Gradient-Enhanced Kriging-Based Parallel Efficient Global Optimization Algorithm and Its Application in Aerodynamic Shape Optimization

The parallel efficient global optimization (EGO) algorithm was developed to leverage the rapid advancements in high-performance computing. However, conventional parallel EGO algorithm based on ordinary kriging (OK) model faces limitations when applied to complex, nonlinear, and high-dimensional engineering optimization problems, as OK model relies only on sample point locations, restricting the available training information. To further enhance the optimization potential of the parallel EGO algorithm, an improved system that integrates the parallel EGO algorithm with gradient-enhanced kriging (GEK) is proposed. The integration serves two main purposes: on the one hand, GEK provides a more comprehensive representation of the design space, improving the surrogate model’s predictive accuracy; on the other hand, as the number of infill points increases, GEK mitigates the unreliability of the pseudo expected improvement (PEI) function, facilitating the efficient search for high-quality global optima. To ensure high performance, various benchmark functions were used to evaluate the impact of different optimizers on the proposed system, ultimately identifying the most effective optimizer. Additionally, optimization tests were conducted on benchmark functions, airfoil aerodynamic optimization, and automotive aerodynamic optimization to compare the proposed system with traditional parallel EGO systems in optimization performance. The results demonstrate that the modified Gaussian bare-bones differential evolution (MGBDE) optimizer consistently accelerated convergence to high-quality solutions in most benchmark functions, achieving the highest average ranking across all tests. Compared to traditional parallel EGO system, the proposed method showed superior convergence speed, solution quality, and computational efficiency. Specifically, for airfoil and automotive aerodynamic optimization, when achieving the target performance improvements of 2.4% and 7.0%, the proposed system reduced the wall-clock time cost from 1.65h to 0.33h and from 203h to 14.5h, respectively, significantly improving optimization efficiency.