Optimizing Objective Functions with Non-Linearly Correlated Variables Using Evolution Strategies with Kernel-Based Dimensionality Reduction

This paper proposes an improvement of Evolutionary Strategies for objective functions with non-linearly correlated variables. It focuses on detecting non-linear local dependencies among variables of the objective function by analyzing the manifold in the search space that contains the current population and transforming individuals to a reduced search space defined by the Kernel Principal Components. Experiments performed on some popular benchmark functions confirm that the method may significantly improve the search process, especially in the case of complex objective functions with a large number of variables, which usually occur in many practical applications.