Hybrid Differential Evolution with Covariance Matrix Adaptation for Digital Filter Design

Digital filter design method utilizing a hybrid algorithm based on a Differential Evolution (DE) and Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is presented. The main goal of the algorithm is to optimize the finite impulse response (FIR) filter coefficients which lead to the minimum error between the actual and the ideal filter frequency response. DE performs the global exploration and optimizes the parameters of exponential functions that define the bounded search space. Next, CMA-ES is used as a local search engine. Its initial search point and boundary constraint estimates are provided by DE. Additionally, periodic feedback from CMA-ES is provided to the DE. The hybrid approach and the idea of search space boundary estimation seems to be a promising method for the FIR filter design task, especially for relatively high dimension filters. The algorithm performance is compared with the classical filter design methods and the other evolutionary proposals found in literature.