Electromagnetic Optimization Using Mixed-Parameter and Multiobjective Covariance Matrix Adaptation Evolution Strategy

Different variations of the covariance matrix adaptation evolution strategy (CMA-ES) are used in the design and optimization of electromagnetic (EM) problems. Two different schemes for the implementation of mixed-parameter CMA-ES and one scheme for the implementation of multiobjective CMA-ES are presented. Mixed-parameter CMA-ES is attractive in EM optimization when both continuous and discrete design parameters are involved. The first mixed-parameter scheme uses a Poisson mutation operator to update the discrete variables, and the second one forces an integer mutation on discrete variables with small variances. Multiobjective CMA-ES, developed in this paper, optimizes designs with respect to multiple objective functions simultaneously. It ranks the candidate solutions according to two levels: nondominated sorting and crowding distance. Several antenna and microwave design problems are presented to evaluate the performance of these schemes and compare them with other nature-based optimization algorithms.