Multi-Strategy Improved Graduate Student Evolutionary Algorithm for Numerical Optimization and Art Image Segmentation

The Graduate Student Evolutionary Algorithm (GSEA) has demonstrated promising optimization capability in several engineering tasks; however, its performance may deteriorate when dealing with high-dimensional and complex multimodal problems due to insufficient adaptive search behavior, weak diversity preservation, and stagnation during later optimization stages. To alleviate these limitations, this paper proposes a Multi-Strategy Improved Graduate Student Evolutionary Algorithm (MIGSEA) for numerical optimization and artistic image multi-threshold segmentation. First, an adaptive mentor-guided learning mechanism is introduced to dynamically regulate the influence of mentors and peers throughout the optimization process, enabling a more effective transition from global exploration to local exploitation. Second, an elite–random cooperative learning strategy is designed to combine high-quality solution guidance with stochastic perturbation, thereby improving population diversity and enhancing the ability to escape local optima. Third, a stagnation-aware local refinement mechanism is developed to activate adaptive neighborhood search when the optimization process becomes trapped, which further accelerates convergence and improves solution precision. To verify the effectiveness of the proposed algorithm, MIGSEA is evaluated on the IEEE CEC2017 and CEC2020 benchmark suites and compared with 11 advanced metaheuristic algorithms under identical experimental conditions. Experimental results demonstrate that MIGSEA achieves competitive optimization accuracy, convergence speed, robustness, and statistical superiority in most benchmark functions. Furthermore, MIGSEA is applied to Otsu-based artistic image multi-threshold segmentation using multiple benchmark images with different threshold levels. Quantitative evaluation based on PSNR, FSIM, and SSIM, together with visual analysis, confirms that the proposed method can generate more accurate and visually consistent segmentation results than existing competitors. Overall, the proposed MIGSEA provides an effective and robust optimization framework for both benchmark optimization and practical image segmentation applications.