Completely Derandomized Self-Adaptation in Evolution Strategies

This paper puts forward two useful methods for self-adaptation of the mutation distribution - the concepts of derandomization and cumulation. Principle shortcomings of the concept of mutative strategy parameter control and two levels of derandomization are reviewed. Basic demands on the self-adaptation of arbitrary (normal) mutation distributions are developed. Applying arbitrary, normal mutation distributions is equiv-alent to applying a general, linear problem encoding. The underlying objective of mutative strategy parameter control is roughly to favor previously selected mutation steps in the future. If this objective is pursued rigor-ously, a completely derandomized self-adaptation scheme results, which adapts arbitrary normal mutation distributions. This scheme, called covariance matrix adaptation (CMA), meets the previously stated demands. It can still be considerably improved by cumulation - utilizing an evolution path rather than single search steps. Simulations on various test functions reveal local and global search properties of the evolution strategy with and without covariance matrix adaptation. Their performances are comparable only on perfectly scaled functions. On badly scaled, non-separable functions usually a speed up factor of several orders of magnitude is ob-served. On moderately mis-scaled functions a speed up factor of three to ten can be expected.

[1]  Ingo Rechenberg,et al.  Evolutionsstrategie : Optimierung technischer Systeme nach Prinzipien der biologischen Evolution , 1973 .

[2]  William H. Press,et al.  Book-Review - Numerical Recipes in Pascal - the Art of Scientific Computing , 1989 .

[3]  F. A. Seiler,et al.  Numerical Recipes in C: The Art of Scientific Computing , 1989 .

[4]  Günter Rudolph,et al.  On Correlated Mutations in Evolution Strategies , 1992, Parallel Problem Solving from Nature.

[5]  Andreas Ostermeier,et al.  An Evolution Strategy with Momentum Adaptation of the Random Number Distribution , 1992, PPSN.

[6]  Joab R Winkler,et al.  Numerical recipes in C: The art of scientific computing, second edition , 1993 .

[7]  Michael Herdy,et al.  The number of offspring as strategy parameter in hierarchically organized evolution strategies , 1993, SIGB.

[8]  Hans-Paul Schwefel,et al.  Evolution and Optimum Seeking: The Sixth Generation , 1993 .

[9]  Thomas Bäck,et al.  An Overview of Evolutionary Algorithms for Parameter Optimization , 1993, Evolutionary Computation.

[10]  Nikolaus Hansen,et al.  A Derandomized Approach to Self-Adaptation of Evolution Strategies , 1994, Evolutionary Computation.

[11]  N. Hansen,et al.  Step-Size Adaptation Based on Non-Local Use Selection Information , 1994 .

[12]  Nikolaus Hansen,et al.  Step-Size Adaption Based on Non-Local Use of Selection Information , 1994, PPSN.

[13]  Ingo Rechenberg,et al.  Evolutionsstrategie '94 , 1994, Werkstatt Bionik und Evolutionstechnik.

[14]  Hans-Georg Beyer,et al.  Toward a Theory of Evolution Strategies: On the Benefits of Sex the (/, ) Theory , 1995, Evolutionary Computation.

[15]  Hans-Paul Schwefel,et al.  Evolution and optimum seeking , 1995, Sixth-generation computer technology series.

[16]  Hans-Georg Beyer,et al.  Toward a Theory of Evolution Strategies: Self-Adaptation , 1995, Evolutionary Computation.

[17]  Nikolaus Hansen,et al.  On the Adaptation of Arbitrary Normal Mutation Distributions in Evolution Strategies: The Generating Set Adaptation , 1995, ICGA.

[18]  Hans-Georg Beyer On the Asymptotic Behavior of Multirecombinant Evolution Strategies , 1996, PPSN.

[19]  David B. Fogel,et al.  A Preliminary Investigation into Directed Mutations in Evolutionary Algorithms , 1996, PPSN.

