A Step Size Preserving Directed Mutation Operator

The main idea of the directed mutation is to focus on mutating into the most beneficial direction by using a customizable asymmetrical distribution. In this way the optimization strategy can adopt the most promising mutation direction over the generations. It thus becomes nearly as flexible as with Schwefel’s correlated mutation [2] but causes only linear growth of the strategy parameters instead of quadratic growth. A normalization function is introduced to decouple asymmetry from the variance, i.e. the step size. By incorporating the normalization function the variance becomes independent of the asymmetry parameter. Given below are the definitions of the density function for the normalized directed mutation and its normalization function: