Noisy Optimization With Evolution Strategies

Foreword. Acknowledgments. 1. Introduction. 2. Preliminaries. 3. The (1+1)-ES: Overvaluation. 4. The (mu, lambda)-ES: Distributed Populations. 5. The (mu/mu, lambda-ES: Genetic Repair. 6. Comparing Approaches to Noisy Optimization. 7. Conclusions. Appendices. A. Some Statistical Basics. B. Some Useful Identities. C. Computing the Overvaluation. D. Determining the Effects of Sampling and Selection. References. Index.

[1]  Hans-Georg Beyer,et al.  Local Performance of the (μ/μ, μ)-ES in a Noisy Environment , 2000, FOGA.

[2]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[3]  A. Neumaier,et al.  A grid algorithm for bound constrained optimization of noisy functions , 1995 .

[4]  V. J. Torczoit,et al.  Multidirectional search: a direct search algorithm for parallel machines , 1989 .

[5]  B. Arnold,et al.  A first course in order statistics , 1994 .

[6]  J. Kiefer,et al.  Stochastic Estimation of the Maximum of a Regression Function , 1952 .

[7]  Michael W. Trosset,et al.  I Know It When I See It: Toward a Definition of Direct Search Methods , 1996 .

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

[9]  Volker Nissen,et al.  On the robustness of population-based versus point-based optimization in the presence of noise , 1998, IEEE Trans. Evol. Comput..

[10]  Margaret H. Wright,et al.  Direct search methods: Once scorned, now respectable , 1996 .

[11]  Nikolaus Hansen,et al.  Completely Derandomized Self-Adaptation in Evolution Strategies , 2001, Evolutionary Computation.

[12]  C. T. Kelley,et al.  An Implicit Filtering Algorithm for Optimization of Functions with Many Local Minima , 1995, SIAM J. Optim..

[13]  D. Farnsworth A First Course in Order Statistics , 1993 .

[14]  Carl Tim Kelley,et al.  Iterative methods for optimization , 1999, Frontiers in applied mathematics.

[15]  Dirk V. Arnold,et al.  Evolution strategies in noisy environments- a survey of existing work , 2001 .

[16]  J. S. Ivey,et al.  Nelder-Mead simplex modifications for simulation optimization , 1996 .

[17]  J. Spall,et al.  Theoretical comparisons of evolutionary computation and other optimization approaches , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[18]  K. I. M. McKinnon,et al.  Convergence of the Nelder-Mead Simplex Method to a Nonstationary Point , 1998, SIAM J. Optim..

[19]  V. Torczon,et al.  From Evolutionary Operation to Parallel Direct Search : Pattern Search Algorithms for Numerical Optimization , 1998 .

[20]  Michael C. Ferris,et al.  A Direct Search Algorithm for Optimization with Noisy Function Evaluations , 2000, SIAM J. Optim..

[21]  W. Daniel Hillis,et al.  Co-evolving parasites improve simulated evolution as an optimization procedure , 1990 .

[22]  Hans-Georg Beyer,et al.  Efficiency and Mutation Strength Adaptation of the (mu, muI, lambda)-ES in a Noisy Environment , 2000, PPSN.

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

[24]  C. T. Kelley,et al.  Detection and Remediation of Stagnation in the Nelder--Mead Algorithm Using a Sufficient Decrease Condition , 1999, SIAM J. Optim..

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

[26]  Michael Herdy,et al.  Reproductive Isolation as Strategy Parameter in Hierarichally Organized Evolution Strategies , 1992, PPSN.

[27]  J. Spall Adaptive stochastic approximation by the simultaneous perturbation method , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

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

[29]  Hans-Georg Beyer,et al.  Analysis of the (/, )-ES on the Parabolic Ridge , 2000, Evolutionary Computation.

[30]  G. R. Walsh,et al.  Methods Of Optimization , 1976 .

[31]  C. Kelley,et al.  The Simplex Gradient and Noisy Optimization Problems , 1998 .

[32]  A I Oyman,et al.  Analysis of the (1, )-ES on the Parabolic Ridge , 2000, Evolutionary Computation.

[33]  J. Spall Multivariate stochastic approximation using a simultaneous perturbation gradient approximation , 1992 .

[34]  V. Torczon,et al.  Direct search methods: then and now , 2000 .

[35]  H. Beyer Evolutionary algorithms in noisy environments : theoretical issues and guidelines for practice , 2000 .

[36]  Günter Rudolph,et al.  On Correlated Mutations in Evolution Strategies , 1992, PPSN.

[37]  G. Box,et al.  On the Experimental Attainment of Optimum Conditions , 1951 .

[38]  Peter J. Angeline,et al.  The Effects of Noise on Self-Adaptive Evolutionary Optimization , 1996, Evolutionary Programming.

[39]  Hans-Georg Beyer,et al.  Theory of evolution strategies - a tutorial , 2001 .

[40]  Hans-Georg Beyer,et al.  Local performance of the (1 + 1)-ES in a noisy environment , 2002, IEEE Trans. Evol. Comput..

[41]  L. Armijo Minimization of functions having Lipschitz continuous first partial derivatives. , 1966 .

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

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

[44]  N. Hansen Invariance, Self-adaptation and Correlated Mutations in Evolution Strategies Invariance, Self-adaptation and Correlated Mutations in Evolution Strategies , 2000 .

[45]  James R. Wilson,et al.  A revised simplex search procedure for stochastic simulation response-surface optimization , 1998, WSC '98.

[46]  H. P. Schwefel,et al.  Numerische Optimierung von Computermodellen mittels der Evo-lutionsstrategie , 1977 .

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

[48]  Eiichi Isogai A stochastic approximation method approximating the roots of time varying regression functions , 1985 .

[49]  John E. Dennis,et al.  Multidirectional search: a direct search algorithm for parallel machines , 1989 .

[50]  G. Unter Rudolph Local Convergence Rates of Simple Evolutionary Algorithms with Cauchy Mutations , 1998 .

[51]  Hans-Georg Beyer,et al.  Performance analysis of evolution strategies with multi-recombination in high-dimensional RN-search spaces disturbed by noise , 2002, Theor. Comput. Sci..

[52]  Hans-Georg Beyer,et al.  Investigation of the (/spl mu/, /spl lambda/)-ES in the presence of noise , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[53]  M. J. D. Powell,et al.  Direct search algorithms for optimization calculations , 1998, Acta Numerica.

[54]  Robert Hooke,et al.  `` Direct Search'' Solution of Numerical and Statistical Problems , 1961, JACM.

[55]  Günter Rudolph,et al.  Global Optimization by Means of Distributed Evolution Strategies , 1990, PPSN.

[56]  D. Fogel Evolutionary algorithms in theory and practice , 1997, Complex..

[57]  BeyerHans-Georg Toward a theory of evolution strategies , 1993 .

[58]  G. R. Hext,et al.  Sequential Application of Simplex Designs in Optimisation and Evolutionary Operation , 1962 .