[20]  L. Darrell Whitley,et al.  Evaluating Evolutionary Algorithms , 1996, Artif. Intell..

[21]  Nikolaus Hansen,et al.  Adapting arbitrary normal mutation distributions in evolution strategies: the covariance matrix adaptation , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[22]  N. Hansen,et al.  Convergence Properties of Evolution Strategies with the Derandomized Covariance Matrix Adaptation: T , 1997 .

[23]  Siegfried Wagner,et al.  Drag reduction and shape optimization of airship bodies , 1997 .

[24]  Thomas Bäck,et al.  Evolutionary computation: comments on the history and current state , 1997, IEEE Trans. Evol. Comput..

[25]  Hans-Georg Beyer Mutate Large, But Inherit Small! On the Analysis of Rescaled Mutations in 1-lambda-ES with Noisy Fitness Data , 1998, PPSN.

[26]  H.-G. Beyer,et al.  Mutate large, but inherit small ! On the analysis of rescaled mutations in (1, λ)-ES with noisy fitness data , 1998 .

[27]  Nikolaus Hansen,et al.  Verallgemeinerte individuelle Schrittweitenregelung in der Evolutionsstrategie - eine Untersuchung zur entstochastisierten, koordinatensystemunabhängigen Adaptation der Mutationsverteilung , 1998 .

[28]  Nikolaus Hansen,et al.  Verallgemeinerte individuelle Schrittweitenregelung in der Evolutionsstrategie , 1998 .

[29]  Lars Hildebrand,et al.  Directed mutation-a new self-adaptation for evolution strategies , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[30]  N. Hansen,et al.  An Evolution Strategy with Coordinate System Invariant Adaptation of Arbitrary Normal Mutation Distr , 1999 .

[31]  Kalyanmoy Deb,et al.  On the Desired Behaviors of Self-Adaptive Evolutionary Algorithms , 2000, PPSN.

[32]  Bernhard Sendhoff,et al.  Optimisation of a Stator Blade Used in a Transonic Compressor Cascade with Evolution Strategies , 2000 .

[33]  Nikolaus Hansen,et al.  Invariance, Self-Adaptation and Correlated Mutations and Evolution Strategies , 2000, PPSN.

[34]  Christian Igel,et al.  Optimization of dynamic neural fields , 2001, Neurocomputing.

[35]  Thomas Bergener,et al.  Parameter optimization for visual obstacle detection using a derandomized evolution strategy , 2001 .

[36]  Pietro Cerveri,et al.  Combined evolution strategies for dynamic calibration of video-based measurement systems , 2001, IEEE Trans. Evol. Comput..

[37]  P. Koumoutsakos,et al.  Multiobjective evolutionary algorithm for the optimization of noisy combustion processes , 2002 .

[38]  Werner von Seelen,et al.  Evolving field models for inhibition effects in early vision , 2002, Neurocomputing.

[39]  Hans-Paul Schwefel,et al.  How to analyse evolutionary algorithms , 2002, Theor. Comput. Sci..

[40]  Kalyanmoy Deb,et al.  A Computationally Efficient Evolutionary Algorithm for Real-Parameter Optimization , 2002, Evolutionary Computation.

[41]  Bernhard Sendhoff,et al.  A framework for evolutionary optimization with approximate fitness functions , 2002, IEEE Trans. Evol. Comput..

[42]  H Ermert,et al.  Registration of bone surfaces, extracted from CT-datasets, with 3D ultrasound , 2002, Biomedizinische Technik. Biomedical engineering.

[43]  Hans-Georg Beyer,et al.  Qualms Regarding the Optimality of Cumulative Path Length Control in CSA/CMA-Evolution Strategies , 2003, Evolutionary Computation.

[44]  Werner von Seelen,et al.  Image processing and behavior planning for intelligent vehicles , 2003, IEEE Trans. Ind. Electron..

[45]  W. Seelen Design of a Field Model for Early Vision : A Case Study of Evolutionary Algorithms in Neuroscience , .