Variable-fidelity optimization with in-situ surrogate model refinement

Owing to the typical low fidelity of surrogate models, it is often challenging to accomplish reliable optimum solutions in Surrogate-Based Optimization (SBO) for complex nonlinear problems. This paper addresses this challenge by developing a new model-independent approach to refine the surrogate model during optimization, with the objective to maintain a desired level of fidelity and robustness "where" and "when" needed. The proposed approach, called Adaptive Model Refinement (AMR), is designed to work particularly with population-based optimization algorithms. In AMR, reconstruction of the model is performed by sequentially adding a batch of new samples at any given iteration (of SBO) when a refinement metric is met. This metric is formulated by comparing (1) the uncertainty associated with the outputs of the current model, and (2) the distribution of the latest fitness function improvement over the population of candidate designs. Whenever the model-refinement metric is met, the history of the fitness function improvement is used to determine the desired fidelity for the upcoming iterations of SBO. Predictive Estimation of Model Fidelity (an advanced surrogate model error metric) is applied to determine the model uncertainty and the batch size for the samples to be added. The location of the new samples in the input space is determined based on a hypercube enclosing promising candidate designs, and a distance-based criterion that minimizes the correlation between the current sample points and the new points. The powerful mixed-discrete PSO algorithm is used in conjunction with different surrogate models (e.g., Kriging, RBF, SVR) to apply the new AMR method. The performance of the proposed AMR-based SBO is investigated through three different benchmark functions.