Algorithms Graphs and Computers by R Cooke, K L. Lockett, J A Bellman

By R Cooke, K L. Lockett, J A Bellman

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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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