## An Overview of Evolutionary Algorithms in Multiobjective Optimization (1995)

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Venue: | Evolutionary Computation |

Citations: | 400 - 12 self |

### BibTeX

@ARTICLE{Fonseca95anoverview,

author = {Carlos M. Fonseca and Peter J. Fleming},

title = {An Overview of Evolutionary Algorithms in Multiobjective Optimization},

journal = {Evolutionary Computation},

year = {1995},

volume = {3},

pages = {1--16}

}

### Years of Citing Articles

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### Abstract

The application of evolutionary algorithms (EAs) in multiobjective optimization is currently receiving growing interest from researchers with various backgrounds. Most research in this area has understandably concentrated on the selection stage of EAs, due to the need to integrate vectorial performance measures with the inherently scalar way in which EAs reward individual performance, i.e., number of offspring. In this review, current multiobjective evolutionary approaches are discussed, ranging from the conventional analytical aggregation of the different objectives into a single function to a number of populationbased approaches and the more recent ranking schemes based on the definition of Pareto-optimality. The sensitivity of different methods to

### Citations

8174 |
Genetic Algorithm
- Goldberg
- 1989
(Show Context)
Citation Context ...ty analysis (MAUA) in conjunction with GAs has been suggested by Horn and Nafpliotis (1993), but without experimental results. Handling constraints with penalty functions (Davis and Steenstrup, 1987; =-=Goldberg, 1989-=-) is yet another example of an additive aggregating function. The fact that penalty functions are generally problem dependent and, as a consequence, difficult to set (Richardson et al., 1989) has prom... |

2571 |
Density Estimation for Statistics and Data Analysis
- Silverman
- 1986
(Show Context)
Citation Context ...tely, such guidelines may be already available, although outside the EA community. In fact, if share count calculation in sharing is recognized to be no more than a form of kernel density estimation (=-=Silverman, 1986-=-) in n dimensions, well studied heuristics for the setting of the corresponding 12ssmoothing parameter (read niche size) can suddenly be used. More advanced methods of density estimation, such as adap... |

550 |
Uniform Crossover in Genetic Algorithms
- Syswerda
- 1989
(Show Context)
Citation Context ...vertices of the hypercube defined by the mating parents. Similarly, single and two-point crossover of concatenated binary strings will change at most one or two decision variables. Uniform crossover (=-=Syswerda, 1989-=-) and shuffle crossover (Caruana et al., 1989) are less biased in this respect, in that the value of all decision variables may be altered in a single recombination step. Finally, multiobjective fitne... |

537 |
Genetic Algorithms with sharing for multimodal function optimization
- Goldberg, Richardson
- 1987
(Show Context)
Citation Context ...cause more good-performers in one objective cause the corresponding average performance to increase and that objective’s weight to decrease accordingly. This is not unlike the way sharing techniques (=-=Goldberg and Richardson, 1987-=-, see below) promote the balanced exploitation of multiple optima in the search space. For the same reason, VEGA can, at least in some cases, maintain different species for many more generations than ... |

485 | Genetic algorithms for multi-objective optimization: Formulation, discussion and generalization
- Fonseca, Fleming
- 1993
(Show Context)
Citation Context ..., that in which diversity appeared to be more important. Srinivas and Deb (1994) performed sharing in the decision variable domain. Although sharing has mainly been used together with Pareto ranking (=-=Fonseca and Fleming, 1993-=-; Cieniawski, 1993; Srinivas and Deb, 1994) and Pareto tournaments (Horn and Nafpliotis, 1993; Horn et al., 1994), it should be noted that Hajela and Lin (1992) had already implemented a form of shar1... |

404 | Multiobjective optimization using nondominated sorting in genetic algorithms. Evolutionary Computation
- Srinivas, Deb
- 1994
(Show Context)
Citation Context ... important. Srinivas and Deb (1994) performed sharing in the decision variable domain. Although sharing has mainly been used together with Pareto ranking (Fonseca and Fleming, 1993; Cieniawski, 1993; =-=Srinivas and Deb, 1994-=-) and Pareto tournaments (Horn and Nafpliotis, 1993; Horn et al., 1994), it should be noted that Hajela and Lin (1992) had already implemented a form of shar11sing to stabilize the population around g... |

383 | Multiple objective optimization with vector evaluated genetic algorithms - Schaffer - 1985 |

361 |
Mulitple Criteria Optimization: Theory, Computation, and Application
- Steuer
- 1986
(Show Context)
Citation Context ...ge-shaped plateau in the cost landscape. As desired, this plateau includes all admissible solutions and, thus, all possible optima produced by any coordinatewise monotonic function of the objectives (=-=Steuer, 1986-=-), of which the methods in Figures 4 to 6 are just examples. 16 x1 0 f2 4sNormalized rank 0 0.5 1 4 0 x2 f1 -4 -4 Figure 6: The cost landscape defined by ranking the maximum of the two objectives 3.2 ... |

