Weighted recombination evolution strategy on a class of PDQF's

摘要

This work is concerned with a weighted recombination method for Evolution Strategies (ES) on a class of positive definite quadratic forms (PDQF). In particular, the λopt-ES and the λopt-CSA-ES will be analyzed. A characteristic of both strategies is the use of weighted recombination of all offspring within an iteration step. After obtaining equations describing the evolutionary process, the weights and the progress rate for the λopt-ES will be derived. It is shown that the optimal mutation strength (step size) for the λopt-ES yields an asymptotic limit value of 2κ, where κ is an user-chosen rescaling factor. Afterwards the cumulative step-length adaptation (CSA) is analyzed to determine the target mutation strength (the mutation strength the strategy tries to reach by means of adaptation) and the actually attained mutation strength. For both the asymptotic values are obtained at √2κ. To justify the theoreticalresults, comparisons with simulations are presented.