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Some comments on evolutionary algorithm theory

Author:

Ralf SalomonAuthors Info & Claims

Evolutionary Computation, Volume 4, Issue 4

Pages 405 - 415

https://doi.org/10.1162/evco.1996.4.4.405

Published: 01 December 1996 Publication History

Abstract

The development of a sound theory that predicts and verifies existing evolutionary algorithms (EA) is one of the most important research issues in the field today. In mathematical proofs, the assumption of spherical symmetry is probably one of the most widely used simplifications. This paper discusses the extent to which spherical symmetry is appropriate for certain EAs. It turns out that spherical symmetry leads to simplifications in (self-adaptive) EAs but seems inappropriate for certain genetic algorithm variants, since small mutation rates bias a search algorithm toward the coordinate axes. This paper also argues that current test suites are weak in that they do not provide problems with significant epistasis that describes the interaction between different parameters. Consequently, when using an empirical test for pushing existing theory beyond its limits, benchmark functions should include more epistatic interaction or at least should use coordinate rotations.

References

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Altenberg, L. (1995). The schema theorem and the Price's theorem. In L. D. Whitley & M. D. Vose (Eds.), Foundations of genetic algorithms 3 (pp. 23-49). San Mateo, CA: Morgan Kaufmann.

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Bäck, T. (1993). Optimal mutation rates in genetic search. In S. Forrest (Ed.), Proceedings of the Fifth International Conference on Genetic Algorithms (pp. 2-8). San Mateo, CA: Morgan Kaufmann.

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Beyer, H.-G. (1993). Toward a theory of evolution strategies: Some asymptotical results from the (1 ± ¿)-theory. Evolutionary Computation 1(2):165-188.

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Beyer, H.-G. (1996). Toward a theory of evolution strategies: Self-adaptation. Evolutionary Computation 3(3):311-347.

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Ostermeier, A., Gawelczyk, A., & Hansen, N. (1994). A derandomized approach to self-adaptation of evolution strategies. Evolutionary Computation 2(4):369-380.

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Salomon, R. (1996a). Performance degradation of genetic algorithms under coordinate rotation. In L.J. Fogel, P.J. Angeline, & T. Bäck (Eds.), Proceedings of the Fifth Annual Conference on Evolutionary Programming. Cambridge, MA: MIT Press.

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Salomon, R. (1996b). Implicit independence assumptions: A notorious problem for genetic algorithms. In P. G. Anderson & K. Warwick (Eds.), Proceedings of the International ICSC Symposia on Intelligent Industrial Automation and on Soft Computing (SOCO'96) (pp. B 93-B 99). Canada/Switzerland: ICSC Academic Press.

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Schlierkamp-Voosen, D., & Mühlenbein, H. (1994). Strategy adaptation by competing subpoputations. In Y. Davidor, H.-P. Schwefel, & R. Männer (Eds.), Parallel Problem Solving from Nature (PPSN III) (pp. 199-208). Berlin: Springer-Verlag.

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Cited By

Ras MWilke DGroenwold AKok S(2014)On rotationally invariant continuous-parameter genetic algorithmsAdvances in Engineering Software10.1016/j.advengsoft.2014.08.00678:C(52-59)Online publication date: 1-Dec-2014
https://dl.acm.org/doi/10.1016/j.advengsoft.2014.08.006
Nobakhti AWang H(2008)A simple self-adaptive Differential Evolution algorithm with application on the ALSTOM gasifierApplied Soft Computing10.1016/j.asoc.2006.12.0058:1(350-370)Online publication date: 1-Jan-2008
https://dl.acm.org/doi/10.1016/j.asoc.2006.12.005
Wilke DKok SGroenwold ALipson H(2007)Reference frame and scale invariant real-parameter genetic and differential evolution algorithmsProceedings of the 9th annual conference on Genetic and evolutionary computation10.1145/1276958.1277267(1538-1538)Online publication date: 7-Jul-2007
https://dl.acm.org/doi/10.1145/1276958.1277267
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Some comments on evolutionary algorithm theory

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cover image Evolutionary Computation

Evolutionary Computation Volume 4, Issue 4

Winter 1996

90 pages

ISSN:1063-6560

EISSN:1530-9304

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Publisher

MIT Press

Cambridge, MA, United States

Publication History

Published: 01 December 1996

Published in EVOL Volume 4, Issue 4

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Cited By

Ras MWilke DGroenwold AKok S(2014)On rotationally invariant continuous-parameter genetic algorithmsAdvances in Engineering Software10.1016/j.advengsoft.2014.08.00678:C(52-59)Online publication date: 1-Dec-2014
https://dl.acm.org/doi/10.1016/j.advengsoft.2014.08.006
Nobakhti AWang H(2008)A simple self-adaptive Differential Evolution algorithm with application on the ALSTOM gasifierApplied Soft Computing10.1016/j.asoc.2006.12.0058:1(350-370)Online publication date: 1-Jan-2008
https://dl.acm.org/doi/10.1016/j.asoc.2006.12.005
Wilke DKok SGroenwold ALipson H(2007)Reference frame and scale invariant real-parameter genetic and differential evolution algorithmsProceedings of the 9th annual conference on Genetic and evolutionary computation10.1145/1276958.1277267(1538-1538)Online publication date: 7-Jul-2007
https://dl.acm.org/doi/10.1145/1276958.1277267
Herrera FLozano MVerdegay J(1998)Tackling Real-Coded Genetic AlgorithmsArtificial Intelligence Review10.1023/A:100650490116412:4(265-319)Online publication date: 1-Aug-1998
https://dl.acm.org/doi/10.1023/A%3A1006504901164

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