## Selective Pressure in Evolutionary Algorithms: A Characterization of Selection Mechanisms (1994)

Venue: | In Proceedings of the First IEEE Conference on Evolutionary Computation |

Citations: | 78 - 2 self |

### BibTeX

@INPROCEEDINGS{Bäck94selectivepressure,

author = {Thomas Bäck},

title = {Selective Pressure in Evolutionary Algorithms: A Characterization of Selection Mechanisms},

booktitle = {In Proceedings of the First IEEE Conference on Evolutionary Computation},

year = {1994},

pages = {57--62},

publisher = {IEEE Press}

}

### Years of Citing Articles

### OpenURL

### Abstract

Due to its independence of the actual search space and its impact on the exploration-exploitation tradeoff, selection is an important operator in any kind of Evolutionary Algorithm. In this paper, all important selection operators are discussed and quantitatively compared with respect to their selective pressure. The comparison clarifies that only a few really different and useful selection operators exist: Proportional selection (in combination with a scaling method), linear ranking, tournament selection, and (¯,)-selection (respectively (¯+)-selection). Their selective pressure increases in the order as they are listed here. The theoretical results are confirmed by an experimental investigation using a Genetic Algorithm with different selection methods on a simple unimodal objective function. I. Introduction Evolutionary Algorithms (EAs) are a class of direct probabilistic search algorithms based on the model of organic evolution. Currently, Genetic Algorithms (GAs) [17; 12], Evolu...

### Citations

2827 |
Adaptation in natural and artificial systems
- Holland
- 1975
(Show Context)
Citation Context ...al objective function. I. Introduction Evolutionary Algorithms (EAs) are a class of direct probabilistic search algorithms based on the model of organic evolution. Currently, Genetic Algorithms (GAs) =-=[17; 12]-=-, Evolution Strategies (ESs) [21; 23], and Evolutionary Programmings(EP) [10; 9] are the most prominent representatives of these algorithms. In general, all Evolutionary Algorithms are characterized b... |

1966 |
Genetic Algorithms + Data Structure = Evolution Programs
- Michalewicz
- 1992
(Show Context)
Citation Context ... variety of different operators developed for search spaces such as binary vectors (GAs), real-valued vectors (ESs and EP), permutations (GAs), and even more complex ones was presented by Michalewicz =-=[20]-=-. Due to the strong impact of selection on the evolutionary search process, it is very desirable to quantify the selective pressure of particular selection mechanisms. Goldberg and Deb started work in... |

1809 |
Genetic algorithms in search, optimization, and machine learning
- Goldberg
(Show Context)
Citation Context ...al objective function. I. Introduction Evolutionary Algorithms (EAs) are a class of direct probabilistic search algorithms based on the model of organic evolution. Currently, Genetic Algorithms (GAs) =-=[17; 12]-=-, Evolution Strategies (ESs) [21; 23], and Evolutionary Programmings(EP) [10; 9] are the most prominent representatives of these algorithms. In general, all Evolutionary Algorithms are characterized b... |

662 |
Evolutionsstrategie: Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. Frommann-Holzboog
- Rechenberg
- 1973
(Show Context)
Citation Context ...n Evolutionary Algorithms (EAs) are a class of direct probabilistic search algorithms based on the model of organic evolution. Currently, Genetic Algorithms (GAs) [17; 12], Evolution Strategies (ESs) =-=[21; 23]-=-, and Evolutionary Programmings(EP) [10; 9] are the most prominent representatives of these algorithms. In general, all Evolutionary Algorithms are characterized by the fact that they work on a popula... |

644 |
Artificial Intelligence through Simulated Evolution
- Fogel, Owens, et al.
- 1966
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Citation Context ...of direct probabilistic search algorithms based on the model of organic evolution. Currently, Genetic Algorithms (GAs) [17; 12], Evolution Strategies (ESs) [21; 23], and Evolutionary Programmings(EP) =-=[10; 9]-=- are the most prominent representatives of these algorithms. In general, all Evolutionary Algorithms are characterized by the fact that they work on a population P = fa 1 ; : : : ; ag 2 I of individua... |

511 |
Numerical Optimization of Computer Models
- Schwefel
- 1981
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Citation Context ...n Evolutionary Algorithms (EAs) are a class of direct probabilistic search algorithms based on the model of organic evolution. Currently, Genetic Algorithms (GAs) [17; 12], Evolution Strategies (ESs) =-=[21; 23]-=-, and Evolutionary Programmings(EP) [10; 9] are the most prominent representatives of these algorithms. In general, all Evolutionary Algorithms are characterized by the fact that they work on a popula... |

