Contemporary Evolution Strategies (Natural Computing Series) by Thomas Bäck, Christophe Foussette, Peter Krause

By Thomas Bäck, Christophe Foussette, Peter Krause

This ebook surveys key set of rules advancements among 1990 and 2012, with short descriptions, a unified pseudocode for every set of rules and downloadable application code. offers a taxonomy to explain similarities and adjustments in addition to ancient relationships.

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2 lmm, nlmm, and p-sep-lmm are abbreviations for local meta model, new local meta model, and partially separable local meta model. 2 Computational complexity of modern evolution strategies, for a single generation 3 Taxonomy of Evolution Strategies Algorithm Computational complexity . 1 C 1/-Cholesky-CMA-ES Active-CMA-ES . 1 C 1/-Active-CMA-ES and the sep-CMA-ES. n6 / is required; see Chap. 2 for an explanation of the reasons causing this. A brief summary of the corresponding adaptation algorithms for endogenous strategy parameters is provided in Sect.

X1W / of the last d10 C 30n= e generations are identical or the difference between their maximum and minimum values is smaller than Tx . , vi < Tx 8i 2 f1; : : : ; ng. The third criterion, noeffectaxis, takes changes with respect to the main coordinate axes induced by C into account. These are given by the eigenvectors ui and eigenvalues i , i 2 f1; : : : ; ng, of C, and they are found (normalized) in the columns of matrix B and the main diagonal elements of D. The termination criterion does not check all main axes at once, but in generation t it takes the axis i D t mod n into p account.

W ; /-CMA-ES, the corresponding covariance matrix is adapted by using the evolution path (rank-one-update) and a matrix Z which is generated from the best mutation vectors (rank- -update). The LS-CMA-ES uses two different modes for covariance matrix adaptation, namely, on the one hand the adaptation algorithm of the . W ; /-CMA-ES, and on the other hand learning the Hessian H from past samples1 by least squares estimation. Provided the estimation O of the Hessian reaches a certain quality level, C D 1 H O 1 is used as the covariance H 2 matrix.

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