## Multiobjective Optimization Using Nondominated Sorting in Genetic Algorithms (1994)

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Venue: | Evolutionary Computation |

Citations: | 404 - 2 self |

### BibTeX

@ARTICLE{Srinivas94multiobjectiveoptimization,

author = {N. Srinivas and Kalyanmoy Deb},

title = {Multiobjective Optimization Using Nondominated Sorting in Genetic Algorithms},

journal = {Evolutionary Computation},

year = {1994},

volume = {2},

pages = {221--248}

}

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### Abstract

In trying to solve multiobjective optimization problems, many traditional methods scalarize the objective vector into a single objective. In those cases, the obtained solution is highly sensitive to the weight vector used in the scalarization process and demands the user to have knowledge about the underlying problem. Moreover, in solving multiobjective problems, designers may be interested in a set of Pareto-optimal points, instead of a single point. Since genetic algorithms(GAs) work with a population of points, it seems natural to use GAs in multiobjective optimization problems to capture a number of solutions simultaneously. Although a vector evaluated GA (VEGA) has been implemented by Schaffer and has been tried to solve a number of multiobjective problems, the algorithm seems to have bias towards some regions. In this paper, we investigate Goldberg's notion of nondominated sorting in GAs along with a niche and speciation method to find multiple Pareto-optimal points sim...

### Citations

2025 |
Genetic algorithms: In search of optimization and machine learning
- Goldberg
- 1989
(Show Context)
Citation Context ...ng results, it suffered from biasness towards some Pareto-optimal solutions. A new algorithm, Nondominated Sorting Genetic Algorithm (NSGA), is presented in this paper based on Goldberg's suggestion (=-=Goldberg 1989-=-). This algorithm eliminates the bias in VEGA and thereby distributes the population over the entire Pareto-optimal regions. Although there exist two other implementations (Fonesca and Fleming 1993; H... |

537 |
Genetic Algorithms with sharing for multimodal function optimization
- Goldberg, Richardson
- 1987
(Show Context)
Citation Context ...hese nondominated individuals. In order to maintain diversity in the population, these classified individuals are then shared with their dummy fitness values. Sharing methods are discussed elsewhere (=-=Goldberg and Richardson 1987-=-; Deb 1989). Sharing is achieved by performing selection operation using degraded fitness values which are obtained by dividing the original fitness value of an individual by a quantity proportional t... |

485 | Genetic algorithms for multi-objective optimization: Formulation, discussion and generalization
- Fonseca, Fleming
- 1993
(Show Context)
Citation Context ...s suggestion (Goldberg 1989). This algorithm eliminates the bias in VEGA and thereby distributes the population over the entire Pareto-optimal regions. Although there exist two other implementations (=-=Fonesca and Fleming 1993-=-; Horn, Nafpliotis, and Goldberg 1994) based on this idea, NSGA is different from their working principles, as explained below. In the remainder of the paper, we briefly describe difficulties of using... |

304 | A Niched Pareto Genetic Algorithm for Multiobjective Optimization - Horn, Nafpliotis, et al. - 1994 |

277 | An investigation of niche and species formation in genetic function optimization - Deb, Goldberg - 1989 |

196 |
Multiobjective Decision Making Theory and Methodology
- Chankong, Haimes
- 1983
(Show Context)
Citation Context ...h space when all objectives are considered but are inferior to other solutions in the space in one or more objectives. These solutions are known as Pareto-optimal solutions or nondominated solutions (=-=Chankong and Haimes 1983-=-; Hans 1988). The rest of the solutions are This paper has appeared in the Journal of Evolutionary Computation, Vol. 2, No. 3, pages 221--248. 1 known as dominated solutions. Since none of the solutio... |

97 |
Optimization theory and applications
- Rao
- 1978
(Show Context)
Citation Context ...l multiobjective optimization problem consists of a number of objectives and is associated with a number of inequality and equality constraints. Mathematically, the problem can be written as follows (=-=Rao 1991-=-): Minimize/Maximize f i (x) i = 1; 2; : : : ; N Subject to g j (x)s0 j = 1; 2; : : : ; J h k (x) = 0 k = 1; 2; : : : ; K (1) 2 The parameter x is a p dimensional vector having p design or decision va... |

72 |
Some experiments in machine learning using vector evaluated genetic algorithm (artificial intelligence, optimization, adaptation, pattern recognition
- Schaffer
- 1984
(Show Context)
Citation Context ...of single-celled organisms with multiple properties or objectives (Rosenberg 1967). The first practical algorithm, called Vector Evaluated Genetic Algorithm (VEGA), was developed by Schaffer in 1984 (=-=Schaffer 1984-=-). One of the problems with VEGA, as realized by Schaffer himself, is its bias towards some Pareto-optimal solutions. Later, Goldberg suggested a nondominated sorting procedure to overcome this weakne... |

65 |
Genetic algorithms in multimodal function optimization
- Deb
- 1989
(Show Context)
Citation Context ... In order to maintain diversity in the population, these classified individuals are then shared with their dummy fitness values. Sharing methods are discussed elsewhere (Goldberg and Richardson 1987; =-=Deb 1989-=-). Sharing is achieved by performing selection operation using degraded fitness values which are obtained by dividing the original fitness value of an individual by a quantity proportional to the numb... |

22 |
A comparison of selection schemes used in genetic algorithms
- Goldberg, Deb
- 1991
(Show Context)
Citation Context ... procedure, there could be a number of points having the same rank. The selection procedure then uses these ranks to select or delete blocks of points to form the mating pool. As discussed elsewhere (=-=Goldberg and Deb, 1991-=-), this type of blocked fitness assignment is likely to produce a large selection pressure which might cause premature convergence. MOGA also uses a niche-formation method to distribute the population... |

13 |
Multicriteria optimization for highly accurate systems.”, Multicirteria optimization in engineering and sciences
- Hans
- 1988
(Show Context)
Citation Context ...s are considered but are inferior to other solutions in the space in one or more objectives. These solutions are known as Pareto-optimal solutions or nondominated solutions (Chankong and Haimes 1983; =-=Hans 1988-=-). The rest of the solutions are This paper has appeared in the Journal of Evolutionary Computation, Vol. 2, No. 3, pages 221--248. 1 known as dominated solutions. Since none of the solutions in the n... |

7 | Some experiments in machine learning using vector evaluated genetic algorithms . Doctoral dissertation - Schaer - 1984 |

1 |
Necessary and sufficient conditions for local and global nondominated solutions in decision problems with multiobjectives
- Tamura, Miura
- 1979
(Show Context)
Citation Context ...(1) and at least one value of x (2) is strictly greater than x (1) . If x (1) is partially less than x (2) , we say that the solution x (1) dominates x (2) or the solution x (2) is inferior to x (1) (=-=Tamura and Miura 1979-=-). Any member of such vectors which is not dominated by any other member is said to be nondominated or non-inferior . Similarly if the objective is to maximize a function we define a dominated point i... |

1 |
Necessary and sucient conditions for local and global nondominated solutions in decision problems with multiobjectives
- Tamura, Miura
- 1979
(Show Context)
Citation Context ...(1) and at least one value of x (2) is strictly greater than x (1) . If x (1) is partially less than x (2) , we say that the solution x (1) dominates x (2) or the solution x (2) is inferior to x (1) (=-=Tamura and Miura 1979-=-). Any member of such vectors which is not dominated by any other member is said to be nondominated or non-inferior . Similarly if the objective is to maximize a function we dene a dominated point if... |