392 | A Comparative Analysis of Selection Schemes Used in Genetic Algorithms, Foundations of Genetic Algorithms
- Goldberg, Deb
- 1991
(Show Context)
Citation Context ... to quantify the selective pressure of particular selection mechanisms. Goldberg and Deb started work into this direction by presenting the concept of takeover time as a measure of selective pressure =-=[14]-=-. In section II, we will summarize and extend their results in order to analyze and compare the most important selection methods which are nowadays used in EAs. Furthermore, probabilistic selection me... |

331 | The GENITOR algorithm and selection pressure: why rankbased allocation of reproductive trials is best
- Whitley
- 1989
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Citation Context ...14]. Whitley presented a linear ranking method equivalent to Baker's, which allows for a direct computation of the index j = i \Gamma 1 2 f0; : : : ;s\Gamma 1g that designates the selected individual =-=[26]: j = b -=-2(c\Gamma1) \Delta (c \Gamma p c 2 \Gamma 4(c \Gamma 1)��)c, where �� 2 [0; 1] denotes a uniform random variable. For 1 ! cs2, the method is practically identical to linear ranking with j + = ... |

329 | Messy genetic algorithms: Motivation, analysis, and first results - Goldberg, Korb, et al. - 1989 |

323 |
Reducing bias and inefficiency in the selection algorithm
- Baker
(Show Context)
Citation Context ...pt the random walk setting q = 1, which corresponds to p i = 1=). C. Linear Ranking The linear ranking selection method by Baker uses a linear function to map indices i to selection probabilities p i =-=[2; 3; 16]-=-. Again, individuals are assumed to be sorted according to fitness. Then, the selection probabilities are given by p i = ` j + \Gamma (j + \Gamma j \Gamma ) \Delta i \Gamma 1s\Gamma 1 ' = : (3) The co... |

212 |
Adaptive selection methods for genetic algorithms
- Baker
- 1985
(Show Context)
Citation Context ...pt the random walk setting q = 1, which corresponds to p i = 1=). C. Linear Ranking The linear ranking selection method by Baker uses a linear function to map indices i to selection probabilities p i =-=[2; 3; 16]-=-. Again, individuals are assumed to be sorted according to fitness. Then, the selection probabilities are given by p i = ` j + \Gamma (j + \Gamma j \Gamma ) \Delta i \Gamma 1s\Gamma 1 ' = : (3) The co... |

108 |
How genetic algorithms work: A critical look at implicit parallelism
- Grefenstette, Baker
- 1989
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Citation Context ... tasks (if \Phi = f is assumed). For these reasons, a variety of scaling functions ffi are nowadays used in combination with proportional selection, including techniques such as linear static scaling =-=[16]-=-, linear dynamic scaling [16], exponential scaling [16], logarithmic scaling [16], and sigma truncation [11; 4]. Here, we focus on linear dynamic scaling, the method which seems to be most widely used... |

62 |
Evolving Artificial Intelligence
- Fogel
- 1992
(Show Context)
Citation Context ...of direct probabilistic search algorithms based on the model of organic evolution. Currently, Genetic Algorithms (GAs) [17; 12], Evolution Strategies (ESs) [21; 23], and Evolutionary Programmings(EP) =-=[10; 9]-=- are the most prominent representatives of these algorithms. In general, all Evolutionary Algorithms are characterized by the fact that they work on a population P = fa 1 ; : : : ; ag 2 I of individua... |

57 |
A Note on Boltzmann Tournament Selection for Genetic Algorithms and Population-Oriented
- Goldberg
- 1990
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Citation Context ...he asymptotic global convergence theory of Simulated Annealing (SA) [25] to GAs and to create a new form of niching mechanism that maintains stable subpopulations of similar objective function values =-=[13]-=-. The method works by performing pairwise competitions between individuals that have to differ from each other in objective function values by a threshold amount \Theta. In order to select one individ... |

55 | An analysis of evolutionary programming
- Fogel
- 1992
(Show Context)
Citation Context ...ned some interest in EAs, namely EPselection, nonlinear ranking, Boltzmann tournament selection, and Boltzmann selection. Evolutionary Programming The selection operator used in modern variants of EP =-=[8; 9]-=- can be regarded as a hybrid of tournament and (+)- selection. Working on the union U (t) = P (t) [ P 0 (t) of parents P (t) 2 I and offspring P 0 (t) 2 I , the method proceeds as follows: For each in... |

