## A comparative analysis of selection schemes used in genetic algorithms (1991)

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Venue: | Foundations of Genetic Algorithms |

Citations: | 392 - 32 self |

### BibTeX

@INPROCEEDINGS{Goldberg91acomparative,

author = {David E. Goldberg and Kalyanmoy Deb},

title = {A comparative analysis of selection schemes used in genetic algorithms},

booktitle = {Foundations of Genetic Algorithms},

year = {1991},

pages = {69--93},

publisher = {Morgan Kaufmann}

}

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### Abstract

This paper considers a number of selection schemes commonly used in modern genetic algorithms. Specifically, proportionate reproduction, ranking selection, tournament selection, and Genitor (or «steady state") selection are compared on the basis of solutions to deterministic difference or differential equations, which are verified through computer simulations. The analysis provides convenient approximate or exact solutions as well as useful convergence time and growth ratio estimates. The paper recommends practical application of the analyses and suggests a number of paths for more detailed analytical investigation of selection techniques. Keywords: proportionate selection, ranking selection, tournament selection, Genitor, takeover time, time complexity, growth ratio. 1

### Citations

1818 |
Genetic algorithm in search, optimization, and machine learning
- Goldberg
- 1989
(Show Context)
Citation Context ...0) solution for k = 2, but the derivation of above is more direct and applies to k alternatives without approximation. pI I, ts(8) 3.2 A Comparative Analysis of Selection Schemes In a previous paper (=-=Goldberg, 1989-=-b), the solution to a differential equation approximation of equation 5 was developed for the two-alternative case. That solution, a solution of the same functional form using powers of 2 instead of e... |

865 | An Analysis of the Behavior of a Class of Genetic Adaptive Systems - Jong - 1975 |

818 | Adaptation in Natural and Artificial Systems. Ann Arbor: The - Holland - 1975 |

527 |
Uniform Crossover in Genetic Algorithms
- Syswerda
- 1989
(Show Context)
Citation Context ...rowth under normal conditions, while proportionate selection without scaling is shown to be less effective in keeping a steady pressure toward convergence. Whitley's (1989) Genitor or "steady state" (=-=Syswerda, 1989-=-) selection mechanism is also examined and found to be a simple combination of block death and birth via ranking. Analysis of this overlapping population scheme shows that the convergence results obse... |

495 |
Genetic Algorithms with Sharing for Multimodal Function Optimization
- Goldberg, Richardson
- 1987
(Show Context)
Citation Context ...d. The idea of preserving useful diversity temporally helps recall the notion of diversity preservation spatially (across a population) through the notion of niching (Deb, 1989; Deb & Goldberg, 1989; =-=Goldberg & Richardson, 1987-=-). If two strings share some bits in common (those salient bits that have already been decided) but they have some disagreement over the remaining positions and are relatively equal in overall functio... |

333 | The GENITOR algorithm and selection pressure: Why rank-based allocation of reproductive trials is best
- Whitley
- 1989
(Show Context)
Citation Context ... 5: Growth of the proportion of best individual versus generation is graphed for a number of tournament sizes. 6 Genitor In this section, we analyze and simulate the selection method used in Genitor (=-=Whitley, 1989-=-). Our purpose is twofold. First, we would like to give a quantitative explanation of the performance Whitley observed in using Genitor, thereby permitting comparison of this technique to others commo... |

330 |
Messy genetic algorithms: motivation, analysis, and � rst results
- Goldberg, Deb, et al.
- 1989
(Show Context)
Citation Context ...her. The elimination of building block noise sounds impossible at first glance, but it is exactly the approach taken in messy genetic algorithms (Goldberg, Deb, & Korb, 1990; Goldberg & Kerzic, 1990; =-=Goldberg, Korb, & Deb, 1990-=-). Messy GAs (mGAs) growsGoldberg and Deb 90 long strings from short ones, but so doing requires that missing bits in a problem of fixed length be filled in. Specifically, partial strings of length k ... |

323 |
Reducing bias and inefficiency in the selection algorithm
- Baker
- 1987
(Show Context)
Citation Context ...ing this probability distribution, including Monte Carlo or roulette wheel selection (De Jong, 1975), stochastic remainder selection (Booker, 1982; Brindle, 1981), and stochastic universal selection (=-=Baker, 1987-=-; Grefenstette & Baker, 1989). As we are uninterested here in stochastic differences, these schemes receive identical analytical treatment when we calculate their expected performance. If we consider ... |

264 |
An investigation of niche and species formation in genetic function optimization
- Deb, Goldberg
- 1989
(Show Context)
Citation Context ... sampling appears sound. The idea of preserving useful diversity temporally helps recall the notion of diversity preservation spatially (across a population) through the notion of niching (Deb, 1989; =-=Deb & Goldberg, 1989-=-; Goldberg & Richardson, 1987). If two strings share some bits in common (those salient bits that have already been decided) but they have some disagreement over the remaining positions and are relati... |

212 |
Adaptive selection methods for genetic algorithms
- Baker
- 1985
(Show Context)
Citation Context ... These equations are solved explicitly or approximated in time using integrable ordinary differential equations. These solutions are shown to agree well with computer simulations, and linear ranking (=-=Baker, 1985-=-) and binary tournament selection (Brindle, 1981) are shown to give identical performance in expectation. Moreover, ranking and tournament selection are shown to maintain strong growth under normal co... |

149 |
Sizing Populations for Serial and Parallel Genetic Algorithms
- Goldberg
- 1988
(Show Context)
Citation Context ...ing appears sound. The idea of preserving useful diversity temporally helps recall the notion of diversity preservation spatially (across a population) through the notion of niching (Deb, 1989; Deb & =-=Goldberg, 1989-=-; Goldberg & Richardson, 1987). If two strings share some bits in common (those salient bits that have already been decided) but they have some disagreement over the remaining positions and are relati... |

