Adaptive in situ model refinement for surrogate-augmented population-based optimization

Abstract

In surrogate-based optimization (SBO), the deception issues associated with the low fidelity of the surrogate model can be dealt with in situ model refinement that uses infill points during optimization. However, there is a lack of model refinement methods that are both independent of the choice of surrogate model (neural networks, radial basis functions, Kriging, etc.) and provides a methodical approach to preserve the fidelity of the search dynamics, especially in the case of population-based heuristic optimization processes. This paper presents an adaptive model refinement (AMR) approach to fill this important gap. Therein, the question of when to refine the surrogate model is answered by a novel hypothesis testing concept that compares the distribution of model error and distribution of function improvement over iterations. These distributions are respectively computed via a probabilistic cross-validation approach and by leveraging the probabilistic improvement information uniquely afforded by population-based algorithms such as particle swarm optimization. Moreover, the AMR method identifies the size of the batch of infill points needed for refinement. Numerical experiments performed on multiple benchmark functions and an optimal (building energy) planning problem demonstrate AMR’s ability to preserve computational efficiency of the SBO process while providing solutions of more attractive fidelity than those provisioned by a standard SBO approach.