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## Multi-Objective Optimization Using Genetic Algorithms: A Tutorial

Citations: | 113 - 0 self |

### Citations

10047 |
Genetic Algorithms
- Goldberg
- 1989
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Citation Context ...herein all objectives are assumed to be minimized. Therefore, a lower rank corresponds to a better solution in the 7sfollowing discussions. The first Pareto ranking technique was proposed by Goldberg =-=[15]-=- as follows: Step 1. Set i=1 and TP=P Step 2. Identify non-dominated solutions in TP and assigned them set to Fi. Step 3. Set TP = TP \ Fi. If TP=∅ go to Step 4, else set i=i+1 and go to Step 2. Step ... |

1918 |
Multi-Objective Optimization using Evolutionary Algorithms.
- Deb
- 2001
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Citation Context ... mainly due to the large number of possible elitist solutions. Earlier multi-objective GA did not use elitism. However, most recent multiobjective GA and their variations use elitism. As discussed in =-=[6, 47, 55]-=-, multi-objective GA using elitist strategies tend to outperform their non-elitist counterparts. Multi-objective GA use two strategies to implement elitism [22]: (i) maintaining elitist solutions in t... |

1814 | A Fast Elitist Multi-Objective Genetic Algorithm: NSGA-II.
- Deb, Pratap, et al.
- 2000
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Citation Context ...nated Sorting Genetic Algorithm (NSGA) [45], Strength Pareto Evolutionary Algorithm (SPEA) [55], Pareto-Archived Evolution Strategy (PAES) [27], Fast Non-dominated Sorting Genetic Algorithm (NSGA-II) =-=[9]-=-, Multi-objective Evolutionary Algorithm (MEA) [42], Rank-Density Based Genetic Algorithm (RDGA) [32]. Note that although there are many variations of multiobjective GA in the literature, these cited ... |

812 | Multiobjective evolutionary algorithms: A comparative case study and the Strength Pareto approach.
- Zitzler, Thiele
- 1999
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Citation Context ...hm (MOGA) [13], Niched Pareto 5sGenetic Algorithm [19], Random Weighted Genetic Algorithm (RWGA)[39], Nondominated Sorting Genetic Algorithm (NSGA) [45], Strength Pareto Evolutionary Algorithm (SPEA) =-=[55]-=-, Pareto-Archived Evolution Strategy (PAES) [27], Fast Non-dominated Sorting Genetic Algorithm (NSGA-II) [9], Multi-objective Evolutionary Algorithm (MEA) [42], Rank-Density Based Genetic Algorithm (R... |

635 |
Genetic algorithms with sharing for multimodel function optimization,
- Goldberg, Richardson
- 1987
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Citation Context ...al, densely populated areas are identified and a fair penalty method is used to penalize the solutions located in such areas. The idea of fitness sharing was first proposed by Goldberg and Richardson =-=[16]-=- in the investigation of multiple local optima for multi-modal functions. Fonseca and Fleming [13] used this idea to penalize clustered solutions with the same rank as follows. Step 1. Calculate the E... |

633 | Genetic algorithm for multiobjective optimization: formulation, discussion and generalization. Paper presented at the fifth international conference on genetic algorithms,
- Fonseca, Fleming
- 1993
(Show Context)
Citation Context ...the literature, these cited GA are well-known and credible algorithms that have been used in many applications and their performances were tested in several comparative studies. Several survey papers =-=[1-3, 12, 14, 22, 51, 54, 55]-=- have been published on evolutionary multi-objective optimization. Coello Coello lists more than 1800 references in his website [4]. Most survey papers on multi-objective evolutionary approaches intro... |

627 | Comparison of multiobjective evolutionary algorithms: Empirical results.
- Zitzler, Deb, et al.
- 2000
(Show Context)
Citation Context ...the literature, these cited GA are well-known and credible algorithms that have been used in many applications and their performances were tested in several comparative studies. Several survey papers =-=[1-3, 12, 14, 22, 51, 54, 55]-=- have been published on evolutionary multi-objective optimization. Coello Coello lists more than 1800 references in his website [4]. Most survey papers on multi-objective evolutionary approaches intro... |

