Genetic algorithm dynamics in two-well potentials with basins and barrier

Genetic algorithm dynamics in two-well potentials with basins and barrier

The dynamics of a simple genetic algorithm is analyzed on a simple two-well function of unitation. In the infinite population limit, there are phase transitions in the dynamics as the selections strength and crossover probability are changed. In one phase, the system always evolves to a population consisting only of strings from the local well starting from any initial population consisting some strings from the local well. In the second phase, the genetic algorithm can evolve to a population consisting of strings from the global well, but only if a finite fraction of the initial population was from the global well. In the third phase, the algorithm will evolve to a population consisting of stings from the global well from any initial population. For a finite population, the increasing correlation of the population changes the nature of the transition; this is analysed in a weak selection limit where the effects are small. Fluctuation effects, which cause the transition to be smooth in a finite population and are important, are not analyzed here. Comparison with simulations show that the results are qualitatively correct. There is a phase in which the GA evolves quickly to the global minimum, which can be orders of magnitude faster than a Monte Carlo algorithm; and another phase in which it evolves to a population dominated by strings from the local well. Quantitatively, the simulations and theory are not in good agreement due to the simplifications of the theory.

1-55860-460-X

101-116

Shapiro, Jonathan L.

761f10d0-adf2-421b-b9b8-3d58eff4765f

Prügel-Bennett, Adam

b107a151-1751-4d8b-b8db-2c395ac4e14e

Belew, R. K.

35dfbbfc-f1ab-4acd-89f7-9d2c6b4ea3ea

Vose, M. D.

8b930eeb-05f5-405e-8e3d-1504dd5882c3

September 1997

Shapiro, Jonathan L.

761f10d0-adf2-421b-b9b8-3d58eff4765f

Prügel-Bennett, Adam

b107a151-1751-4d8b-b8db-2c395ac4e14e

Belew, R. K.

35dfbbfc-f1ab-4acd-89f7-9d2c6b4ea3ea

Vose, M. D.

8b930eeb-05f5-405e-8e3d-1504dd5882c3

Shapiro, Jonathan L. and Prügel-Bennett, Adam
(1997)
Genetic algorithm dynamics in two-well potentials with basins and barrier.
Belew, R. K. and Vose, M. D.
(eds.)
*
Foundations of Genetic Algorithms - 4.
*
.

Record type:
Conference or Workshop Item
(Other)

## Abstract

The dynamics of a simple genetic algorithm is analyzed on a simple two-well function of unitation. In the infinite population limit, there are phase transitions in the dynamics as the selections strength and crossover probability are changed. In one phase, the system always evolves to a population consisting only of strings from the local well starting from any initial population consisting some strings from the local well. In the second phase, the genetic algorithm can evolve to a population consisting of strings from the global well, but only if a finite fraction of the initial population was from the global well. In the third phase, the algorithm will evolve to a population consisting of stings from the global well from any initial population. For a finite population, the increasing correlation of the population changes the nature of the transition; this is analysed in a weak selection limit where the effects are small. Fluctuation effects, which cause the transition to be smooth in a finite population and are important, are not analyzed here. Comparison with simulations show that the results are qualitatively correct. There is a phase in which the GA evolves quickly to the global minimum, which can be orders of magnitude faster than a Monte Carlo algorithm; and another phase in which it evolves to a population dominated by strings from the local well. Quantitatively, the simulations and theory are not in good agreement due to the simplifications of the theory.

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## More information

Published date: September 1997

Additional Information:
Address: San Francisco

Venue - Dates:
Foundations of Genetic Algorithms - 4, 1997-08-31

Organisations:
Southampton Wireless Group

## Identifiers

Local EPrints ID: 254245

URI: http://eprints.soton.ac.uk/id/eprint/254245

ISBN: 1-55860-460-X

PURE UUID: 8197b5b5-b385-43b8-b6b7-4afa850a3dbc

## Catalogue record

Date deposited: 12 Jan 2001

Last modified: 10 Dec 2021 20:37

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## Contributors

Author:
Jonathan L. Shapiro

Author:
Adam Prügel-Bennett

Editor:
R. K. Belew

Editor:
M. D. Vose

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