An improved Grey Wolf Optimizer based on mutation operator, evolutionary population dynamics, and nonlinear population size reduction strategy

Grey Wolf Optimizer (GWO) is limited by slow convergence speed, premature convergence, and exploration-exploitation imbalance. These limitations constrain the performance of GWO, and addressing these issues is of significant importance for enhancing its efficiency in engineering applications across multiple optimization domains within real-world scenarios. To address these limitations, this study proposes a novel GWO variant, called MENGWO, incorporating a mutation operator, an evolutionary population dynamics (EPD) mechanism, and a nonlinear population size reduction (NPSR) strategy. Inspired by Differential Evolution (DE), the update process of the introduced mutation operator can switch between exploration and exploitation modes based on a probability that varies iteratively. The enhanced EPD mechanism repositions underperforming search agents based on a probability that varies across iterations, either relocating them nearer to the current optimum or redistributing them randomly within the search space. Meanwhile, the NPSR strategy reduces the population size nonlinearly to improve computational efficiency. All three components incorporate dynamically adjusted mechanisms that depend on the progression of iterations, which are designed to work synergistically to enhance both exploration and exploitation. Experimental comparisons with Particle Swarm Optimization (PSO), standard GWO, and five other GWO variants demonstrate the effectiveness of the proposed algorithm. On low-dimensional CEC2005 benchmark functions, MENGWO outperforms other algorithms for 1 of 7 unimodal, 4 of 6 multimodal, and all 10 fixed-dimensional multimodal functions. In addition, on high-dimensional CEC2005 benchmark functions, MENGWO outperforms other algorithms for 2 of 7 unimodal and 4 of 6 multimodal functions. These results indicate that it enhances exploration capability while maintaining competitive exploitation capability. On CEC2022 benchmark functions, MENGWO outperforms other algorithms for 6 of 15 10-dimensional functions and 9 of 15 20-dimensional functions, demonstrating its efficacy on complex problems. Furthermore, the proposed algorithm achieves the best performance for 5 of 7 engineering design problems. In summary, this work proposes an effective optimization algorithm with balanced exploration and exploitation capabilities for engineering applications and complex problem domains.