#### DMCA

## A Fast and Elitist Multi-Objective Genetic Algorithm: NSGA-II (2000)

### Cached

### Download Links

Citations: | 1814 - 60 self |

### Citations

1918 |
Multi-Objective Optimization using Evolutionary Algorithms.
- Deb
- 2001
(Show Context)
Citation Context ...s, it has to be applied many times, hopefully finding a different solution at each simulation run. Over the past decade, a number of multiobjective evolutionary algorithms (MOEAs) have been suggested =-=[1]-=-, [7], [13], Manuscript received August 18, 2000; revised February 5, 2001 and September 7, 2001. The work of K. Deb was supported by the Ministry of Human Resources and Development, India, under the ... |

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 ...as to be applied many times, hopefully finding a different solution at each simulation run. Over the past decade, a number of multi-objective evolutionary algorithms (MOEAs) have been suggested [18], =-=[6]-=-, [11], [24]. The primary reason for this is their ability to find multiple Pareto-optimal solutions in one single simulation run. Since EAs work with a population of solutions, a simple EA can be ext... |

627 | Comparison of multiobjective evolutionary algorithms: Empirical results.
- Zitzler, Deb, et al.
- 2000
(Show Context)
Citation Context ...sive algorithm for large population sizes. This large complexity arises because of the complexity involved in the non-dominated sorting procedure in every generation. Lack of elitism: Recent results (=-=[23]-=-, [16]) show clearly that elitism can speed up the performance of the GA significantly, also can help preventing the loss of good solutions once they are found. Need for specifying the sharing paramet... |

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 ...cant past studies in this area. Veldhuizen [20] cited a number of test problems which many researchers have used in the past. Of them, we choose four problems, we call them SCH (from Schaffer's study =-=[17]-=-), FON (from Fonseca and Fieming's study [8]), POL (from Poloni's study [14]), and KUR (from Kursawe's study [13]). In 1999, the first author has suggested a systematic way of developing test problems... |

450 | Evolutionary Algorithms for Multiobjective Optimization: Methods and Applications,
- Zitzler
- 1999
(Show Context)
Citation Context ...ults on a number of difficult test problems, we find that NSGA-II outperforms two other contemporary multi-objective EAs--Pareto-archived evolution strategy (PAES), [12] and strength Pareto EA (SPEA) =-=[22]-=---in terms of finding a diverse set of solutions and in converging near the true Pareto-optimal set. Constrained multi-objective optimization is important from the point of view of practical problem s... |

440 | Multiobjective evolutionary algorithms: Analyzing the state-of-the-art;
- Veldhuizen, Lamont
- 2000
(Show Context)
Citation Context ...lems We first describe the test problems used to compare different multi-objective evolutionary algorithms. Test problems are chosen from a number of significant past studies in this area. Veldhuizen =-=[20]-=- cited a number of test problems which many researchers have used in the past. Of them, we choose four problems, we call them SCH (from Schaffer's study [17]), FON (from Fonseca and Fieming's study [8... |

407 | A niched Pareto genetic algorithm for multiobjective optimization.
- Horn, Nafpliotis, et al.
- 1994
(Show Context)
Citation Context ... be applied many times, hopefully finding a different solution at each simulation run. Over the past decade, a number of multi-objective evolutionary algorithms (MOEAs) have been suggested [18], [6], =-=[11]-=-, [24]. The primary reason for this is their ability to find multiple Pareto-optimal solutions in one single simulation run. Since EAs work with a population of solutions, a simple EA can be extended ... |

385 |
Messy genetic algorithms: Motivation, analysis, and first results.
- Goldberg, Korb, et al.
- 1989
(Show Context)
Citation Context ...ted problem. NSGA-II are able to converge to the Pareto-optimal front (with g(y) = 1 resulting f2 = exp(-f)). This example problem demonstrates that one of the known difficulties (the linkage problem =-=[9]-=-, [10]). of single-objective optimization algorithm can also cause difficulties in a multi-objective problem. However, more systematic studies are needed to amply address the linkage issue in multi-ob... |

309 |
An investigation of niche and species formation in genetic function optimization,
- Deb, Goldberg
- 1989
(Show Context)
Citation Context ... parameter denotes the largest value of that distance metric within which any two solutions share each other’s fitness. This parameter is usually set by the user, although there exist some guidelines =-=[4]-=-. There are two difficulties with this sharing function approach. 1) The performance of the sharing function method in maintaining a spread of solutions depends largely on the chosen value. - - - for ... |

