Symmetry-Guided Multi-Elite Gekko Japonicus Optimization Algorithm for Global Optimization and Artistic Image Segmentation

This paper presents a symmetry-guided multi-elite Gekko Japonicus Algorithm, termed MIGJA, for global optimization and multi-threshold image segmentation. The method modifies the original GJA from three aspects. In the movement stage, a success-rate feedback mechanism is used to adapt the Lévy-flight probability and step-size coefficient according to recent search behavior, allowing the population to switch more flexibly between exploration and exploitation. In the guidance stage, several elite individuals are combined to form a weighted collaborative center, which reduces the excessive dependence on a single best solution and provides a more balanced search direction. In the reconstruction stage, historical memory and differential information are introduced into the tail reconstruction process to help inferior or stagnant individuals move out of local regions during the later search phase. The proposed MIGJA is tested on the CEC2017 and CEC2020 benchmark suites and further applied to Otsu-based multi-threshold image segmentation. The numerical results show that MIGJA performs competitively in terms of convergence accuracy and stability. According to the Friedman mean-rank results, MIGJA ranks first in all test settings, with mean-rank reductions of about 78.8–84.5% compared with the original GJA and 66.7–76.1% compared with the strongest competitor. In the segmentation experiments, MIGJA also obtains favorable objective function values and image quality metrics, including PSNR, FSIM, and SSIM. These findings suggest that the proposed algorithm is suitable for both benchmark optimization and multi-threshold image segmentation tasks.