Approximation of the objective insensitivity regions using Hierarchic Memetic Strategy coupled with Covariance Matrix Adaptation Evolutionary Strategy

One of the most challenging types of ill-posedness in global optimization is the presence of insensitivity regions in design parameter space, so the identification of their shape will be crucial, if ill-posedness is irrecoverable. Such problems may be solved using global stochastic search followed by post-processing of a local sample and a local objective approximation. We propose a new approach of this type composed of Hierarchic Memetic Strategy (HMS) powered by the Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES) well-known as an effective, self-adaptable stochastic optimization algorithm and we leverage the distribution density knowledge it accumulates to better identify and separate insensitivity regions. The results of benchmarks prove that the improved HMS-CMA-ES strategy is effective in both the total computational cost and the accuracy of insensitivity region approximation. The reference data for the tests was obtained by means of a well-known effective strategy of multimodal stochastic optimization called the Niching Evolutionary Algorithm 2 (NEA2), that also uses CMA-ES as a component.