Model Assisted Evolution Strategies

Abstract

In many engineering optimization problems the number of fitness function evaluations is limited by time and cost. These problems pose a special challenge to the field of evolutionary computation, since existing evolutionary methods require a very large number of problem function evaluations. One innovative way to address this challenge is the application of approximation models as a surrogate of the real fitness function. Thereby two major points have to be considered. The selection of an appropriate model to approximate the fitness landscape and the coupling of model with the evolutionary algorithm. We discuss both points in detail and investigate different alternatives how knowledge from the model can support the evolutionary optimization process. Special attention is given to probabilistic models like Gaussian Processes, which have the advantage of providing a probabilistic interpretation of the model prediction. We describe a model assisted Evolution Strategy, which uses a Gaussian Process approximation model to preselect the most promising solutions. To refine the preselection process we determine the likelihood of each individual to improve the overall best found solution. Due to this, the new algorithm has a much better convergence behavior and achieves better results than standard evolutionary optimization approaches with less fitness evaluations. Numerical results from extensive simulations on several high dimensional test functions including multimodal functions are presented. These results show that the incorporation of knowledge by fitness approximation considerably enhances the performance of Evolution Strategies.