A Derandomized Approach to Self Adaptation of Evolution Strategies
 
    Andreas Ostermeier, Andreas Gawelczyk and Nikolaus Hansen 

 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
 ``de-randomization''. The derandomized scheme of mutative step-size
 control facilitates a reliable self-adaptation of individual
 step-sizes.