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## Analysis of Selection, Mutation and Recombination in Genetic Algorithms (1993)

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Venue: | Neural Network World |

Citations: | 15 - 1 self |

### Citations

10012 |
Genetic Algorithms
- Goldberg
- 1989
(Show Context)
Citation Context ...production is characterized by recombining two parent strings into an o spring. The recombination is called crossover. Genetic algorithms were invented by Holland [18]. Recent surveys can be found in =-=[14]-=- and the proceedings of the international conferences on genetic algorithms [25] [5] [13]. Genetic Algorithm STEP0: De ne a genetic representation of the problem STEP1: Create an initial population P ... |

3872 |
Adaptation in Natural and Artificial Systems
- Holland
- 1975
(Show Context)
Citation Context ...er experiments and a misssing theory, he did not find a good combination of the ingredients. In the 70's two different evolutionary algorithms independently emerged - the genetic algorithm of Holland =-=[18]-=- and the evolution strategies of Rechenberg [24] and Schwefel [27]. Holland was not so much interested in optimization, but in adaptation. He investigated the genetic algorithm with decision theory fo... |

1581 |
The genetical theory of natural selection
- Fisher
- 1930
(Show Context)
Citation Context ...By setting p(GEN 1\Gammaffl ) = 1 \Gamma ffl equation 21 is easily obtained. Remark: If we assume R(t) = S(t) we obtain from equation 19 a version of Fisher's fundamental theorem of natural selection =-=[12]-=- [9]. By comparing truncation selection and proportionate selection one observes that proportionate selection gets weaker when the population approaches the optimum. An infinite population will need a... |

1358 |
The Neutral Theory of Molecular Evolution
- Kimura
- 1983
(Show Context)
Citation Context ...ulation converges tosthe optimum value. In this area GENe is constant. This is an important result, because it is commonly believed in population genetics that GENe increases with the population size =-=[19]-=-. This is only the case in the second region. Here the population size is too small. The population does not converge to the optimum. GENe increases with the population size because the quality of the... |

1060 |
Introduction to quantitative genetics
- Falconer
- 1960
(Show Context)
Citation Context ...s principle by the term Natural Selection in order to mark its relation to man's power of selection." In this section we will rst analyze arti cial selection by methods found in quantitative genetics =-=[11]-=-, [8] and [7]. A mathematically oriented book on quantitative genetics and natural selection is [9]. We willshowattheendof this section that natural selection can be investigated by the same methods. ... |

828 |
Evolutionstrategie: Optimierung technisher Systeme nach Prinzipien der biologishen Evolution, Fromman-Holzboog
- Rechenberg
- 1973
(Show Context)
Citation Context ... +1) is created byrandom mating, without selection. If the regression equation with x 0 ij (t +1)=a(t)+bX 0 X(t) xi(t)+xj(t) 2 E( ij) =0 is valid, where x 0 ij is the o spring of xi and xj, then + ij =-=(24)-=- bX 0 X(t) b(t) (25) Proof. From the regression equation we obtain for the averages E(x 0 (t + 1)) = a(t)+bX 0 X(t)M(t) Because the o spring generation is created by random mating without selection, t... |

616 |
Simulated crossover in genetic algorithms
- Syswerda
- 1993
(Show Context)
Citation Context ...th a given probability pm eachbitof the selected string. The crossover operator works with two strings. If two strings x =(x1�:::�xn) and y =(y1�:::�yn) are given, then the uniform crossover operator =-=[28]-=- combines the two strings as follows z =(z1�:::�zn) zi = xi or zi = yi Normally xi or yi are chosen with equal probability. In genetic algorithms many di erent crossover operators are used. Most popul... |

611 |
Numerical Optimization of Computer Models
- SCHWEFEL
- 1981
(Show Context)
Citation Context ...ination of the ingredients. In the 70's two di erent evolutionary algorithms independently emerged - the genetic algorithm of Holland [18] and the evolution strategies of Rechenberg [24] and Schwefel =-=[27]-=-. Holland was not so much interested in optimization, but in adaptation. He investigated the genetic algorithm with decision theory for discrete domains. Holland emphasized the importance of recombina... |

399 | Predictive models for the breeder genetic algorithms: I. continuous parameter optimization
- Mühlenbein, Schlierkamp-Voosen
- 1993
(Show Context)
Citation Context ...the PGA is a totally distributed algorithm without any central control. The PGA models the natural evolution process which self-organizes itself. The next algorithm, the breeder genetic algorithm BGA =-=[22]-=- is inspired by the science of breeding animals. In this algorithm, each one of a set of virtual breeders has the task to improve its own subpopulation. Occasionally the breeder imports individuals fr... |

