Surrogate-based optimization method with adaptive sampling

In a typical engineering design workflow, optimization is a highly iterative process, requiring several evaluations of the performance of the item that is being designed. The main goal of the design workflow is to create a cost-effective solution that is fit for purpose. Cost is typically a significant driver in the optimization design process. Complex and costly experiments or situations can be reduced in number by using an appropriate design of experiment (DoE). Two popular DoE are the Latin Hypercube and the Optimal Latin Hypercube (OLH). In combination with DoE, the use of surrogate based optimization process is growing strongly in industry. Using a surrogate model with an effective interpolation and sampling method reduces the number of numerical simulations that are required to construct a database to a specific confidence level. The surrogate model can then be interrogated to identify design parameters that lead to the best design performance, within a pre-defined parameter space search area. In this work, a surrogate based optimization method with and without adaptive sampling is presented. For the design of experiment, the Optimal Latin Hypercube method is used. This is combined with Kriging modelling (KRG), which provides a surrogate model for the engineering performance (functional performance) of the item being designed. The Kriging model is selected as it can give a good compromise between the solution cost and the prediction accuracy. The low cost overhead of the Kriging model and its robustness are attractive for accelerating the design iterations used in industry. A newly adaptive sampling technique is presented for obtaining more accurate predictions from Kriging model. The technique is also based on the design of the experiment Optimal Latin Hypercube method. An example application of the technique is given, which provided positive but modest improvements in performance with respect to judiciously selected initial sampling. However, the adaptive sampling technique appears to be an interesting approach in its own right. This approach has the potential to identify more optimal configurations in problems where the response function has greater complexity in shape, a complexity that may not be known a priori and that the adaptive sampling should be able to uncover.