Step Length Adaptation by Generalized Predictive Control

This paper puts forward a useful method for step length adaptation of the mutation distribution in ES- using the GPC (Generalized Predictive Control) to adapt the global step size. Similar to the concept of evolution path, the mutation step is the function of historical information generated by the iterative processes of ES algorithm. In our method, the ES algorithm is regarded as a controlled system and modeled as a CARIMA (Controlled Auto Regressive Integrated Moving Average) model. The parameters of CARIMA model are estimated by RLS (the recursive least squares) with forgetting factor, and then the current global optimum step size (the control parameter) is calculated by the GPC to feed back to ES, the output and the control quantum are used to estimate the parameters of CARIMA model iteratively.