The Analysis of the (µ, λ)-ES
This chapter is dedicated to the analysis of the (µ, λ)-ES on the sphere model. It has three parts. The theoretical background is presented in the first section. In the second section, the program established in the previous section is carried out in the linear approximation. It will hereby be possible to perform the calculations for the final progress rate formulae analytically. The results obtained are compared with the simulation results in the third section, along with a discussion. For small σ*, the progress rate formula for the hyperplane is obtained as a byproduct. This can be used for the empirical verification of the cµ, λ progress coefficients. The exploration behavior of the (µ, λ)-ES is investigated on the sphere model. As a result, it is shown that the search behavior observed cannot be characterized as a “diffusion along the gradient.”
KeywordsRandom Walk Sphere Model Progress Rate Central Moment Integral Identity
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