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Extra info for Contemporary Evolution Strategies
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. 2 gives an overview of the computational complexity of the key variants of modern evolution strategies—excluding the restart heuristics, since they depend on the underlying evolution strategy used for restarts. 2 Convergence Behavior In this section, we provide a short summary of relevant results of empirical investigations of modern evolution strategies concerning their convergence behavior, following the results discussed in the original literature.
They use the aformentioned mutation approaches together with self-adaptation for the endogenous parameters. An overview of other approaches for handling mixed search spaces is given by Li . 3 Multiobjective Optimization In single-objective optimization fitness values can be ordered to decide whether one solution is better than another. In multiobjective optimization, where fitness values are represented as vectors, such a strict ordering does not exist anymore. Solutions are partially ordered and based on the partial order solutions can be either dominated or non-dominated by other solutions.
16 The column vectors of the matrix B form a so-called generating set, which motivates the terminology generating set adaptation. 1=n/I// 2 Rn m initialize x, ı, B t 0 repeat t t C1 for i D 1 ! 0; I/ where zi 2 Rm zi yi cm Bzi xi x C ı i yi where P . i D 2=3/ D P . cu sel ysel / ı . 1 . W ; /-CMA-ES Algorithms DR1, DR2 and DR3, as described in Sect. 1, are derandomized evolution strategies in the sense of adapting endogenous strategy parameters depending on the selected mutation vector. This has also been called the first level of derandomization .