Gaussian Process-Based Robust Optimization with Symmetry Modeling and Variable Selection

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Gaussian process (GP)-based robust optimization is an effective tool in product quality improvement. However, most existing variable selection methods are designed for parametric models and are unsuitable for nonparametric GP models. Additionally, improving the prediction accuracy of GP models with limited design points remains a significant challenge in robust optimization. To address these issues, this article proposes a GP-based multi-stage robust parameter optimization method that integrates symmetry modeling, sensitivity analysis (SA), and Markov Chain Monte Carlo (MCMC) techniques. First, a modified expected improvement (EI) criterion is introduced to enhance the utilization efficiency of design points. Second, a nonparametric variable selection technique based on SA is developed for GP models to identify significant variables. This method considers both independent variables and their interactions, improving the interpretability of GP models. Finally, the selected variables are used to construct the robust optimization model, and the genetic algorithm (GA) is employed to search for the optimal solution within the feasible domain. Numerical simulations and real-world experiments demonstrate the effectiveness of the proposed method. Comparative results indicate that the proposed method obtains more robust optimal input parameter settings compared to existing approaches.