This study proposes a new hybrid model that aims to eliminate the problem of getting stuck in local minima during the training process of Artificial Neural Networks (ANNs) using derivative-based techniques. To overcome this problem, a new metaheuristic algorithm called LevySAO is presented, which combines the Snow Ablation Optimizer (SAO) algorithm with the Levy Flight mechanism. The proposed LevySAO algorithm was used to create a YSA-LevySAO hybrid model by optimizing the weights and bias values of the YSA. The classification performance of the model was tested on 15 different datasets commonly known in the literature, and the results obtained were evaluated using basic metrics such as sensitivity, specificity, precision, and F1-score. The success of the YSA-LevySAO hybrid model was compared with hybrid models developed with 12 different meta-heuristic algorithms in the literature. According to comprehensive experimental studies and Friedman test results, the proposed YSALevySAO model was found to have the best Average Success Ranking (ASR) in three of the four metrics (specificity, sensitivity, and F1-score). These findings prove that the developed LevySAO algorithm is a highly promising and effective alternative for addressing optimization problems in ANN training.