An adaptive decreasing sigmoid convergence factor for enhancing Grey Wolf Optimizer performance in high-dimensional optimization problems

Abstract

Optimization algorithms require an effective balance between exploration and exploitation to achieve fast convergence and high solution quality. The Grey Wolf Optimizer (GWO) has demonstrated promising performance in various engineering applications; however, its conventional linear convergence factor often leads to premature convergence or insufficient exploitation, particularly in high-dimensional search spaces. To address this limitation, this study proposes an adaptive decreasing sigmoid convergence factor that dynamically regulates the transition between exploration and exploitation throughout the optimization process. Unlike the standard linear reduction scheme, the proposed sigmoid-based mechanism maintains stronger exploration during the early search stages and accelerates exploitation in later iterations through a controlled nonlinear decline. The proposed approach was evaluated using four widely adopted benchmark functions, namely Sphere, Rosenbrock, Rastrigin, and Griewank, under different dimensionalities, population sizes, and iteration limits. Experimental results demonstrate that the proposed method improves performance in most benchmark scenarios compared with the standard GWO. The best performance was obtained with a sigmoid parameter n = 0.75, which yielded near-optimal solutions for the Sphere and Griewank functions while maintaining stable convergence for the Rosenbrock function. The results further indicate that the proposed strategy scales effectively across medium- and high-dimensional optimization problems. These findings confirm that the adaptive decreasing sigmoid convergence factor provides a simple yet effective enhancement to GWO, offering improved convergence behavior and optimization accuracy across benchmark optimization problems.