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Rugged NK landscapes contain the highest peaks

Rugged NK landscapes contain the highest peaks
Rugged NK landscapes contain the highest peaks
NK models provide a family of tunably rugged fitness landscapes used in a wide range of evolutionary computation studies. It is well known that the average height of local optima regresses to the mean of the landscape with increasing ruggedness, K. This fact has been confirmed with both theoretical studies of landscape structure and empirical studies of evolutionary search. However, we show mathematically that the global optimum behaves quite differently: the expected value of the global optimum is highest in the maximally rugged case. Furthermore, we demonstrate that this expected value increases with K, despite the fact that the average fitness of the local optima decreases. We find the asymptotic value of the global optimum as N approaches infinity for both the smooth and maximally rugged cases. We interpret these results in the context of evolutionary search, and describe the relationship between the global optimum, local optima and found optima as search effort is geometrically increased.
NK, epistastis, fitness landscapes, rugged
1-59593-010-8
579-584
Association for Computing Machinery
Skellett, B
58b09c82-9eb5-4b48-9d1b-f2d8ca7fee1e
Cairns, B
59a872ee-3e97-4059-9dce-977ff0fbdd47
Geard, N
19c3888b-1e2d-4ee5-bcc6-d14c683d0be6
Tonkes, B
827a3449-5221-48d0-a619-0cbc3fd87000
Wiles, J
4b566453-d3c4-441a-97bd-404c378d1f67
Beyer, H -G
Skellett, B
58b09c82-9eb5-4b48-9d1b-f2d8ca7fee1e
Cairns, B
59a872ee-3e97-4059-9dce-977ff0fbdd47
Geard, N
19c3888b-1e2d-4ee5-bcc6-d14c683d0be6
Tonkes, B
827a3449-5221-48d0-a619-0cbc3fd87000
Wiles, J
4b566453-d3c4-441a-97bd-404c378d1f67
Beyer, H -G

Skellett, B, Cairns, B, Geard, N, Tonkes, B and Wiles, J (2005) Rugged NK landscapes contain the highest peaks. Beyer, H -G (ed.) In Genetic and Evolutionary Computation Conference, GECCO 2005, Proceedings. Association for Computing Machinery. pp. 579-584 .

Record type: Conference or Workshop Item (Paper)

Abstract

NK models provide a family of tunably rugged fitness landscapes used in a wide range of evolutionary computation studies. It is well known that the average height of local optima regresses to the mean of the landscape with increasing ruggedness, K. This fact has been confirmed with both theoretical studies of landscape structure and empirical studies of evolutionary search. However, we show mathematically that the global optimum behaves quite differently: the expected value of the global optimum is highest in the maximally rugged case. Furthermore, we demonstrate that this expected value increases with K, despite the fact that the average fitness of the local optima decreases. We find the asymptotic value of the global optimum as N approaches infinity for both the smooth and maximally rugged cases. We interpret these results in the context of evolutionary search, and describe the relationship between the global optimum, local optima and found optima as search effort is geometrically increased.

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More information

Published date: 2005
Additional Information: Event Dates: 25-29 June, 2005
Venue - Dates: the Genetic and Evolutionary Computation Conference (GECCO 2005), Washington D. C., United States, 2005-06-25 - 2005-06-29
Keywords: NK, epistastis, fitness landscapes, rugged
Organisations: Electronics & Computer Science

Identifiers

Local EPrints ID: 264087
URI: http://eprints.soton.ac.uk/id/eprint/264087
ISBN: 1-59593-010-8
PURE UUID: c38f4b3a-2694-4964-af8e-389d36c4157a

Catalogue record

Date deposited: 25 May 2007
Last modified: 14 Mar 2024 07:42

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Contributors

Author: B Skellett
Author: B Cairns
Author: N Geard
Author: B Tonkes
Author: J Wiles
Editor: H -G Beyer

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