Evolution strategies with threshold convergence

When optimizing multi-modal spaces, effective search techniques must carefully balance two conflicting tasks: exploration and exploitation. The first refers to the process of identifying promising areas in the search space. The second refers to the process of actually finding the local optima in these areas. This balance becomes increasingly important in stochastic search, where the only knowledge about a function's landscape relies on the relative comparison of random samples. Thresheld convergence is a technique designed to effectively separate the processes of exploration and exploitation. This paper addresses the design of thresheld convergence in the context of evolution strategies. We analyze the behavior of the standard (μ, λ)-ES on multi-modal landscapes and argue that part of it's shortcomings are due to an ineffective balance between exploration and exploitation. Afterwards we present a design for thresheld convergence tailored to ES, as a simple yet effective mechanism to increase the performance of (μ, λ)-ES on multimodal functions.