Bayesian Optimization for Robust Parameter Design Based on Quantiles of the Loss Distribution
DescriptionThis project will develop Bayesian optimization methods for optimizing robust design objective functions (RDOFs) that are quantiles of the quality loss distribution in product design simulations. We shall focus on the case of deterministic simulations where the vector of input noise factors is a fixed vector in each simulation run, but it is a random vector with a known distribution in actual system operation. Due to increasing availability of computers and modelling software, simulators are becoming widely used for product design. Many of these simulators are computer codes that implement numerical algorithms such as the finite element method to solve partial differential equations, which are deterministic in nature, i.e., a fixed output is obtained given fixed user-specified inputs. To improve quality in product design, it is imperative to evaluate the performance of the product under random manufacturing and/or operating conditions, which are modelled by input noise factor variations, and to find the control (i.e., design) factor setting that minimizes the deleterious effect of the noise variations on quality as quantified by an RDOF. This is a quality improvement approach called robust parameter design (RPD). While Gaussian process (GP) models have been widely used to build emulators for time-consuming simulators to facilitate RPD, there is a lack of Bayesian optimization methods based on the GP emulator for finding control factor settings that optimize RDOFs given by quantiles of the loss distribution. However, such objective functions are favored by some decision-makers such as those who would like to make conservative decisions that ensure the product works well under most operating conditions. This project will develop acquisition functions (AFs) for selecting follow-up design points (i.e., simulator evaluation points) in Bayesian optimization based on a GP emulator of the simulator output for a broad class of RDOFs that consists of quantiles of the loss distribution given by continuous loss functions. AFs for optimizing one quantile of the loss distribution and AFs for simultaneously optimizing a profile of quantiles will be developed. By discretizing the distribution of the noise factors and employing general methods for computing integrals of functions, methods for efficiently computing the proposed AFs will be developed. The finite sample performance and convergence properties of the proposed AFs will be also studied, and the best AFs will be identified. Thus, the project is expected to deliver urgently needed efficient global optimization methods for RPD with costly simulators to the engineering design community.
|Effective start/end date||1/01/23 → …|