358 | Predictive models for the breeder genetic algorithm: I. Continuous parameter optimization
- Muhlenbein, Schlierkamp-Voosen
- 1993
(Show Context)
Citation Context ...inimax approaches may not be parallel to any of the decision variable axes, or even follow a straight line. Although ridges, or equivalently, valleys, need not occur in single-objective optimization (=-=Mühlenbein and Schlierkamp-Voosen, 1993-=-), they do appear in this context, and can certainly be expected in almost any multiobjective problem. Ridge-shaped plateaus raise two problems already encountered with other types of multimodality. F... |

354 | Reducing bias and inefficiency in the selection algorithm - Baker - 1987 |

304 | A Niched Pareto Genetic Algorithm for Multiobjective Optimisation
- Horn, Nafpliotis, et al.
- 1994
(Show Context)
Citation Context ...ble domain. Although sharing has mainly been used together with Pareto ranking (Fonseca and Fleming, 1993; Cieniawski, 1993; Srinivas and Deb, 1994) and Pareto tournaments (Horn and Nafpliotis, 1993; =-=Horn et al., 1994-=-), it should be noted that Hajela and Lin (1992) had already implemented a form of shar11sing to stabilize the population around given regions of the trade-off surface. VEGA’s selection has also been ... |

277 |
An investigation of niche and species formation in genetic function optimization
- Deb, Goldberg
- 1989
(Show Context)
Citation Context ...), has been observed in natural as well as in artificial evolution, and can also occur in Pareto-based evolutionary optimization. The additional use of fitness sharing (Goldberg and Richardson, 1987; =-=Deb and Goldberg, 1989-=-) was proposed by Goldberg (1989) to prevent genetic drift and to promote the sampling of the whole Pareto set by the population. Fonseca and Fleming (1993) implemented fitness sharing in the objectiv... |

237 | A Survey of Evolution Strategies
- Back, Hoffmeister, et al.
- 1991
(Show Context)
Citation Context ...eases. Fast progression cannot be achieved unless the genetic operators tend to produce individuals which stay inside the corridor. The self-adaptation of mutation variances and correlated mutations (=-=Bäck et al., 1991-=-), as implemented in evolution strategies, addresses this same problem, but has not yet been tried in Pareto-based search. Binary mutation, as usually implemented in genetic algorithms, can be particu... |

142 |
Some Guidelines for Genetic Algorithms with Penalty Functions
- Richardson, Palmer, et al.
(Show Context)
Citation Context ... Steenstrup, 1987; Goldberg, 1989) is yet another example of an additive aggregating function. The fact that penalty functions are generally problem dependent and, as a consequence, difficult to set (=-=Richardson et al., 1989-=-) has prompted the de5svelopment of alternative approaches based on ranking (Powell and Skolnick, 1993). 2.2 Population-based non-Pareto approaches Schaffer (1985, see also Schaffer and Grefenstette (... |

128 |
Nonstationary Function Optimization using Genetic Algorithms with Dominance and Diploidy
- Goldberg, Smith
- 1987
(Show Context)
Citation Context ...ust try to adapt to constant change. As hinted above, different choices of objectives could result in significant changes in the cost landscape seen by the ES at each generation. Diploid individuals (=-=Goldberg and Smith, 1987-=-) were used for their improved ability to adapt to sudden environmental changes and, since the population was not expected to converge, a picture of the trade-off surface was produced from the points ... |

124 | Multiobjective optimization using the niched Pareto genetic algorithm”, IlliGAL
- Horn, Nafpliotis
- 1993
(Show Context)
Citation Context ...aring in the decision variable domain. Although sharing has mainly been used together with Pareto ranking (Fonseca and Fleming, 1993; Cieniawski, 1993; Srinivas and Deb, 1994) and Pareto tournaments (=-=Horn and Nafpliotis, 1993-=-; Horn et al., 1994), it should be noted that Hajela and Lin (1992) had already implemented a form of shar11sing to stabilize the population around given regions of the trade-off surface. VEGA’s selec... |

117 | Genetic Algorithms for Changing Environments - Grefenstette - 1992 |

111 |
Finite Markov chain analysis of genetic algorithms
- Goldberg, Segrest
- 1987
(Show Context)
Citation Context ... VEGA can, at least in some cases, maintain different species for many more generations than a GA optimizing a pure weighted sum of the same objectives with fixed weights would, due to genetic drift (=-=Goldberg and Segrest, 1987-=-). Unfortunately, the balance reached necessarily depends on the scaling of the objectives. Fourman (1985) also addressed multiple objectives in a non-aggregating manner. Selection was performed by co... |