246 | An efficient constraint handling method for genetic algorithms,”
- Deb
- 2000
(Show Context)
Citation Context ... outlines the crowding distance computation procedure of all solutions in an nondominated set Z: crowding-distance-assignment (Z) for each i, set Z[i]distance = 0 for each objective m Z = sort(Z, m) Z=-=[1]-=-istace = Z[l]istace = ec for i = 2 to (l - 1) = + + 1].m - - 1].m) number of solutions in Z initialize distance sort using each objective value so that boundary points are always selected for all othe... |

232 | Multiobjective Optimization and Multiple Constraint Handling with Evolutionary Algorithms. I: A Unified Formulation.
- Fonseca, Fleming
- 1998
(Show Context)
Citation Context ...the concept of sharing. The main problem with sharing is that it requires the specification of a sharing parameter (ashare). Though there has been some work on dynamic sizing of the sharing parameter =-=[8]-=-, a parameter-less diversity preservation mechanism is desirable. In this paper, we address all of these issues and propose an improved version of NSGA, which we call NSGA-II. From the simulation resu... |

230 | Multiobjective optimization using evolutionary algorithms - A comparative case study.
- Zitzler, Thiele
- 1998
(Show Context)
Citation Context ...plied many times, hopefully finding a different solution at each simulation run. Over the past decade, a number of multi-objective evolutionary algorithms (MOEAs) have been suggested [18], [6], [11], =-=[24]-=-. The primary reason for this is their ability to find multiple Pareto-optimal solutions in one single simulation run. Since EAs work with a population of solutions, a simple EA can be extended to mai... |

220 | Simulated binary crossover for continuous search space,”
- Deb, Agrawal
- 1995
(Show Context)
Citation Context ...on probability of Pm -- 1/n or 1/ (where n is the number of decision variables for real-coded GAs andsis the string length for binary-coded GAs). For NSGA-II (real-coded), we use distribution indices =-=[5]-=- for crossover and mutation operators as /c = 20 and ]m = 20, respectively. The population obtained at the end of 250 generations (the population after elitism mechanism is applied) is used to calcula... |

207 | Multi-objective genetic algorithms: Problem difficulties and construction of test problems,”
- Deb
- 1999
(Show Context)
Citation Context ... (such as O'sbar e needed in the NSGA) is required here. Although the crowding distance is calculated in the objective function space, it can also be implemented in the parameter space, if so desired =-=[2]-=-. However, in all simulations performed in this study, we have used the objective function space niching. IV. SIMULATION RESULTS In this section, we first describe the test problems used to compare th... |

166 |
The Pareto archived evolution strategy: A new baseline algorithm for multiobjective optimization,”
- Knowles, Corne
- 1999
(Show Context)
Citation Context ...ll NSGA-II. From the simulation results on a number of difficult test problems, we find that NSGA-II outperforms two other contemporary multi-objective EAs--Pareto-archived evolution strategy (PAES), =-=[12]-=- and strength Pareto EA (SPEA) [22]--in terms of finding a diverse set of solutions and in converging near the true Pareto-optimal set. Constrained multi-objective optimization is important from the p... |

153 |
Multi-Objective function optimization using the non-dominated sorting genetic algorithm »,
- Srinivas, Deb
- 1994
(Show Context)
Citation Context ..., it has to be applied many times, hopefully finding a different solution at each simulation run. Over the past decade, a number of multi-objective evolutionary algorithms (MOEAs) have been suggested =-=[18]-=-, [6], [11], [24]. The primary reason for this is their ability to find multiple Pareto-optimal solutions in one single simulation run. Since EAs work with a population of solutions, a simple EA can b... |

121 | Evolution strategies for vector optimization »,
- Kursawe
- 1992
(Show Context)
Citation Context ...in the past. Of them, we choose four problems, we call them SCH (from Schaffer's study [17]), FON (from Fonseca and Fieming's study [8]), POL (from Poloni's study [14]), and KUR (from Kursawe's study =-=[13]-=-). In 1999, the first author has suggested a systematic way of developing test problems for multi-objective optimization [2]. Zitzler, Deb, and Thiele [23] followed those guidelines and suggested six ... |

103 | On the performance assessment and comparison of stochastic multiobjective optimizers
- Fonseca, Fleming
- 1996
(Show Context)
Citation Context ...f diversity in solutions of the Pareto-optimal set. Clearly, these two tasks cannot be measured with one performance metric adequately. A number of performance metrics have been suggested in the past =-=[7]-=-, [22]. But, here, we define two performance metrics which are more direct in evaluating each of the above two goals in a solution set obtained by a multi-objective optimization algorithm. The first m... |

75 | Learning gene linkage to efficiently solve problems of bounded difficulty using genetic algorithms
- Harik
- 1997
(Show Context)
Citation Context ...roblem. NSGA-II are able to converge to the Pareto-optimal front (with g(y) = 1 resulting f2 = exp(-f)). This example problem demonstrates that one of the known difficulties (the linkage problem [9], =-=[10]-=-). of single-objective optimization algorithm can also cause difficulties in a multi-objective problem. However, more systematic studies are needed to amply address the linkage issue in multi-objectiv... |

