Handling sharp ridges with local supremum transformations

A particular strength of many evolution strategies is their invariance against strictly monotonic and therefore rank-preserving transformations of the objective function. Their view onto a continuous fitness landscape is therefore completely determined by the shapes of the level sets. Most modern algorithms can cope well with diverse shapes as long as these are sufficiently smooth. In contrast, the sharp angles found in level sets of ridge functions can cause premature convergence to a non-optimal point. We propose a simple and generic family of transformation of the fitness function to avoid this effect. This allows general purpose evolution strategies to solve even extremely sharp ridge problems.