A Joint Optimization Algorithm Based on the Optimal Shape Parameter–Gaussian Radial Basis Function Surrogate Model and Its Application

We propose a joint optimization algorithm that combines the optimal shape parameter–Gaussian radial basis function (G-RBF) surrogate model with global and local optimization techniques to improve accuracy and reduce costs. We analyze factors that affect the accuracy of the G-RBF surrogate model and use the particle swarm optimization (PSO) algorithm to determine the optimal shape parameter and control the number and spacing of the sampling points for a high-precision surrogate model. Global optimization refines the surrogate model, serving as the initial value for local optimization to further refine the problem. Our experiments show that this method significantly reduces computation costs. We optimize the section size of cantilever beams for different materials, obtaining the optimal section size and mass for each. We find that hard aluminum alloy is the optimal choice, meeting yield strength and deflection requirements through finite element analysis verification. Our work highlights the effectiveness of the joint optimization algorithm based on the surrogate model, providing valuable tools and insights into optimizing various structures.