Success Rate of Evolution Strategies on the Multimodal Griewank Function

The Griewank function is one of the widely used multimodal benchmark functions. The function is known for its counter intuitive behavior of getting simpler to be optimized with increasing dimension, although the number of local minima increases with the problem dimension. A frozen noise model is introduced that is able to partially explain the empirically observed behaviors. The influence of the different Evolution Strategies and their parameters on the success rate are analyzed. Empirical investigations are used to show the limitations of this model. These investigations reveal some unexpected behaviors regarding the influence of the population size on the success rate of the Evolution Strategies that cannot be explained by the current theory.