334 |
The CHC adaptive search algorithm: How to have safe search when engaging in nontraditional genetic recombination
- Eshelman
- 1991
(Show Context)
Citation Context ...oldberg [15] observed a scaling of O(n 1:7 ) for his best algorithm. To our knowledge the previous best results for DECEPTION and uniform crossover have been achieved by the CHC algorithm of Eshelman =-=[10]-=-. The CHC algorithm needed 20960 function evaluations to find the optimum. The BGA needs about 16000 function evaluations. The efficiency can be increased if steepest ascent hillclimbing is used [21].... |

275 | Genetic algorithms, noise, and the sizing of populations
- Goldberg, Deb, et al.
- 1992
(Show Context)
Citation Context ...pared to other algorithms. We will only mention ONEMAX and DECEPTION. For ONEMAX the numberoffunctionevaluations needed to locate the optimum (FEopt) scales like e n ln(n) (empirical law 1). Goldberg =-=[15]-=- observed a scaling of O(n 1:7 ) for his best algorithm. To our knowledge the previous best results for DECEPTION and uniform crossover have been achieved by the CHC algorithm of Eshelman [10]. The CH... |

263 | Metamodel-assisted evolution strategies
- Bäck, Giannakoglou
- 2002
(Show Context)
Citation Context ...ed Breeder Genetic Algorithm. Competition of strategies can be done on different levels, for example the level of the individuals, the level of subpopulations or the level of populations. Back et al. =-=[3]-=- have implemented the adaptation of strategy parameters on the individual level. The strategy parameters of the best individuals are recombined, giving the new stepsize for the mutation. Herdy [17] us... |

253 |
An Introduction to Population Genetics Theory. Harper and Row
- Crow, Kimura
- 1970
(Show Context)
Citation Context ..." In this section we will rst analyze arti cial selection by methods found in quantitative genetics [11], [8] and [7]. A mathematically oriented book on quantitative genetics and natural selection is =-=[9]-=-. We willshowattheendof this section that natural selection can be investigated by the same methods. A detailed investigation can be found in [23]. 3.1 Arti cial Selection The change produced by selec... |

172 |
Adaptation in natural and arti cial system
- Holland
- 1975
(Show Context)
Citation Context ...puter experiments and a misssing theory, he did not nd a good combination of the ingredients. In the 70's two di erent evolutionary algorithms independently emerged - the genetic algorithm of Holland =-=[18]-=- and the evolution strategies of Rechenberg [24] and Schwefel [27]. Holland was not so much interested in optimization, but in adaptation. He investigated the genetic algorithm with decision theory fo... |

144 |
The Mathematical Theory of Quantitative Genetics
- Bulmer
- 1980
(Show Context)
Citation Context ... the term Natural Selection in order to mark its relation to man's power of selection." In this section we will rst analyze arti cial selection by methods found in quantitative genetics [11], [8] and =-=[7]-=-. A mathematically oriented book on quantitative genetics and natural selection is [9]. We willshowattheendof this section that natural selection can be investigated by the same methods. A detailed in... |

132 | Optimal mutation rates in genetic search
- Bäck
- 1993
(Show Context)
Citation Context ... total numberisobtainedby summation.sFor 0 p0 < 0:9 the above equation can be approximated by FEopt = e n ln ((1 ; p0)n) (29) We have con rmed the formula by intensive simulations [21]. Recently Back =-=[2]-=- has shown that FEopt can be only marginally reduced if a theoretically optimal variable mutation rate is used. This mutation rate depends on the number of bits which are still wrong. This result has ... |

116 | Evolution in Time and Space – The Parallel Genetic Algorithm
- Mühlenbein
- 1991
(Show Context)
Citation Context ...ion needs the average tness of the population. The result is a highly synchronized algorithm, which is di cult to implement e ciently on parallel computers. In the parallel genetic algorithm PGA [20],=-=[21]-=-, a distributed selection scheme is used. This is achievedsas follows. Each individual does the selection by itself. It looks for a partner in its neighborhood only. The set of neighborhoods de nes a ... |

115 | The Science of Breeding and its Application to the Breeder Genetic Algorithm
- Mühlenbein, Schlierkamp-Voosen
- 1994
(Show Context)
Citation Context ...book on quantitative genetics and natural selection is [9]. We willshowattheendof this section that natural selection can be investigated by the same methods. A detailed investigation can be found in =-=[23]-=-. 3.1 Arti cial Selection The change produced by selection that mainly interests the breeder is the response to selection, which is symbolized by R. R is de ned as the di erence between the populatio... |

100 |
Evolution Algorithms in Combinatorial Optimization. Parallel Computing 7: 65–85
- Mühlenbein, Gorges-Schleuter, et al.
- 1988
(Show Context)
Citation Context ...een these two strategies. Then numerical results are given for a test suite of discrete functions. 2 Evolutionary Algorithms A previous survey of search strategies based on evolution has been done in =-=[20]-=-. Evolutionary algorithms for continuous parameter optimization are surveyed in [4]. Algorithms which are driven mainly by mutation and selection have been developed by Rechenberg [24] andSchwefel [27... |

