  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.
