu sear... |

1 |
Rahli M, Meziane R, Zeblah A. Ant colony optimization for new redesign problem of multi-state electrical power systems
- Oiddir
(Show Context)
Citation Context ...ngra [18] presented a multi-objective reliability apportionment problem.1. Introduction The redundancy allocation prob problem in the ‘‘design-for-reliabili application in the real-world, such design =-=[1]-=-, transportation systems d cations design [3]. The reliability of allocating redundancies to its subsolve sub-problems, and then systematically combine the solutions. The decomposition-based approach ... |

1 |
Moorsel APA. Optimal allocation of test resources for software reliability growth modeling in software development
- MR, Rangarajan, et al.
(Show Context)
Citation Context ...lity apportionment problem.1. Introduction The redundancy allocation prob problem in the ‘‘design-for-reliabili application in the real-world, such design [1], transportation systems d cations design =-=[3]-=-. The reliability of allocating redundancies to its subsolve sub-problems, and then systematically combine the solutions. The decomposition-based approach can efficiently generate all the Pareto-optim... |

1 | Dynamic programming formulation of the redundancy allocation problem - KB - 1971 |

1 | Optimal allocation of redundant components for large * Proposed Method Δ NSGA2 ns in the space of cost vs. weight.systems - RL, CY - 1985 |

1 | AE, Coit DW. Efficiently solving the redundancy allocation problem using tabu search - Kulturel-Konak, Smith |

1 |
Determining component reliability and redundancy for optimum system reliability
- FA, CL, et al.
- 1977
(Show Context)
Citation Context ...and telecommunim can be increased by s, but this can also been used to solve such formulations, including dynamic programming [4–6], integer programming [7–9], mixed integer and nonlinear programming =-=[16]-=-, column generation method [17], and meta-heuristics [10–15]. These single-objective optimization techniques have their own advantages. However, in practical applications, multiple considerations must... |

1 |
Optimal apportionment of reliability and redundancy in series systems under multiple objectives
- AK
(Show Context)
Citation Context ...ds: (1) single objective optimization with constraints, (2) aggregated objective function for multi-objective optimization, and (3) Pareto-based ranking for multi-objective optimization. The However, =-=[18]-=- solved a multi-objective, nonlinear, mixed-in mathematical programming problem by sequential unconstr minimization techniques in conjunction with heuristic algorit The parallel-series system consider... |

1 |
Zuo MJ. Redundancy allocation for multi-state systems using physical programming and genetic algorithms. Reliability Engineering & System Safety 2006;91:1049–56
- ZG
(Show Context)
Citation Context ...–163solve the RAP.ratna.chinnam@wayne.edu (R.B. Chinnam).annealing algorithm based optimization approach. Studies [20–22] used multi-criteria formulations with genetic algorithm (GA). The approach in =-=[21]-=- was based on GA and Monte Carlo simulation; while in [22] GA and physical programming were combined to 0951-8320/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.10... |

1 |
Multiobjective decision marking theory and methodology
- Chankong, Haimes
- 1983
(Show Context)
Citation Context ...ch to address these limitations. A key step of the proposed approach is the exact solution of multi-objective sub-problems to generate the whole set of nondominated solutions. The A-constraint method =-=[28]-=- is a classical method to generate whole set of non-dominated solutions, but it is generally computationally impractical for large problems. To improve the computational efficiency of the A-constraint... |

1 |
Multi-objective NSGA-II code in C; 2005. Available from: /http:// www.iitk.ac.in/kangal/codes.shtmlS
- Deb
(Show Context)
Citation Context ...P2[x; e2 : f 2ðxÞ1 16: End if 17: Else 18: P2 : P2[x0; e2 : f 2 x0ð Þ12.3 GHz and 8 GB of RAM. The proposed method is coded in MATLABs R2008b and NSGA2 is coded in C, available from Deb’s Lab =-=[31]-=-. For NSGA2, we vary its population size from 100 up to 5000, with parameters set as follows: generations100, crossover probability .8 and mutation probability .008. Results from the proposed meth... |

1 |
Lecture notes in economics and mathematical systems, vol. 491. Multicriteria Optimization
- Ehrgott
- 2005
(Show Context)
Citation Context ...malize the objective space might affect the set of Pareto solutions found. In addition, the aggregation of multiple objectives may eliminate the possibility of identifying some nondominated solutions =-=[32]-=-. To cope with these drawbacks, other multiobjective optimization approaches have been proposed. Multiobjective optimization refers to the process of solving problems with two or more objectives to be... |

1 |
Algorithms to identify pareto pointsin multi-dimensional data sets
- Yukish
(Show Context)
Citation Context ...dominated solutions, we gain efficiency in the filtering task. For instance, consider the Simple Cull filtering algorithm which has a complexity of O(p2) where p is the number of solutions in the set =-=[33]-=-. Let pi denote the number of non-dominated solutions for subsystem i1, 2, 3, 4. The complexity of the Cartesian combination and filtering is O p21p 2 2 for subsystem pair 1 and 2 and is O p23p 2... |

1 |
Ismail-Yahaya A, Mattson CA. The normalized normal constraint method for generating the Pareto frontier. Structural and Multidisciplinary Optimization 2003;25:86–98
- Messac
(Show Context)
Citation Context ...nto deterministic and stochastic approaches based on whether the solutions found are on the Pareto frontier. Two commonly used deterministic approximate methods are Normal Boundary Intersection (NBI) =-=[34]-=- and Normal Constraint (NC) [35] methods. While these methods are shown to be effective for solving large multi-objective optimization problems, they are not suitable for solving the subsystems’ sub-p... |

1 | Coit DW. Data clustering of solutions for multiple objective system reliability optimization problems. Quality Technology & Quantitative Management Journal 2007;4(2):35–54 - Taboada |