Differential Evolution Algorithm With Two-Step Subpopulation Strategy and Its Application in Microwave Circuit Designs

Abstract

Differential evolution (DE) is a simple yet powerful evolutionary algorithm for both single objective and multiobjective optimizations (MOPs). In nature, good parents are more likely to produce good offspring, because genes from good individuals propagate throughout the population. Inspired by this phenomenon, a two-step subpopulation strategy is proposed, in which individuals in the current population are sorted based on evaluation metrics, and are divided into superior and inferior subpopulations. The inferior subpopulation evolves to generate offspring. If the generated offspring has better evaluation metric values than individuals in the superior subpopulation, they will replace the latter and be used as vectors for mutation strategies. The proposed strategy is incorporated into several advanced DE variants for both single-objective optimization (SOP) and MOPs to verify its effectiveness. Experiments are conducted on 25 single objective, 5 bi-objective, and 4 tri-objective Deb, Thiele, Laumanns and Zitzler (DTLZ) benchmark problems. Results indicate that the proposed subpopulation strategy is capable of improving the performance of both single objective and multiobjective algorithms. The application of the proposed approach is demonstrated by solving a microwave circuit design problem with stringent requirements. The better performance achieved by the proposed approach in quality of solutions, convergence rate, and diversity is verified by the performance comparison with competitive optimization algorithms in the literature.