128 | Parallel genetic algorithms, population genetics and combinatorial optimisation - Muhlenbein - 1989 |

122 |
Nonstationary function optimization using genetic algorithms with dominance and diploidy
- Goldberg, Smith
- 1987
(Show Context)
Citation Context ... of the correct function-related alleles when those poorer alleles become salient. This mechanism is not unlike that achieved through the use of dominance and diploidy as has been explored elsewhere (=-=Goldberg & Smith, 1987-=-; Smith, 1988). Simply stated, dominance and diploidy permit currently out-of-favor alleles to remain in abeyance, sampling currently poorer alleles at lower rates, thereby permitting them to be broug... |

108 |
How genetic algorithms work: A critical look at implicit parallelism
- Grefenstette, Baker
- 1989
(Show Context)
Citation Context ...ability distribution, including Monte Carlo or roulette wheel selection (De Jong, 1975), stochastic remainder selection (Booker, 1982; Brindle, 1981), and stochastic universal selection (Baker, 1987; =-=Grefenstette & Baker, 1989-=-). As we are uninterested here in stochastic differences, these schemes receive identical analytical treatment when we calculate their expected performance. If we consider a nonoverlap ping population... |

105 |
Finite markov chain analysis of genetic algorithms
- Goldberg, Segrest
- 1987
(Show Context)
Citation Context ... relatively equal samples in the next and future generations. The schema theorem says they will (in ex.pectation), but small population selection schemes are subject to the vagaries of genetic drift (=-=Goldberg & Segrest, 1987-=-). Simply stated, small stochastic errors of selection can cause equally good alternatives to converge to one alternative or another. Niching introduces a pressure to balance the subpopulation sizes i... |

83 | Genetic Algorithms and the Optimal Allocation of Trials - Holland - 1973 |

75 |
Intelligent behavior as an adaptation to the task environment, Doctoral dissertation
- Booker
- 1982
(Show Context)
Citation Context ...dividuals sums to n. Various methods have been suggested for sampling this probability distribution, including Monte Carlo or roulette wheel selection (De Jong, 1975), stochastic remainder selection (=-=Booker, 1982-=-; Brindle, 1981), and stochastic universal selection (Baker, 1987; Grefenstette & Baker, 1989). As we are uninterested here in stochastic differences, these schemes receive identical analytical treatm... |

57 |
A Note on Boltzmann Tournament Selection for Genetic Algorithms and Population-Oriented
- Goldberg
- 1990
(Show Context)
Citation Context ...A Comparison of Takeover Time Values SCHEME t. Proportionate XC Proportionate ecx Linear ranking Co = 2 Linear ranking (cliff. eq.) Tournament p Tournament s Genitor accentuation of salient features (=-=Goldberg, 1990-=-). ~(n Inn -1) !n In n C logn + log(lnn) ~ co-1 log(n -1 ) ' same as linear ranking with Co = 2p _,1 [Inn + In(lnn)] n$ 1 -In(n Co -1) As was mentioned earlier, linear ranking and binary tournament se... |

17 | An extension to the theory of convergence and a proof of the time complexity of genetic algorithms - Ankenbrandt - 1990 |

14 |
An investigation of diploid genetic algorithms for adaptive search of nonstationary functions (MS thesis and
- Smith
- 1988
(Show Context)
Citation Context ...-related alleles when those poorer alleles become salient. This mechanism is not unlike that achieved through the use of dominance and diploidy as has been explored elsewhere (Goldberg & Smith, 1987; =-=Smith, 1988-=-). Simply stated, dominance and diploidy permit currently out-of-favor alleles to remain in abeyance, sampling currently poorer alleles at lower rates, thereby permitting them to be brought out of abe... |

9 |
Genetic algorithms for function optimization, doctoral dissertation
- Brindle
- 1981
(Show Context)
Citation Context ...oximated in time using integrable ordinary differential equations. These solutions are shown to agree well with computer simulations, and linear ranking (Baker, 1985) and binary tournament selection (=-=Brindle, 1981-=-) are shown to give identical performance in expectation. Moreover, ranking and tournament selection are shown to maintain strong growth under normal conditions, while proportionate selection without ... |

3 |
mGA1.0: A common LISP implementation of a messy genetic algorithm
- Goldberg
- 1990
(Show Context)
Citation Context ...nate the conflict altogether. The elimination of building block noise sounds impossible at first glance, but it is exactly the approach taken in messy genetic algorithms (Goldberg, Deb, & Korb, 1990; =-=Goldberg & Kerzic, 1990-=-; Goldberg, Korb, & Deb, 1990). Messy GAs (mGAs) growsGoldberg and Deb 90 long strings from short ones, but so doing requires that missing bits in a problem of fixed length be filled in. Specifically,... |

1 |
Messy Genetic Algorithms Revisited: Nonuniform Size and Scale
- Goldberg, Deb, et al.
- 1990
(Show Context)
Citation Context ... last proposal seeks to eliminate the conflict altogether. The elimination of building block noise sounds impossible at first glance, but it is exactly the approach taken in messy genetic algorithms (=-=Goldberg, Deb, & Korb, 1990-=-; Goldberg & Kerzic, 1990; Goldberg, Korb, & Deb, 1990). Messy GAs (mGAs) growsGoldberg and Deb 90 long strings from short ones, but so doing requires that missing bits in a problem of fixed length be... |

1 | A Comparative Analysis of Selection Schemes - Suh, D - 1987 |