### Abstract

In this work, evolutionary algorithms are modeled as random dynamical systems. The combined action of selection and variation is expressed as a stochastic operator acting on the space of populations. The long term behavior of selection and variation is studied separately. Then the combined effect is analyzed by characterizing the attractor and stationary measure of the dynamics. As a main result it is proved that the stationary measure is supported on populations made up of optimizers. Also, some experiments are carried out in order to visualize the evolvable populations, the attractor sets and the stationary measure. Some geometric properties of such sets are discussed.

Original language | English |
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Title of host publication | Proceedings of the 2004 Congress on Evolutionary Computation, CEC2004 |

Pages | 1240-1247 |

Number of pages | 8 |

Volume | 2 |

Publication status | Published - 13 Sep 2004 |

Externally published | Yes |

Event | Proceedings of the 2004 Congress on Evolutionary Computation, CEC2004 - Portland, OR, United States of America Duration: 19 Jun 2004 → 23 Jun 2004 |

### Conference

Conference | Proceedings of the 2004 Congress on Evolutionary Computation, CEC2004 |
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Country | United States of America |

City | Portland, OR |

Period | 19/06/04 → 23/06/04 |

### Cite this

*Proceedings of the 2004 Congress on Evolutionary Computation, CEC2004*(Vol. 2, pp. 1240-1247)

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*Proceedings of the 2004 Congress on Evolutionary Computation, CEC2004.*vol. 2, pp. 1240-1247, Proceedings of the 2004 Congress on Evolutionary Computation, CEC2004, Portland, OR, United States of America, 19/06/04.

**On geometric and statistical properties of the attractors of a generic evolutionary algorithm.** / Hernandez, German; Nino, Fernando; Garcia, Julian; Dasgupta, Dipankar.

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

TY - GEN

T1 - On geometric and statistical properties of the attractors of a generic evolutionary algorithm

AU - Hernandez, German

AU - Nino, Fernando

AU - Garcia, Julian

AU - Dasgupta, Dipankar

PY - 2004/9/13

Y1 - 2004/9/13

N2 - In this work, evolutionary algorithms are modeled as random dynamical systems. The combined action of selection and variation is expressed as a stochastic operator acting on the space of populations. The long term behavior of selection and variation is studied separately. Then the combined effect is analyzed by characterizing the attractor and stationary measure of the dynamics. As a main result it is proved that the stationary measure is supported on populations made up of optimizers. Also, some experiments are carried out in order to visualize the evolvable populations, the attractor sets and the stationary measure. Some geometric properties of such sets are discussed.

AB - In this work, evolutionary algorithms are modeled as random dynamical systems. The combined action of selection and variation is expressed as a stochastic operator acting on the space of populations. The long term behavior of selection and variation is studied separately. Then the combined effect is analyzed by characterizing the attractor and stationary measure of the dynamics. As a main result it is proved that the stationary measure is supported on populations made up of optimizers. Also, some experiments are carried out in order to visualize the evolvable populations, the attractor sets and the stationary measure. Some geometric properties of such sets are discussed.

UR - http://www.scopus.com/inward/record.url?scp=4344648028&partnerID=8YFLogxK

M3 - Conference Paper

SN - 0780385152

SN - 9780780385153

VL - 2

SP - 1240

EP - 1247

BT - Proceedings of the 2004 Congress on Evolutionary Computation, CEC2004

ER -