Population size reduction methods in differential evolution: a comprehensive review and experimental analysis

Optimization plays a crucial role in modern engineering and science. Evolutionary computing techniques are a branch of artificial intelligence (AI) and have attracted a lot of attention recently. Scientists, engineers, and practitioners need to understand how evolutionary computing techniques work and be fluent in using AI-based optimization techniques to solve engineering optimization problems. The Differential Evolution (DE) algorithm, which is classified as a population-based evolutionary algorithm, is primarily intended for solving complex optimization problems. The original DE algorithm uses a fixed population size, whereas modern DE variants adopt advanced strategies for reducing the population size over the evolution process. In this review article, 204 studies are included and we offer not only an overview of the population size reduction methods, but also a comparative analysis of selected methods by integrating them into the state-of-the-art algorithm and performing experimental work on the CEC 2024 benchmark functions and two real-world problems. Benchmarking demonstrates that the choice of population size adjustment strategy affects optimization performance, with its effectiveness depending on the problem characteristics and dimensionality. According to the Friedman test applied to 15 methods, 10 non-linear population size reduction methods were ranked higher than the linear population size reduction method on 100-dimensional problems. Moreover, a non-linear population size reduction method achieved the top rank on both real-world optimization problems. However, no single population size adjustment strategy consistently dominates across all problem dimensions and function families.