A Derandomized Approach to Self-Adaptation of Evolution Strategies

Comparable to other optimization techniques, the performance of evolution strategies (ESs) depends on a suitable choice of internal strategy control parameters. Apart from a fixed setting, ESs facilitate an adjustment of such parameters within a self-adaptation process. For step-size control in particular, various adaptation concepts have been evolved early in the development of ESs. These algorithms mostly work very efficiently as long as the scaling of the parameters to be optimized is known. If the scaling is not known, the strategy has to adapt individual step-sizes for all the parameters. In general, the number of necessary step-sizes (variances) equals the dimension of the problem. In this case, step-size adaptation proves to be difficult, and the algorithms known are not satisfactory. The algorithm presented in this paper is based on the well-known concept of mutative step-size control. Our investigations indicate that the adaptation by this concept declines due to an interaction of the random elements involved. We show that this weak point of mutative step-size control can be avoided by relatively small changes in the algorithm. The modifications may be summarized by the word “derandomization.” The derandomized scheme of mutative step-size control facilitates a reliable self-adaptation of individual step-sizes.