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

German Hernandez; Fernando Nino; Julian Garcia; Dipankar Dasgupta

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

German Hernandez, Fernando Nino, Julian Garcia, Dipankar Dasgupta

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

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
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	IEEE Congress on Evolutionary Computation 2004 - Portland, United States of America Duration: 19 Jun 2004 → 23 Jun 2004 https://ieeexplore.ieee.org/xpl/conhome/9256/proceeding (Proceedings)

Conference

Conference	IEEE Congress on Evolutionary Computation 2004
Abbreviated title	IEEE CEC 2004
Country	United States of America
City	Portland
Period	19/06/04 → 23/06/04
Internet address	https://ieeexplore.ieee.org/xpl/conhome/9256/proceeding (Proceedings)

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Link to publication in Scopus

Cite this

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title = "On geometric and statistical properties of the attractors of a generic evolutionary algorithm",

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.",

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

Proceedings of the 2004 Congress on Evolutionary Computation, CEC2004. Vol. 2 2004. p. 1240-1247.

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

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