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 xed setting, ESs facilitate an adjustment of such parameters within a selfadaptation process. For step-size control in particular, various adaptation concepts have been evolved early in the development of ESs. These algorithms mostly work very e ciently 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 di cult, 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 modi cations may be summarized by the word \de-randomization". The derandomized scheme of mutative step-size control facilitates a reliable self-adaptation of individual step-sizes.