38 | Understanding Interactions among Genetic Algorithm Parameters
- Deb, Agrawal
- 1998
(Show Context)
Citation Context ...HIS STUDY. ALL OBJECTIVE FUNCTIONS ARE TO BE MINIMIZED. Problem n Variable Objective Optimal Comments bounds functions solutions SCH i [-10 u, 10 u] f(x) = x 2 xs[0, 2] convex f2(x) = (x - 2) 2 FON 3 =-=[-4,4]-=- f(x)-- 1-exp i= (xi- ) x--x2--x3 non-convex f2(x) = 1 - exp Ei= xi +s[-1/v/, 1/v/] roL 2 [-, ] (x) = [1 + (A - B) 2 + (A2 - B2) 2] non-convex, f2(x) = [(x + 3) 2 + (x2 + 1) 2] disconnected A = 0.5 si... |

30 | Evolutionary search under partially ordered fitness sets - RUDOLPH - 1999 |

29 |
GA-Based Decision Support System for Multicriteria Optimization.
- Tanaka, Watanabe, et al.
- 1995
(Show Context)
Citation Context ...lem SRN was used in the original study of NSGA [20]. Here, the constrained Pareto-optimal set is a subset of the unconstrained Pareto-optimal set. The third problem TNK was suggested by Tanaka et al. =-=[21]-=- and has a discontinuous Pareto-optimal region, falling entirely on the first constraint boundary. In the next section, we show the constrained Pareto-optimal region for each of the above problems. Th... |

28 | Multiple objective optimization with vector evaluated genetic algorithms - Schaer - 1985 |

22 |
Hybrid GA for Multi Objective Aerodynamic Shape Optimization,” Genetic Algorithms in Engineering and
- Poloni
- 1995
(Show Context)
Citation Context ...ems which many researchers have used in the past. Of them, we choose four problems, we call them SCH (from Schaffer's study [17]), FON (from Fonseca and Fieming's study [8]), POL (from Poloni's study =-=[14]-=-), and KUR (from Kursawe's study [13]). In 1999, the first author has suggested a systematic way of developing test problems for multi-objective optimization [2]. Zitzler, Deb, and Thiele [23] followe... |

14 |
Multiobjective Design Optimization by an Evolutionary Algorithm,”
- Ray, Tai, et al.
- 2001
(Show Context)
Citation Context ...change the computational complexity of NSGA-II. The rest of the NSGA-II procedure as described can be used as usual. B. Ray-Kang- Chye ' s Constraint Handling Approach T. Ray, T. Kang, and S. K. Chye =-=[15]-=- suggested a more elaborate constraint handling technique, where constraint violations of all constraints are not simply summed together, instead a non-domination check of constraint violations is als... |

12 | Learning gene linkage to e±ciently solve problems of bounded di±culty using genetic algorithms. Doctoral dissertation - Harik - 1999 |

5 |
K.C.: An evolutionary algorithm for multiobjective optimization.
- Ray, Tai, et al.
- 2001
(Show Context)
Citation Context ...domination checks with the constraint-violation values, the proposed approach of this paper is computationally less expensive and is simpler. B. Ray–Tai–Seow’s Constraint-Handling Approach Ray et al. =-=[17]-=- suggested a more elaborate constraint-handling technique, where constraint violations of all constraints are not simply summed together. Instead, a nondomination check of constraint violations is als... |

1 | et al., "CA-based decision support system for multi-criteria optimization - Tanaka - 1995 |

1 | et al., \GA-based decision support system for multi-criteria optimization - Tanaka - 1995 |

1 |
efficient constraint-handling method for genetic algorithms
- “An
- 2000
(Show Context)
Citation Context ...e optimization. VI. CONSTRAINT HANDLING In the past, the first author and his students implemented a penalty-parameterless constraint-handling approach for singleobjective optimization. Those studies =-=[2]-=-, [6] have shown how a tournament selection based algorithm can be used to handle constraints in a population approach much better than a number of other existing constraint-handling approaches. A sim... |

1 |
the performance assessment and comparison of stochastic multiobjective optimizers,” in Parallel Problem Solving from Nature IV
- “On
- 1996
(Show Context)
Citation Context ...et and 2) maintenance of diversity in solutions of the Pareto-optimal set. These two tasks cannot be measured adequately with one performance metric. Many performance metrics have been suggested [1], =-=[8]-=-, [24]. Here, we define two performance metrics that are more direct in evaluating each of the above two goals in a solution set obtained by a multiobjective optimization algorithm. The first metric m... |