A Comparison of Three Uniquely Different State of the Art and Two Classical Multiobjective Optimization Algorithms as Applied to Electromagnetics

This paper compares three modern and two classical multiobjective optimizers (MOOs) as applied to real-world problems in electromagnetics. The behavior of sophisticated optimizers on simple test functions has been studied exhaustively. In contrast, the algorithms here are tested on practical applications, where the function evaluations are computationally expensive, making the convergence rate a crucial factor. The examples considered include the optimization of a narrowband slot antenna, a mushroom-type electromagnetic bandgap structure, and an ultrawideband Vivaldi antenna. Another popular topic in the literature is in comparing classical MOOs on electromagnetics problems. The modern optimizers chosen in this paper are state of the art and each has a distinct design philosophy. This paper introduces two unique MOOs to the electromagnetics community: BORG, an auto-adaptive genetic algorithm and the Multi-Objective Covariance Matrix Adaptation Evolutionary Strategy (MO-CMA-ES), an extension of the popular single-objective CMA-ES. These algorithms are compared to the Multi-objective Evolutionary Algorithm based on Decomposition (MOEA/D), a Chebysheff scalarization algorithm, and two classical MOOs. This paper will study the behavior of these algorithms on problems in electromagnetics with a limited number of function evaluations using five distinct metrics and will provide useful guidelines and recommended optimizer settings.