Optimal number of evolution strategies mutation step sizes in dynamic environments

The optimum xt moves during the optimization process and therefore depends on the time t. In the case of dynamic environments the main task is not to find one good solution. Instead, the algorithm must follow the moving target with a small distance. For this purpose many evolutionary algorithms consists of self-adaptive mechanisms. This means, that they can adjust their parameter settings during the evolutionary run. In evolution strategies (ES) [1] the adaptation is done on a set of strategy parameters which influence the variation of the object variables. One variant of ES consists of up to n mutation step sizes. On the one hand, using a separate step size for every single coordinate the adaptation of the algorithm to the problem at hand is regarded to work better. On the other hand, the higher the number of strategy parameters the higher is the time needed for adaptation [2]. Therefore, one must find the silver bullet between a fast and a good adaptation by choosing an appropriate number of step sizes. Several options are lying between the two extremes of one and n mutation step sizes. A frequent choice is to choose two mutation step sizes. In this case, usually the first step size is used for one coordinate and the second step size is used for the others. Mostly, it is not known in advance which of the n coordinates should be varied by the separate step