article

The choice of the offspring population size in the (1,λ) evolutionary algorithm

Authors:

Jonathan E. Rowe,

Dirk SudholtAuthors Info & Claims

Theoretical Computer Science, Volume 545

Pages 20 - 38

https://doi.org/10.1016/j.tcs.2013.09.036

Published: 01 August 2014 Publication History

Abstract

We extend the theory of non-elitist evolutionary algorithms (EAs) by considering the offspring population size in the (1,@l) EA. We establish a sharp threshold at @l=log"e"e"-"1n~5log"1"0n between exponential and polynomial running times on OneMax. For any smaller value, the (1,@l) EA needs exponential time on every function that has only one global optimum. We also consider arbitrary unimodal functions and show that the threshold can shift towards larger offspring population sizes. In particular, for the function LeadingOnes there is a sharp threshold at @l=2log"e"e"-"1n~10log"1"0n. Finally, we investigate the relationship between the offspring population size and arbitrary mutation rates on OneMax. We get sharp thresholds for @l that decrease with the mutation rate. This illustrates the balance between selection and mutation.

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Published In

cover image Theoretical Computer Science

Theoretical Computer Science Volume 545, Issue

August, 2014

128 pages

ISSN:0304-3975

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Copyright © Elsevier B.V. © 2013.

Publisher

Elsevier Science Publishers Ltd.

United Kingdom

Publication History

Published: 01 August 2014

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