539 | Multiobjective optimization using nondominated sorting in genetic algorithm.
- Srinivas, Deb
- 1994
(Show Context)
Citation Context ...re developed such as Multi-objective Genetic Algorithm (MOGA) [13], Niched Pareto 5sGenetic Algorithm [19], Random Weighted Genetic Algorithm (RWGA)[39], Nondominated Sorting Genetic Algorithm (NSGA) =-=[45]-=-, Strength Pareto Evolutionary Algorithm (SPEA) [55], Pareto-Archived Evolution Strategy (PAES) [27], Fast Non-dominated Sorting Genetic Algorithm (NSGA-II) [9], Multi-objective Evolutionary Algorithm... |

474 |
Multiple objective optimization with vector evaluated genetic algorithms. Paper presented at the international conference on genetic algorithm and their applications.
- Schaffer
- 1985
(Show Context)
Citation Context ...echnique, and 70% of all meta-heuristics approaches were based on evolutionary approaches. The first multi-objective GA, called Vector Evaluated Genetic Algorithms (or VEGA), was proposed by Schaffer =-=[44]-=-. Afterward, several major multi-objective evolutionary algorithms were developed such as Multi-objective Genetic Algorithm (MOGA) [13], Niched Pareto 5sGenetic Algorithm [19], Random Weighted Genetic... |

440 | Multiobjective evolutionary algorithms: Analyzing the state-of-the-art;
- Veldhuizen, Lamont
- 2000
(Show Context)
Citation Context ... mainly due to the large number of possible elitist solutions. Earlier multi-objective GA did not use elitism. However, most recent multiobjective GA and their variations use elitism. As discussed in =-=[6, 47, 55]-=-, multi-objective GA using elitist strategies tend to outperform their non-elitist counterparts. Multi-objective GA use two strategies to implement elitism [22]: (i) maintaining elitist solutions in t... |

407 | A niched Pareto genetic algorithm for multiobjective optimization.
- Horn, Nafpliotis, et al.
- 1994
(Show Context)
Citation Context ...was proposed by Schaffer [44]. Afterward, several major multi-objective evolutionary algorithms were developed such as Multi-objective Genetic Algorithm (MOGA) [13], Niched Pareto 5sGenetic Algorithm =-=[19]-=-, Random Weighted Genetic Algorithm (RWGA)[39], Nondominated Sorting Genetic Algorithm (NSGA) [45], Strength Pareto Evolutionary Algorithm (SPEA) [55], Pareto-Archived Evolution Strategy (PAES) [27], ... |

321 | Approximating the Nondominated Front Using the Pareto Archived Evolution Strategy.
- Knowles, Corne
- 2000
(Show Context)
Citation Context ...m [19], Random Weighted Genetic Algorithm (RWGA)[39], Nondominated Sorting Genetic Algorithm (NSGA) [45], Strength Pareto Evolutionary Algorithm (SPEA) [55], Pareto-Archived Evolution Strategy (PAES) =-=[27]-=-, Fast Non-dominated Sorting Genetic Algorithm (NSGA-II) [9], Multi-objective Evolutionary Algorithm (MEA) [42], Rank-Density Based Genetic Algorithm (RDGA) [32]. Note that although there are many var... |

292 | A Comprehensive Survey of Evolutionary-Based Multiobjective Optimization Techniques; - Coello - 1999 |

232 | Multiobjective Optimization and Multiple Constraint Handling with Evolutionary Algorithms. I: A Unified Formulation.
- Fonseca, Fleming
- 1998
(Show Context)
Citation Context ...the literature, these cited GA are well-known and credible algorithms that have been used in many applications and their performances were tested in several comparative studies. Several survey papers =-=[1-3, 12, 14, 22, 51, 54, 55]-=- have been published on evolutionary multi-objective optimization. Coello Coello lists more than 1800 references in his website [4]. Most survey papers on multi-objective evolutionary approaches intro... |

172 |
Multi-objective genetic local search algorithm and its applications to flowshop scheduling”
- Ishibuchi, Murata
- 1998
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Citation Context ...ation Pt∪Et, and then, N solutions are selected for the next generation Pt+1 based on the assigned fitness values. Another strategy is to reserve a room for n elitist solutions in the next population =-=[20]-=-. In this strategy, N - n solutions are selected from parents and newly created offspring and n solutions are selected from Et. 4.4. Constraint Handling Most real-world optimization problems include c... |