104 | A Variant of Evolution Strategies for Vector Optimization - Kursawe - 1991 |

90 |
Using genetic algorithms in engineering design optimization with non-linear constraints
- Powell, Skolnick
- 1993
(Show Context)
Citation Context ...act that penalty functions are generally problem dependent and, as a consequence, difficult to set (Richardson et al., 1989) has prompted the de5svelopment of alternative approaches based on ranking (=-=Powell and Skolnick, 1993-=-). 2.2 Population-based non-Pareto approaches Schaffer (1985, see also Schaffer and Grefenstette (1985)) was probably the first to recognize the possibility of exploiting EA populations to treat nonco... |

89 | Genetic search strategies in multicriterion optimal design - Hajela, Lin - 1992 |

84 | Adding learning to the cellular development of neural networks
- Gruau, Whitley
- 1993
(Show Context)
Citation Context ..., and/or the corresponding operators, is another important avenue for research. Combinations of genetic search and local optimization resulting in either Lamarckian or developmental Baldwin learning (=-=Gruau and Whitley, 1993-=-) may also provide a means of addressing the difficulties imposed by ridge-shaped landscapes. The question of which fitness assignment method is better remains largely open, although Pareto-based meth... |

77 |
A naturally occurring niche and species phenomenon: the model and first results
- Davidor
- 1991
(Show Context)
Citation Context ...earning paradigms may be particularly appropriate. As far as the search strategy is concerned, much work has certainly yet to be done. In particular the emergence of niches in structured populations (=-=Davidor, 1991-=-) suggests the study of such models in the multiobjective case. The development of adaptive representations capable of capturing and exploiting directional trends in the fitness landscape, well advanc... |

68 | Compaction of symbolic layout using genetic algorithms - Fourman - 1985 |

58 |
Using genetic algorithms to solve a multiple objective groundwater pollution containment problem
- Ritzel, Eeheart, et al.
- 1994
(Show Context)
Citation Context ...g for their lack of sensitivity to the possible concavity of the trade-off surface. In the few comparative studies of multiobjective EAs available to date (Wilson and Macleod, 1993; Cieniawski, 1993; =-=Ritzel et al., 1994-=-; Srinivas and Deb, 1994), VEGA has understandably been a strong point of reference, but the comparison has remained largely qualitative. No extensive, quantitative comparison of multiobjective EAs ha... |

50 |
The application of genetic algorithms to resource scheduling
- Syswerda, Palmucci
- 1991
(Show Context)
Citation Context ...be required until a suitable solution is found. Several applications of evolutionary algorithms in the optimization of aggregating functions have been reported in the literature. A number of authors (=-=Syswerda and Palmucci, 1991-=-; Jakob et al., 1992; Jones et al., 1993) provide examples of the use of the popular weighted sum approach. Using target vector optimization, which consists of minimizing the distance in objective spa... |

38 |
Genetic Al- gorithms and Simulated Annealing: An Overview
- Davis, Steenstrup
- 1987
(Show Context)
Citation Context ... of multiple attribute utility analysis (MAUA) in conjunction with GAs has been suggested by Horn and Nafpliotis (1993), but without experimental results. Handling constraints with penalty functions (=-=Davis and Steenstrup, 1987-=-; Goldberg, 1989) is yet another example of an additive aggregating function. The fact that penalty functions are generally problem dependent and, as a consequence, difficult to set (Richardson et al.... |

20 | Multi-objective learning via genetic algorithms - Schaffer, Grefenstette - 1985 |

19 |
Application of Genetic Algorithms to Task Planning and Learning
- Jakob, Gorges-Schleuter, et al.
- 1992
(Show Context)
Citation Context ...solution is found. Several applications of evolutionary algorithms in the optimization of aggregating functions have been reported in the literature. A number of authors (Syswerda and Palmucci, 1991; =-=Jakob et al., 1992-=-; Jones et al., 1993) provide examples of the use of the popular weighted sum approach. Using target vector optimization, which consists of minimizing the distance in objective space to a given goal v... |

18 | Pareto optimality, GA-easiness and deception - Louis, Rawlins - 1993 |

17 |
Characterization of pareto and lexicographic optimal solutions
- Ben-Tal
- 1979
(Show Context)
Citation Context ...pared according to the objective with the highest priority. If this resulted in a tie, the objective with the second highest priority was used, and so on. This is known as the lexicographic ordering (=-=Ben-Tal, 1980-=-). A second version, reported to work surprisingly well, consisted of randomly selecting the objective to be used in each comparison. Similarly to VEGA, this corresponds to averaging fitness across fi... |

