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On the Long String Limit

On the Long String Limit
On the Long String Limit
To gain a clearer understanding of the dynamics of evolving populations the limit of infinitely long strings is examined. The limit clarifies some of the behaviour of evolving systems. For example, this limit removes any complications due to transient behaviour. Care is required in taking the limit to ensure that the quantities considered are meaningful. For concreteness a simple Genetic Algorithm acting on the problem of ones-counting is considered. A population evolving under selection and mutation alone is first examined. In this limit a remarkably simple picture of the evolutionary flow emerges. The discussion is widened to include crossover. This gives a new insight into how diversity induced by crossover improves search. Finally the approach to the limit is examined. The limit provides a way of separating the initial transient dynamics from the long time (asymptotic) dynamics.
1-55860-559-2
45-56
Prügel-Bennett, A
b107a151-1751-4d8b-b8db-2c395ac4e14e
Banzhaf, W.
bd19e095-747b-460d-95e0-5d6037187fb4
Reeves, C.
83967b17-a349-42f5-a2b2-a0ad4c54d922
Prügel-Bennett, A
b107a151-1751-4d8b-b8db-2c395ac4e14e
Banzhaf, W.
bd19e095-747b-460d-95e0-5d6037187fb4
Reeves, C.
83967b17-a349-42f5-a2b2-a0ad4c54d922

Prügel-Bennett, A (1999) On the Long String Limit. Banzhaf, W. and Reeves, C. (eds.) Foundations of Genetic Algorithms 5. pp. 45-56 .

Record type: Conference or Workshop Item (Other)

Abstract

To gain a clearer understanding of the dynamics of evolving populations the limit of infinitely long strings is examined. The limit clarifies some of the behaviour of evolving systems. For example, this limit removes any complications due to transient behaviour. Care is required in taking the limit to ensure that the quantities considered are meaningful. For concreteness a simple Genetic Algorithm acting on the problem of ones-counting is considered. A population evolving under selection and mutation alone is first examined. In this limit a remarkably simple picture of the evolutionary flow emerges. The discussion is widened to include crossover. This gives a new insight into how diversity induced by crossover improves search. Finally the approach to the limit is examined. The limit provides a way of separating the initial transient dynamics from the long time (asymptotic) dynamics.

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More information

Published date: 1999
Additional Information: Address: San Francisco
Venue - Dates: Foundations of Genetic Algorithms 5, 1999-01-01
Organisations: Southampton Wireless Group

Identifiers

Local EPrints ID: 250479
URI: http://eprints.soton.ac.uk/id/eprint/250479
ISBN: 1-55860-559-2
PURE UUID: a3561c12-dca5-45f3-a778-60864cf0b9c2

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Date deposited: 25 Oct 2000
Last modified: 29 Jan 2020 14:58

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