166 |
The Pareto archived evolution strategy: A new baseline algorithm for multiobjective optimization,”
- Knowles, Corne
- 1999
(Show Context)
Citation Context ...e solutions are in the same nondominated front, the solution with a higher crowding distance wins. Otherwise, the solution with the lowest rank is selected. 4.2.3. Cell-Based Density In this approach =-=[26, 27, 32, 53]-=-, the objective space is divided into K-dimensional cells (see Figure 2c). The number of solutions in each cell is defined as the density of the cell, and the density of a solution is equal to the den... |

129 | An Updated Survey of GA-Based Multiobjective Optimization Techniques. - Coello - 2000 |

121 | Evolution strategies for vector optimization »,
- Kursawe
- 1992
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Citation Context ...rformed on the new population in the same way with the single objective GA. A similar approach is to use only a single objective function which is randomly determined each time in the selection phase =-=[31]-=-. These approaches are easy to implement and computationally as efficient as a singleobjective GA. The major drawback of objective switching is that the population tends to converge to solutions which... |

100 | Balance between genetic search and local search in memetic algorithms for multiobjective permutation flow shop scheduling. In:
- Ishibuchi, Yoshida, et al.
- 2003
(Show Context)
Citation Context ...ch [20], a local search procedure is applied to each offspring generated by crossover, using the same weight vector of the offspring’s parents to evaluate neighborhood solutions. Similarly, Ishibuchi =-=[21]-=- also used the weighted sum of the objective functions to evaluate solution during the local search. However, the local search is selectively applied to only promising solutions, and weights are also ... |

98 |
Genetic search strategies in multi-criterion optimal design. Structural Optimization
- Hajela, Y-Lin
- 1992
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Citation Context ... problem should be solved multiple times with different weight combinations. The main difficulty with this approach is selecting a weight vector for each run. To automate this process, Hajela and Lin =-=[17]-=- proposed the weight-based genetic algorithm for multi-objective optimization (WBGA-MO). In the WBGA-MO, each solution xi in the population uses a different weight vector wi = { w1, w2, … , wk} in the... |

89 | An Updated Survey of Evolutionary Multiobjective Optimization Techniques: State of the Art and Future Trends”, - Coello, A - 1999 |

76 | Memetic algorithms for multiobjective optimization: issues, methods and prospects
- Knowles, Corne
- 2004
(Show Context)
Citation Context ...the local search. However, the local search is selectively applied to only promising solutions, and weights are also randomly generated, instead of using the parents’ weight vector. Knowles and Corne =-=[28]-=- presented a memetic version of the PAES, called M-PAES. The PAES uses the dominance concept to evaluate solutions. Therefore, in M-PAES, a set of local non-dominated solutions is used as a comparison... |

64 | Genetic algorithms with dynamic niche sharing for multimodal function optimization.
- MILLER, SHAW
- 1995
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Citation Context ... disadvantage of niching is computational effort to calculate niche counts. However, benefits of fitness sharing surpass the burden of extra computational effort in many applications. Miller and Shaw =-=[36]-=- proposed a dynamic niche sharing approach to increase effectiveness of computing niche counts. 4.2.2. Crowding Distance Crowding distance approaches aim to obtain a uniform spread of solutions along ... |

55 |
Multi-objective genetic algorithm and its applications to flowshop-scheduling.
- Murata, Ishibuchi, et al.
- 1996
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Citation Context ...olution xi. 6 k k ∑sTherefore, multiple solutions can be simultaneously searched in a single run. In addition, weight vectors can be adjusted to promote diversity of the population. Other researchers =-=[39, 40]-=- have proposed a multi-objective genetic algorithm based on a weighted sum of multiple objective functions where a normalized weight vector wi is randomly generated for each solution xi during the sel... |

50 | Using Unconstrained Elite Archives for Multiobjective Optimization,”
- Fieldsend, Everson, et al.
- 2003
(Show Context)
Citation Context ...w solution if it is not dominated by any existing elitist solution. This is a computationally expensive operation. Several data structures were proposed to efficiently store, update, search in list E =-=[11, 38]-=-. Another issue is the size of list E. Since there might possibly exist a very large number of Pareto optimal solutions for a problem, the elitist list can grow extremely large. Therefore, pruning tec... |

