Multi-objective Optimization Design of Coaxial Through Silicon Via Arrays Based on Genetic Algorithm

This paper proposes a surrogate-driven multi-objective optimization framework for complex electromagnetic structures. A General Regression Neural Network (GRNN) is employed to approximate the nonlinear mapping between structural parameters and performance metrics, while Particle Swarm Optimization (PSO) is used to adaptively tune the smoothing parameter to enhance prediction stability. The trained surrogate model is embedded into a Genetic Algorithm (GA) to enable efficient global search without repeated full-wave simulations, significantly reducing computational cost. A closed-loop procedure integrating modeling, prediction, optimization, and verification is established to ensure reliability of the optimization process. To enhance model transparency, SHAP-based interpretability analysis is introduced to quantify parameter contributions and reveal underlying design trade-offs. Comparative studies with SVR and BPNN demonstrate the suitability of GRNN for iterative optimization scenarios in terms of structural simplicity and computational efficiency. Cross-scale validation further confirms that the proposed framework maintains consistent optimization behavior under different structural scales. The results indicate that the proposed method provides an efficient, interpretable, and scalable solution for multi-objective electromagnetic design optimization.