Dirk V. Arnold
Alexander MacLeod
ABSTRACT
Organising evolution strategies hierarchically has been proposed as a means for adapting strategy parameters such as step lengths. Experimental research has shown that on ridge functions, hierarchically organised strategies can significantly outperform strategies that rely on mutative self-adaptation. This paper presents a first theoretical analysis of the behaviour of a hierarchically organised evolution strategy. Quantitative results are derived for the parabolic ridge that describe the dependence on the length of the isolation periods of the mutation strength and the progress rate. The issue of choosing an appropriate length of the isolation periods is discussed and comparisons with recent results for cumulative step length adaptation are drawn.
- D. V. Arnold and H.-G. Beyer. Performance analysis of evolutionary optimization with cumulative step length adaptation. IEEE Transactions on Automatic Control, 49(4):617--622, 2004.Google Scholar
Cross Ref
- D. V. Arnold and H.-G. Beyer. Evolution strategies with cumulative step length adaptation on the noisy parabolic ridge. Technical Report CS-2006-02, Faculty of Computer Science, Dalhousie University, 2006. Available at http://www.cs.dal.ca/research/techreports/2006/CS-2006-02.shtml.Google Scholar
- H.-G. Beyer. Toward a theory of evolution strategies: Self-adaptation. Evolutionary Computation, 3(3):311--347, 1996. Google ScholarDigital Library
- H.-G. Beyer. On the performance of (1,λ)-evolution strategies for the ridge function class. IEEE Transactions on Evolutionary Computation, 5(3):218--235, 2001. Google ScholarDigital Library
- H.-G. Beyer and H.-P. Schwefel. Evolution strategies - A comprehensive introduction. Natural Computing, 1(1):3--52, 2002. Google ScholarDigital Library
- N. Hansen and A. Ostermeier. Completely derandomized self-adaptation in evolution strategies. Evolutionary Computation, 9(2):159--195, 2001. Google ScholarDigital Library
- M. Herdy. Reproductive isolation as strategy parameter in hierarchically organized evolution strategies. In R. Männer and B. Manderick, editors, Parallel Problem Solving from Nature - PPSN II, pages 207--217. Elsevier, Amsterdam, 1992.Google Scholar
- M. Herdy. The number of offspring as strategy parameter in hierarchically organized evolution strategies. ACM SIGBIO Newsletter, 13(2):2--9, 1993. Google ScholarDigital Library
- A. Ostermeier, A. Gawelczyk, and N. Hansen. Step-size adaptation based on non-local use of selection information. In Y. Davidor et al., editors, Parallel Problem Solving from Nature - PPSN III, pages 189--198. Springer Verlag, Heidelberg, 1994. Google ScholarDigital Library
- A. I. Oyman and H.-G. Beyer. Analysis of the (μ/μλλ)-ES on the parabolic ridge. Evolutionary Computation, 8(3):267--289, 2000. Google ScholarDigital Library
- A. I. Oyman, H.-G. Beyer, and H.-P. Schwefel. Where elitists start limping: Evolution strategies at ridge functions. In A. E. Eiben et al., editors, Parallel Problem Solving from Nature - PPSN V, pages 109--118. Springer Verlag, Heidelberg, 1998. Google ScholarDigital Library
- A. I. Oyman, H.-G. Beyer, and H.-P. Schwefel. Analysis of the (1,λ)-ES on the parabolic ridge. Evolutionary Computation, 8(3):249--265, 2000. Google ScholarDigital Library
- I. Rechenberg. Evolutionsstrategie - Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. Friedrich Frommann Verlag, Stuttgart, 1973.Google Scholar
- I. Rechenberg. Evolutionsstrategien. In B. Schneider and U. Ranft, editors, Simulationsmethoden in der Medizin und Biologie, pages 83--114. Springer Verlag, Berlin, 1978.Google ScholarCross Ref
- I. Rechenberg. Evolutionsstrategie '94. Friedrich Frommann Verlag, Stuttgart, 1994.Google Scholar
- H.-P. Schwefel. Numerical Optimization of Computer Models. Wiley, Chichester, 1981. Google ScholarDigital Library
- D. Whitley, M. Lunacek, and J. Knight. Ruffled by ridges: How evolutionary algorithms can fail. In K. Deb et al., editors, Genetic and Evolutionary Computation - GECCO 2004, pages 294--306. Springer Verlag, Heidelberg, 2004.Google ScholarCross Ref
Index Terms
- Hierarchically organised evolution strategies on the parabolic ridge
Recommendations
Step length adaptation on ridge functions
Step length adaptation is central to evolutionary algorithms in real-valued search spaces. This paper contrasts several step length adaptation algorithms for evolution strategies on a family of ridge functions. The algorithms considered are cumulative ...
A novel approach to adaptive isolation in evolution strategies
GECCO '09: Proceedings of the 11th Annual conference on Genetic and evolutionary computationHierarchically organised evolution strategies have been seen to be able to successfully adapt step lengths where mutative self-adaptation fails. However, the computational costs of such strategies are high due to the need to evolve several ...
Evolution strategies with cumulative step length adaptation on the noisy parabolic ridge
This paper presents an analysis of the performance of the (μ/μ, )-ES with isotropically distributed mutations and cumulative step length adaptation on the noisy parabolic ridge. Several forms of dependency of the noise strength on the distance from the ...
Comments