49 | Considerations in engineering parallel multiobjective evolutionary algorithms. - Veldhuizen, Zydallis, et al. - 2003 |

42 |
MOGA: multi-objective genetic algorithms.
- Murata, Ishibuchi
- 1995
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Citation Context ...ral major multi-objective evolutionary algorithms were developed such as Multi-objective Genetic Algorithm (MOGA) [13], Niched Pareto 5sGenetic Algorithm [19], Random Weighted Genetic Algorithm (RWGA)=-=[39]-=-, Nondominated Sorting Genetic Algorithm (NSGA) [45], Strength Pareto Evolutionary Algorithm (SPEA) [55], Pareto-Archived Evolution Strategy (PAES) [27], Fast Non-dominated Sorting Genetic Algorithm (... |

41 |
Reducing the Run-time Complexity of Multiobjective EAs: The NSGA-II and Other Algorithms.
- Jensen
- 2003
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Citation Context |

37 |
Reducing the size of the nondominated set: Pruning by clustering
- Morse
- 1980
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Citation Context ...utions for a problem, the elitist list can grow extremely large. Therefore, pruning techniques were proposed to control the size of E. For example, the SPEA uses the average linkage clustering method =-=[37]-=- to reduce the size of E to an upper limit N when the number of the non-dominated solutions exceeds N as follows. Step 1. Initially, assign each solution x∈E to a cluster ci, 1 2 13 C = { c , c , … , ... |

36 |
Multi-objective meta-heuristics: an overview of the current state-of-the-art,”
- Jones, Mirrazavi, et al.
- 2002
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Citation Context ...tive GA do not require the user to prioritize, scale, or weigh objectives. Therefore, GA has been the most popular heuristic approach to multi-objective design and optimization problems. Jones et al. =-=[25]-=- reported that 90% of the approaches to multiobjective optimization aimed to approximate the true Pareto front for the underlying problem. A majority of these used a meta-heuristic technique, and 70% ... |

30 | A Hybrid Multi-Objective Evolutionary Approach to Engineering Shape Design,”
- Deb, Goel
- 2001
(Show Context)
Citation Context ...s these two issues as follows. 16sPaquete and Stutzle [41] described a bi-objective GA where a local search is used to generate initial solutions by optimizing only one single objective. Deb and Goel =-=[7]-=- applied a local search to only final solutions. In Ishibuchi and Murata’s approach [20], a local search procedure is applied to each offspring generated by crossover, using the same weight vector of ... |

23 |
Dynamic multiobjective evolutionary algorithm: adaptive cell-based rank and density estimation
- Yen, Lu
- 2003
(Show Context)
Citation Context ...e solutions are in the same nondominated front, the solution with a higher crowding distance wins. Otherwise, the solution with the lowest rank is selected. 4.2.3. Cell-Based Density In this approach =-=[26, 27, 32, 53]-=-, the objective space is divided into K-dimensional cells (see Figure 2c). The number of solutions in each cell is defined as the density of the cell, and the density of a solution is equal to the den... |

21 | A two-phase local search for the biobjective traveling salesman problem
- Paquete, Stützle
- 2003
(Show Context)
Citation Context ...on in the neighborhood as the new best solution when multiple non-dominated local solutions exist. Several approaches have been proposed to address these two issues as follows. 16sPaquete and Stutzle =-=[41]-=- described a bi-objective GA where a local search is used to generate initial solutions by optimizing only one single objective. Deb and Goel [7] applied a local search to only final solutions. In Ish... |

20 |
Evolutionary algorithms with dynamic population size and local exploration for multiobjective optimization,”
- Tan, Lee, et al.
- 2001
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Citation Context ...y updates are performed. The local search is terminated after a maximum number of local solutions are investigated or a maximum number of local moves are performed without any improvement. Tan et al. =-=[46]-=- proposed applying a local search procedure to only solutions that are located apart from others. In addition, the neighborhood size in the local search depends on the density or crowdedness of soluti... |

