The idea of using a meta-ga can be found quite early. here, an upperlevel ga tries to tune the control parameters of a lower-level algorithm which tries in turn to solve the original problem. the first suggestion stems from weinberg [71] giving rise to the work by mercer and sampson [45]. concerning evolution strategies, the need to adapt the mutation strength or strengths ; appropriately during the evolutionary process was recognized in rechenberg's seminal book evolutionsstrategie [50]. he proposed the well-known 1 5th rule, which was originally developed for 1 + 1 ; -es. it relies on counting the successful and unsuccessful mutations for a certain number of generations. if more than 1 5th of mutations leads to an improvement the mutation strength is increased and decreased otherwise. the aim was to stay in the so-called evolution window guaranteeing nearly optimal progress. in addition to the 1 5th rule, rechenberg [50] also proposed to couple the evolution of the strategy parameters with that of the object parameters. the strategy parameters were randomly changed. the idea of explicit ; selfadaptation was born. to compare the performance of this learning population with that of an es using the 1 5th rule, rechenberg conducted some experiments on the sphere and corridor model. the learning population exhibited a higher convergence speed and even more important it proved to be applicable in cases where it is improper to use the 1 5th rule. self-adaptation thus appeared as a more universally usable method. since then various methods for adapting control parameters in evolutionary algorithms have been developed ranging from adapting crossover probabilities in genetic algorithms to a direct adaptation of the distribution [16]. schwefel [56, 58] introduced a self-adaptive method for changing the strategy parameters in evolution strategies which is today commonly associated with the term self-adaptation. in its most general form, the full covariance matrix of a general multidimensional normal distribution is adapted. a similar method of adapting the strategy parameters was offered by fogel et al. [25] in the area of evolutionary programming the so-called meta-ep operator for changing the mutation strength. a more recent technique, the cumulative path-length control, stems from ostermeier, hansen, and gawelczyk [48]. one of the aims is to derandomize the adaptation of the strategy parameters. the methods developed, the cumulative step-size adaptation csa ; as well as the covariance matrix adaptation cma ; [32], make use of an evolution path, p g + 1 ; zsel , which cumulates the selected mutation steps. to illustrate this concept, consider an evolution path where purely random selection is applied. since the mutations are normally distributed, the cumulated evolution g path is given by u g ; where n 0, 1 ; is random vector with identically independently distributed n 0, 1 ; normally distributed components with zero mean and variance 1. the length of u g ; -distributed with expectation u . fitness based selection changes the situation. too large mutation steps result in a selection of smaller mutations. thus, the path and hot poker.

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