An Adaptive PSO–GA Hybrid Optimization with Diversity-Aware and Stagnation-Resistant Mathematical Framework for SVR
Support Vector Regression (SVR) is a reliable and generalizable model for non-linear regression, but its performance depends strongly on selecting proper hyperparameters such as the penalty parameter $C$, kernel width $\gamma$, and the $\epsilon$-insensitive loss. Because the SVR objective is highly nonconvex with a multimodal error surface, manual tuning and grid search become inefficient. Metaheuristic optimizers therefore offer a more practical alternative through population-based search. Although Particle Swarm Optimization (PSO) and Genetic Algorithms (GA) have both shown promise, each has clear limitations: PSO converges quickly but often stagnates in local optima due to loss of diversity, whereas GA preserves diversity but converges slowly because of excessive random exploration. To address these complementary weaknesses, this work introduces a mathematically formulated hybrid framework called Adaptive PSO-GA (A-PSO-GA). Experiments on the Housing, Concrete, and Abalone benchmarks show that A-PSO-GA consistently outperforms PSO-only, GA-only, and non-adaptive hybrid baselines in RMSE, MAE, MAPE, and $R^{2}$. It also achieves faster and more stable convergence across multiple seeds, demonstrating improved prediction accuracy, robustness, and optimization reliability. These results confirm that mathematically justified adaptive mechanisms are important for effective evolutionary hyperparameter tuning of SVR.