15 |
Rank-Density-Based Multiobjective Genetic Algorithm and Benchmark Test Function Study”,
- Lu, Yen
- 2003
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Citation Context ...eto-Archived Evolution Strategy (PAES) [27], Fast Non-dominated Sorting Genetic Algorithm (NSGA-II) [9], Multi-objective Evolutionary Algorithm (MEA) [42], Rank-Density Based Genetic Algorithm (RDGA) =-=[32]-=-. Note that although there are many variations of multiobjective GA in the literature, these cited GA are well-known and credible algorithms that have been used in many applications and their performa... |

12 |
Availability allocation to repairable systems with genetic algorithms: a multi-objective formulation”,
- Elegbede, Adjallah
- 2003
(Show Context)
Citation Context ...o included in the reliability allocation process creating a multi-objective problem. GA was applied to the reliability allocation problem of a typical pressurized water reactor. Elegbede and Adjallah =-=[10]-=- present a methodology to optimize the availability and the cost of repairable parallel-series systems. It is a multi-objective combinatorial optimization, modeled with continuous and discrete variabl... |

11 |
Application of genetic algorithm for reliability allocation in nuclear power plants”, Reliability Engineering and System Safety,
- Yang, Hwang, et al.
- 1999
(Show Context)
Citation Context ...their method, a large-scale optimal system reliability design problem was analyzed. Reliability allocation to minimize total plant costs, subject to an overall plant safety goal, is presented by Yang =-=[52]-=-. For their problem, design optimization is needed to improve the design, operation and safety of new and/or existing nuclear power plants. They presented an approach to determine the reliability char... |

10 | Comparison of data structures for storing Pareto sets
- Mostaghim, Teich, et al.
- 2002
(Show Context)
Citation Context ...w solution if it is not dominated by any existing elitist solution. This is a computationally expensive operation. Several data structures were proposed to efficiently store, update, search in list E =-=[11, 38]-=-. Another issue is the size of list E. Since there might possibly exist a very large number of Pareto optimal solutions for a problem, the elitist list can grow extremely large. Therefore, pruning tec... |

9 | Multiobjective Evolutionary Algorithms for solving Constrained Optimization Problems
- Sarker, Ray
- 2005
(Show Context)
Citation Context ...gth Pareto Evolutionary Algorithm (SPEA) [55], Pareto-Archived Evolution Strategy (PAES) [27], Fast Non-dominated Sorting Genetic Algorithm (NSGA-II) [9], Multi-objective Evolutionary Algorithm (MEA) =-=[42]-=-, Rank-Density Based Genetic Algorithm (RDGA) [32]. Note that although there are many variations of multiobjective GA in the literature, these cited GA are well-known and credible algorithms that have... |

7 | Parallel strength Pareto multiobjective evolutionary algorithm - Xiong, Li - 2003 |

6 | PSFGA: a parallel genetic algorithm for multiobjective optimization
- Toro, Ortega, et al.
- 2002
(Show Context)
Citation Context ...ing execution time and resource requirement of multi-objective GA using advanced data structures. One of the latest trends in this avenue is parallel and distributed processing. Several recent papers =-=[5, 48-50]-=- presented parallel implementation of multi-objective GA over multiple processors. Hybridization of GA with local search algorithms is frequently applied in singleobjective GAs. This approach is usual... |

6 |
An evolutionary algorithm for constrained multi-objective optimization
- Jimenez, Gomez-Skarmeta, et al.
- 2002
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Citation Context ...ossible, customizing genetic operators to always produce feasible solutions, and (iv) repairing infeasible solutions. Handling of constraints has not been adequately researched for multi-objective GA =-=[23]-=-. For instance, all major multi-objective GA assumed problems without any constraints. While constraint handling strategies (i), (iii), and (iv) are directly applicable in the multiobjective case, imp... |

5 |
Alternatives and challenges in optimizing industrial safety using genetic algorithms. Reliab Eng Syst Saf
- Martorell, Sanchez, et al.
- 2004
(Show Context)
Citation Context ... multi-objective problem. They demonstrated the viability and significance of their proposed approach using multi-objective GA for an emergency diesel generator system. Additionally, Martorell et al. =-=[34]-=- considered the optimal allocation of more reliable equipment, testing and maintenance activities to assure high RAM levels for safety-related systems. For these problems, the decision-maker encounter... |

