A study of adaptive population sizing in a self-adaptive differential evolution

Abstract

Differential Evolution (DE) is extensively applied due to its simplicity, robustness, and computational efficiency. However, the performance of DE is influenced by several factors, including the nature of the problem, the specific algorithm variant, and user-defined settings. Numerous studies have explored adaptive parameter settings to reduce the sensitivity of DE’s performance to user inputs, parameter choices, and problem characteristics. DE’s ability to find optimal solutions depends on offspring generation and population diversity. One of the ways to improve DE’s population diversity is by adjusting the population size, either by introducing new individuals or eliminating existing ones. This work investigates the adaptation of population sizing of a self-adaptive differential evolution algorithm called Self-Adaptive Ensemble-based DE with Enhanced Population Sizing (SAEDE-EP). The adaptation of population sizing in SAEDE-EP is influenced by two parameters: the threshold value for stagnation comparison of the best individual over generations and the population size’s growth rate. The effect of these two parameters on population sizing adaptation is evaluated using 26 benchmark single-objective unconstrained optimization functions consisting of unimodal, multimodal, hybrid, and composition functions. SAEDE-EP is compared against 18 state-of-the-art evolutionary algorithms on 10 functions from the 100-Digit Challenge on CEC 2019 single-objective real parameter optimization. Additionally, SAEDE-EP is tested on 57 problems from the CEC-2020 Competitions on Real-World Single Objective Constrained Optimization. Comparative analysis indicates that SAEDE-EP performs well in single-objective unconstrained optimization problems with various characteristics and solves 86% of the real-world single-objective constrained optimization, requiring less computational time and less exhaustive effort to set parameters.