Performance Study of Gradient-Enhanced Kriging Based Parallel Efficient Global Optimization

In engineering optimization, machine learning has become a mainstream approach due to its ability to intelligently approximate continuous representations of discrete samples, thereby significantly reducing the costs of expensive experiments. Mathematical models trained through machine learning facilitate several critical steps in engineering optimization, including the search for optimal values, sensitivity analysis, visualization of approximate relationships and statistical analysis. This approach is commonly referred to as surrogate-based optimization (SBO). Among various surrogate models, gradient-enhanced Kriging (GEK) has shown substantial potential for engineering applications. By utilizing not only the approximate mapping between sample locations and corresponding objective values but also the gradient information between these sample locations and objective values, which enhances the fitting accuracy of surrogate model. Furthermore, the optimization performance of GEK based parallel efficient global optimization (EGO) algorithm can also be significantly improved. However, compared to the ordinary Kriging (OK) surrogate model, the incorporation of additional gradient information-obtained through methods such as finite difference and adjoint solving-demands more computational resources when constructing surrogate model. Therefore, when employing GEK based parallel EGO optimization system, it's crucial to explore how the effective selection of sample size and space-filling property of sample points can efficiently reduce computational resource consumption while maintaining high optimization performance. This study investigates the influence of sample size and space-filling quality of sample points on the optimization performance of GEK based parallel EGO optimization system. The convergence performance of the current optimization system is compared across various multimodal test functions using different sample sizes and space-filling quality levels. Statistical analysis results shown that, increasing sample size does not consistently improve optimization performance under the same space-filling quality level. Additionally, under the same sample size, the non-completely convergent optimal Latin-hypercube design (OLHD) effectively promotes the optimization system to rapidly converge to a high-quality solution within a limited number of iterations.