74 |
Messy genetic Algorithms Revisited: Studies in Mixed Size and Scale”,
- Goldberg
- 1990
(Show Context)
Citation Context ...ops sharply to zero. The response to selection is almost 0. For the PLATEAU function k bits have to be ipped in order that the tness increases by k. The DECEPTION function has been de ned by Goldberg =-=[16]-=-. The tness of DECEPTION(k,l) is given by thesumofl deceptive functions of size k. A deceptive function and a smoothed version of order k = 3 is de ned in the following table bit DECEP SYMBA bit DECEP... |

39 |
On Crossover as an Evolutionary Viable Strategy, in:
- Schaffer, Eshelman
- 1991
(Show Context)
Citation Context ...ns no heritability. Instead there is an o set, de ned by the di erence of the probabilities of getting better or worse. The importance of ut and vt has been independently discovered by Scha er et al. =-=[26]-=-. They did not use the di erence of the probabilities, but the quotient which they called the safety factor. F = ut vt In order to apply the theorem we have to estimate S(t), ut and vt. The last two v... |

36 |
Basic concepts in population, quantitative, and evolutionary genetics.
- Crow
- 1986
(Show Context)
Citation Context ...ciple by the term Natural Selection in order to mark its relation to man's power of selection." In this section we will rst analyze arti cial selection by methods found in quantitative genetics [11], =-=[8]-=- and [7]. A mathematically oriented book on quantitative genetics and natural selection is [9]. We willshowattheendof this section that natural selection can be investigated by the same methods. A det... |

33 |
Reproductive Isolation as Strategy Parameter in Hierarchically Organized Evolution Strategies. In
- Herdy
- 1992
(Show Context)
Citation Context ...etal.[3]have implemented the adaptation of strategy parameters on the individual level. The strategy parameters of the best individuals are recombined, giving the new stepsize for the mutation. Herdy =-=[17]-=- uses an competition on the population level. In this case whole populations are evaluated at certain intervals. The strategies of the succesful populations proliferate, strategies in populations with... |

29 |
and Hans-Paul Schwefel. An Overview of Evolutionary Algorithms for Parameter Optimization
- Bäck
- 1993
(Show Context)
Citation Context ...ete functions. 2 Evolutionary Algorithms A previous survey of search strategies based on evolution has been done in [20]. Evolutionary algorithms for continuous parameter optimization are surveyed in =-=[4]-=-. Algorithms which are driven mainly by mutation and selection have been developed by Rechenberg [24] andSchwefel [27] for continuous parameter optimization. Their algorithms are called evolution stra... |

28 |
Global Properties of Evolution Processes”,
- Bremermann, Rogson, et al.
- 1966
(Show Context)
Citation Context ...tionary algorithms which model natural evolution processes were already proposed for optimization in the 60's. We cite just one representative example, the outstanding work of Bremermann. He wrote in =-=[6]-=-. \The major purpose of the work is the study of the e ects of mutation, mating, and selection on the evolution of genotypes in the case of non-linear tness functions. In view of the mathematical di c... |

7 |
The CHC adaptive search algorithm: How tohave safe search when engaging in nontraditional genetic recombination
- Eshelman
- 1991
(Show Context)
Citation Context ...oldberg [15] observed a scaling of O(n 1:7 ) for his best algorithm. To our knowledge the previous best results for DECEPTION and uniform crossover have been achieved by the CHC algorithm of Eshelman =-=[10]-=-. The CHC algorithm needed 20960 function evaluations to nd the optimum. The BGA needs about 16000 function evaluations. The e ciency can be increased if steepest ascent hillclimbing is used [21]. In ... |

3 |
On the mean convergence time of genetic populations without selection
- Asoh, Muhlenbein
- 1994
(Show Context)
Citation Context ...stand. It is related to the genetic drift. It has been known for quite a time that the population converges also without any kind of selection just because of random sampling in a nite population. In =-=[1]-=- it has been shown that GENe increases proportional to the size of the population N and to the logarithm of the size of the problem n. Thus GENe is surprisingly small. This important result demonstrat... |

2 |
Hans-Paul Schwefel. ASurvey of Evolution Strategies
- Back
- 1991
(Show Context)
Citation Context ...buted Breeder Genetic Algorithm. Competition of strategies can be done on di erent levels, for example the level of the individuals, the level of subpopulations or the level of populations. Back etal.=-=[3]-=-have implemented the adaptation of strategy parameters on the individual level. The strategy parameters of the best individuals are recombined, giving the new stepsize for the mutation. Herdy [17] use... |

1 |
The Genetical TheoryofNatural Selection
- Fisher
- 1958
(Show Context)
Citation Context ... (1 ; 1 n )t (1 ; p0) By setting p(GEN1; )=1; equation 21 is easily obtained. Remark: If we assume R(t) =S(t) we obtain from equation 19 a version of Fisher's fundamental theorem of natural selection =-=[12]-=- [9]. By comparing truncation selection and proportionate selection one observes that proportionate selection gets weaker when the population approaches the optimum. An in nite population will need an... |