17 | The in£uence of variation and of developmental constraints on the rate of multivariate phenotypic evolution - Wagner - 1988 |

15 |
Vector optimization for control with performance and parameter sensitivity indices
- Gembicki
- 1974
(Show Context)
Citation Context ...ctor optimization, which consists of minimizing the distance in objective space to a given goal vector, Wienke et al. (1992) report work on a problem in atomic emission spectroscopy. Goal attainment (=-=Gembicki, 1974-=-), a related technique which seeks to minimize the weighted difference between objective values and the corresponding goals, was used amongst other methods by Wilson and Macleod (1993), who also monit... |

10 |
Representation and Hidden Bias II: Eliminating Defining Length Bias in Genetic Search via Shuffle Crossover
- Caruana, Eshelman, et al.
- 1989
(Show Context)
Citation Context ...e mating parents. Similarly, single and two-point crossover of concatenated binary strings will change at most one or two decision variables. Uniform crossover (Syswerda, 1989) and shuffle crossover (=-=Caruana et al., 1989-=-) are less biased in this respect, in that the value of all decision variables may be altered in a single recombination step. Finally, multiobjective fitness landscapes become non-stationary once the ... |

9 |
An investigation of the ability of genetic algorithms to generate the tradeoff curve of a multi-objective groundwater monitoring problem
- Cieniawski
- 1993
(Show Context)
Citation Context ...ppeared to be more important. Srinivas and Deb (1994) performed sharing in the decision variable domain. Although sharing has mainly been used together with Pareto ranking (Fonseca and Fleming, 1993; =-=Cieniawski, 1993-=-; Srinivas and Deb, 1994) and Pareto tournaments (Horn and Nafpliotis, 1993; Horn et al., 1994), it should be noted that Hajela and Lin (1992) had already implemented a form of shar11sing to stabilize... |

9 |
Searching databases of two-dimensional and three-dimensional chemical structures using genetic algorithms
- Jones, Brown, et al.
- 1993
(Show Context)
Citation Context ...everal applications of evolutionary algorithms in the optimization of aggregating functions have been reported in the literature. A number of authors (Syswerda and Palmucci, 1991; Jakob et al., 1992; =-=Jones et al., 1993-=-) provide examples of the use of the popular weighted sum approach. Using target vector optimization, which consists of minimizing the distance in objective space to a given goal vector, Wienke et al.... |

9 | Multicriteria target vector optimization of analytical procedures using a genetic algorithm: part II. polyoptimization of the phothometric calibration graph of dry glucose sensors for quantitative clinical analysis. Analytica Chimica Acta - Wienke, Lucasius, et al. - 1993 |

7 |
Computer aided control system design using a multiobjective optimization approach
- Fleming, Pashkevich
- 1985
(Show Context)
Citation Context ... which Schaffer called speciation. In fact, points in concave regions of a trade-off surface cannot be found by optimizing a linear combination of the objectives, for any set of weights, as noted in (=-=Fleming and Pashkevich, 1985-=-). Although VEGA, like the plain weighted-sum approach, is not well suited to address problems with concave trade-off surfaces, the weighting scheme it implicitly implements deserves closer attention.... |

6 | Multiple Criteria Decision Making Theory and Application - Fandel, Gal - 1980 |

5 | Genetic Algorithms - Belew, Booker - 1991 |

2 |
Multicriteria decision models with specified goal levels
- Dinkelbach
- 1980
(Show Context)
Citation Context ...y dependent on the power of the numerical techniques available to support it. Certain decision models, although simple to formulate, do not necessarily lead to numerically easy optimization problems (=-=Dinkelbach, 1980-=-). By easing the numerical difficulties inherent to other optimization methods, evolutionary algorithms open the way to the development of simpler, if not new, decision making approaches. A very attra... |

2 |
Goal setting and compromise solutions
- Shi, Yu
- 1989
(Show Context)
Citation Context ...ce, but also to adjust the current preferences in the search for a compromise between the ideal and the possible in a limited amount of time. Goal setting, for example, is itself the object of study (=-=Shi and Yu, 1989-=-). This is an area where combinations of EAs and other learning paradigms may be particularly appropriate. As far as the search strategy is concerned, much work has certainly yet to be done. In partic... |

1 |
Adding learning to the cellular developmentof neural networks: Evolution and the baldwin effect
- Gruau, Whitley
- 1993
(Show Context)
Citation Context ..., and/or the corresponding operators, is another important avenue for research. Combinations of genetic search and local optimization resulting in either Lamarckian or developmental Baldwin learning (=-=Gruau and Whitley, 1993-=-) may also provide a means of addressing the difficulties imposed by ridge-shaped landscapes. Acknowledgement The first author gratefully acknowledges support by Programa CIENCIA, Junta Nacional de In... |