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Adaptive Grey Wolf Optimizer for SVM Hyperparameter Tuning

• 1、Management School, Wuhan University of Science and Technology, Wuhan 430070

Abstract：Standard Grey Wolf Optimizer (GWO) and Sequential Minimal Optimization (SMO) algorithms demonstrate limited optimization accuracy and poor stability when solving parameters for nonlinear Support Vector Machines. This paper proposes an Adaptive Tracking Grey Wolf Optimizer (ATGWO) based on the GWO framework, incorporating both adaptive and tracking operators. The adaptive operator automatically adjusts the movement positions of grey wolves by analyzing positional changes between consecutive generations of leading wolves and considering weight factors among three hierarchical wolf levels, thereby enhancing the algorithm\'s exploration capability. The tracking operator controls whether wolves should track, as well as their tracking direction and distance, to improve the algorithm\'s exploitation ability. To satisfy the constraints of the Lagrangian objective function, a specialized mapping encoding scheme for grey wolf individuals is designed. Experimental results demonstrate that the proposed mapping encoding effectively resolves equality constraint problems, and the ATGWO algorithm achieves more stable and superior minimization of the Lagrangian objective function compared to both standard GWO and its variants, while significantly improving classification accuracy over the SMO algorithm. When the hyperparameter multiplier increases from 0.01 to 10.00, the minimum objective function value shows an approximately linear negative growth, which can enhance classification performance. However, excessively high multipliers may cause numerical instability, necessitating a balance between performance improvement and numerical stability.

Keywords： Nonlinear Support Vector Machine Parameter Optimization Sequential Minimal Optimization Grey Wolf Optimizer Gaussian Kernel Function