A Fuzzy Hybrid Sequential Design Strategy for Global Surrogate Modeling of High-Dimensional Computer Experiments

Complex real-world systems can accurately be modeled by simulations. Evaluating high-fidelity simulators can take several days, making them impractical for use in optimization, design space exploration and analysis. Often, these simulators are approximated by relatively simple math known as a surrogate model. The data points to construct this model are simulator evaluations meaning the choice of these points is crucial: each additional data point can be very expensive in terms of computing time. Sequential design strategies offer a huge advantage over one-shot experimental design because information gathered from previous data points can be used in the process of determining new data points. Previously, LOLA-Voronoi was presented as a hybrid sequential design method which balances exploration and exploitation: the former involves selecting data points in unexplored regions of the design space, while the latter suggests adding data points in interesting regions which were previously discovered. Although this approach is very successful in terms of the required number of data points to build an accurate surrogate model, it is computationally intensive. This paper presents a new approach to the exploitation component of the algorithm based on Fuzzy logic. The new approach has the same desirable properties of the old method but is less complex, especially when applied to high-dimensional problems. Experiments on several test problems show the new approach is a lot faster, without losing robustness or requiring additional samples to obtain similar model accuracy.