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## Conditions for Implicit Parallelism (1991)

Venue: | Foundations of Genetic Algorithms |

Citations: | 17 - 4 self |

### Citations

2597 |
Genetic Algorithms in Search, Optimization and Machine Learning
- Goldberg
- 1989
(Show Context)
Citation Context ...itness function might be a simple linear transformation, or may be more exotic (logarithmic, exponential, polynomial) and might also be time-varying in order to scale the problem (Grefenstette, 1986; =-=Goldberg, 1989-=-). The selection algorithm is also chosen by the GA programmer to map fitness values into (an expected) number of offspring. A wide variety of selection algorithms have been studied, including proport... |

1097 |
Adaptation in natural and artificial systems. Ann Arbor
- Holland
- 1975
(Show Context)
Citation Context ...ficult to assess. Theoretical comparisons offer more robust insights, but our existing theory is sparse. The seminal result used in the analysis of genetic algorithms is of course the Schema Theorem (=-=Holland, 1975-=-), which has also provided the foundation for a number of attempts to characterize problems thought to be especially difficult for genetic algorithms (Bethke, 1981; Goldberg, 1987). We take a slightly... |

509 |
Optimization of control parameters for genetic algorithms
- Grefenstette
- 1986
(Show Context)
Citation Context ...al, say [0,1]. The fitness function might be a simple linear transformation, or may be more exotic (logarithmic, exponential, polynomial) and might also be time-varying in order to scale the problem (=-=Grefenstette, 1986-=-; Goldberg, 1989). The selection algorithm is also chosen by the GA programmer to map fitness values into (an expected) number of offspring. A wide variety of selection algorithms have been studied, i... |

423 |
Reducing bias and inefficiency in the selection algorithm
- Baker
- 1987
(Show Context)
Citation Context ...s paper that the task is to maximize the objective function. 2 The final step in the select phase of Figure 1 is to apply a sampling algorithm to assign an integer number of offspring to each parent (=-=Baker, 1987-=-). This step will not concern us here. 3 The reader should feel free to interpret the results in terms of hyperplanes, but should bear in mind that the results apply to arbitrary subsets of the search... |

154 |
Simple genetic algorithms and the minimal, deceptive problem
- Goldberg
- 1987
(Show Context)
Citation Context ...e the Schema Theorem (Holland, 1975), which has also provided the foundation for a number of attempts to characterize problems thought to be especially difficult for genetic algorithms (Bethke, 1981; =-=Goldberg, 1987-=-). We take a slightly different approach to understanding genetic algorithms. This paper offers an extension to the analysis begun in James Baker's dissertation (Baker, 1989) and carried forward in (G... |

125 |
How genetic algorithms work: a critical look at implicit parallelism
- Grefenstette, Baker
- 1989
(Show Context)
Citation Context ... among superficially different versions of the genetic algorithm. These results can also serve to spotlight the features which distinguish broad classes of genetic algorithms from one another. As in (=-=Grefenstette and Baker, 1989-=-), this paper focuses on invariants among genetic algorithms that differ along two dimensions: (1) the way user-defined objective function is mapped to a fitness measure, and (2) the way the fitness m... |

40 |
Genetic Algorithms as Function Optimizers, Doctoral dissertation
- Bethke
- 1981
(Show Context)
Citation Context ...ed by solving 2-armed bandit problems, followed by k = 4, k = 8, and so on (Goldberg, 1989). This statement of the building-block hypothesis, which underlies much of the work on "deceptive proble=-=ms" (Bethke, 1981-=-; Goldberg, 1987), needs to be re-examined in light of the discussion above. It also follows from these considerations that the notion that implicit parallelism can be quantified by counting the numbe... |

18 |
An analysis of the effects of selection in genetic algorithms
- Baker
- 1989
(Show Context)
Citation Context ...gorithms (Bethke, 1981; Goldberg, 1987). We take a slightly different approach to understanding genetic algorithms. This paper offers an extension to the analysis begun in James Baker's dissertation (=-=Baker, 1989-=-) and carried forward in (Grefenstette and - 253 - Baker, 1989). This approach aims to identify properties that are invariant across different versions of the genetic algorithm. Such results provide a... |

2 | Grefenstette (1988) Genetic algorithms in noisy environments - Fitzpatrick, J |

1 |
Optimal initial population size for binary-encorded genetic algorithms
- Goldberg
- 1985
(Show Context)
Citation Context ... of the discussion above. It also follows from these considerations that the notion that implicit parallelism can be quantified by counting the number of hyperplane partitions in a random population (=-=Goldberg, 1985-=-; Fitzpatrick and Grefenstette, 1988) is probably misguided. It is always necessary to consider the dynamic distribution of samples within the population in order to accurately assess how many hyperpl... |