4 |
Capacitated network design considering survivability: An evolutionary approach
- Konak, Smith
- 2004
(Show Context)
Citation Context ...t. This approach will not work when the total number of non-dominated parent and offspring solutions is larger than NP. To address this problem, several approaches have been proposed. Konak and Smith =-=[29, 30]-=- proposed a multi-objective GA with dynamic population size and a pure elitist strategy. In this multi-objective GA, the population includes only nondominated solutions. If the size of the population ... |

4 |
Optimal Reliability/Availability of Uncertain Systems via Multi-Objective Genetic Algorithms
- Marseguerra, Zio, et al.
- 2004
(Show Context)
Citation Context ...eral interesting and successful implementations of multi-objective GA for this class of problems. A few successful examples are described in the following paragraphs. Marseguerra, Zio and Podofillini =-=[33]-=- determine optimal surveillance test intervals using multi-objective GA with the goal of improving reliability and availability. Their research implemented a multi-objective GA which transparently and... |

4 | Parallel genetic algorithm for search and constrained multiobjective optimization - Wilson, Moore, et al. - 2004 |

4 |
Overview of multi-objective optimization methods,
- Xiujuan, Zhongke
- 2004
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Citation Context |

3 |
Multiobjective genetic algorithms. in IEE Colloquium on `Genetic Algorithms for Control Systems Engineering
- Fonseca, Fleming
- 1993
(Show Context)
Citation Context ...Evaluated Genetic Algorithms (or VEGA), was proposed by Schaffer [44]. Afterward, several major multi-objective evolutionary algorithms were developed such as Multi-objective Genetic Algorithm (MOGA) =-=[13]-=-, Niched Pareto 5sGenetic Algorithm [19], Random Weighted Genetic Algorithm (RWGA)[39], Nondominated Sorting Genetic Algorithm (NSGA) [45], Strength Pareto Evolutionary Algorithm (SPEA) [55], Pareto-A... |

3 | Evolutionary techniques for constrained multiobjective optimization problems
- Jiménez, Verdegay, et al.
- 1999
(Show Context)
Citation Context ... is not straightforward in multiobjective GA, mainly due to fact that fitness assignment is usually based on the non-dominance rank of a solution, not on its objective function values. Jimenez et al. =-=[24]-=- proposed a niched selection strategy to address infeasibility in multiobjective problems as follows: Step 1. Randomly chose two solutions x and y from the population. Step 2. If one of the solutions ... |

3 |
Multiobjective Optimization of Survivable Networks Considering Reliability
- Konak, Smith
(Show Context)
Citation Context ...t. This approach will not work when the total number of non-dominated parent and offspring solutions is larger than NP. To address this problem, several approaches have been proposed. Konak and Smith =-=[29, 30]-=- proposed a multi-objective GA with dynamic population size and a pure elitist strategy. In this multi-objective GA, the population includes only nondominated solutions. If the size of the population ... |

2 |
RAMS+C informed decision-making with application to multi-objective optimization of technical specifications and maintenance using genetic algorithms,” Reliability Engineering and System Safety,
- Martorell, Villanueva, et al.
- 2005
(Show Context)
Citation Context ...th high assurance, i.e., low estimation variance. They successfully applied their procedure to a complex system, a residual heat removal safety system for a boiling water reactor. 17sMartorell et al. =-=[35]-=- studied the selection of technical specifications and maintenance activities at nuclear power plants to increase reliability, availability and maintainability (RAM) of safety-related equipment. Howev... |

2 |
A method of fuzzy multi-objective nonlinear programming with GUB structure by hybrid genetic algorithm
- Sasaki, Gen
- 2003
(Show Context)
Citation Context ...y using both single-objective GA and multi-objective GA, which were demonstrated to solve the problem of testing and maintenance optimization based on unavailability and cost criteria. Sasaki and Gen =-=[43]-=- introduce a multi-objective problem which had fuzzy multiple objective functions and constraints with GUB (Generalized Upper Bounding) structure. They solved this problem by using a new hybridized GA... |

1 |
An investigation of of niche an species fromation in genetic function optimization
- Deb, Goldberg
- 1989
(Show Context)
Citation Context ...ace while they have very different structural features. Therefore, fitness sharing based on the objective function space may reduce diversity in the decision variable space. However, Deb and Goldberg =-=[8]-=- reported that fitness sharing on the objective function space usually performs better than one based on the decision variable space. One of the disadvantages of the fitness sharing based on niche cou... |