47 |
Fast genetic selection of features for neural network classifiers
- Brill, Brown, et al.
- 1992
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Citation Context ...combination with proportional selection, including techniques such as linear static scaling [16], linear dynamic scaling [16], exponential scaling [16], logarithmic scaling [16], and sigma truncation =-=[11; 4]-=-. Here, we focus on linear dynamic scaling, the method which seems to be most widely used. For a minimization task, its functional form ffi (y i ) = y i \Gamma minff(a j ) j a j 2 P (t \Gamma !)g (max... |

44 | Extended selection mechanisms in genetic algorithms
- Back, Hoffmeister
- 1991
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Citation Context ...re thatsa does not go extinct by chance, which would cause �� to become infinite, a guaranteed survival of one copy ofsa is assumed (an 1-elitist selection method according to the terminology used=-= in [1]). T-=-he basic idea of the takeover time concept consists in the assumption that smaller (larger) takeover times correspond with stronger (weaker) selective pressure. The minimal value of �� is one and ... |

25 |
An analysis of selection procedures with particular attention paid to proportional and Boltzmann selection
- Maza, Tidor
- 1993
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Citation Context ...th the method discussed in the previous section, Boltzmann selection is a misleading name for yet another scaling method for proportional selection, using a scaling function ffi (y i ) = exp(y i =T ) =-=[5]-=-. The authors indicate selective pressure to be low (high) when the control parameter T is high (low). The method, however, suffers from the drawback common to all combinations of proportional selecti... |

14 |
Documentation for Prisoner’s Dilemma and Norms Programs that use the Genetic Algorithm. The University of New
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Citation Context ...combination with proportional selection, including techniques such as linear static scaling [16], linear dynamic scaling [16], exponential scaling [16], logarithmic scaling [16], and sigma truncation =-=[11; 4]-=-. Here, we focus on linear dynamic scaling, the method which seems to be most widely used. For a minimization task, its functional form ffi (y i ) = y i \Gamma minff(a j ) j a j 2 P (t \Gamma !)g (max... |

6 |
An analysis of Boltzmann tournament selection
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6 | Natural evolution and collective optimumseeking
- Schwefel
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Citation Context ...n (3). D. (��,)- and (��+)-Selection Both (��,)- and (��+)-selection [23] are used in ESs, but the (��,)-method is preferred because it facilitates the selfadaptation of strategy p=-=arameters (see e.g. [24]). Originall-=-y, these methods are designed to reduce an offspring population (created by recombination and mutation) of sizes�� to a new parent population of size ��. While (��,)-selection achieves thi... |

2 |
Mathematik fur Informatiker, volume 1
- Dorfler
- 1977
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Citation Context ...m f0; 1; : : :; q \Gamma 1g. Following the theory of exponential generating functions, this number is given by the coefficient of the term x q =q! in the corresponding exponential generating function =-=[6]-=-: (exp(x) \Gamma 1) \Delta exp(x) \Gammai = 1+ 1 X q=1 (( \Gamma i+1) q \Gamma ( \Gamma i) q ) \Delta x q q! ; and the coefficient turns into the desired probability p i by observing that each of the ... |

1 |
Mathematik fur Informatiker, volume 2
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Citation Context ...: : ; 2g: P(w k = v) = ` q v ' p v (1 \Gamma p) q\Gammav : In addition, the absolute frequencies H k (B k ) of B k are also random variables, following a binomial distribution with parameters q and p =-=[7]-=-, and the same is true for the relative frequencies h k = H k =q with expectation E(h k ) = p and variance Var(h k ) = p \Delta (1 \Gamma p)=q. As lim q!1 Var(h k ) = 0, the expectations are experimen... |

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Introduction to Combinatorial Mathematics. Computer Science Series
- Liu
- 1968
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Citation Context ... This results in a recurrence of the form N t+1 = �� \Delta (N t + N t\Gamma1 ), where N 0 = 1 and N 1 = =��. The recurrence (a generalized Fibonacci sequence) can be solved by standard method=-=s (e.g. [18]) and yields N t = (-=-ff t+1 1 \Gamma ff t+1 2 )= r �� \Delta i �� + 4 j ; (5) where ff 1;2 = 2�� \Sigma 1 2 \Delta ( �� \Delta ( �� + 4)) 1=2 are the roots of the characteristic equation ff 2 \Gamma ff... |

1 | Evolving Artzficial Intelligence - Fogel - 1992 |