Adaptive in situ model refinement for surrogate-augmented population-based optimization
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RESEARCH PAPER
Adaptive in situ model refinement for surrogate-augmented population-based optimization Payam Ghassemi1 · Ali Mehmani2 · Souma Chowdhury1 Received: 16 October 2019 / Revised: 9 March 2020 / Accepted: 29 March 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
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. Keywords Adaptive model refinement · Surrogate-based optimization · Predictive estimation of model fidelity · Sequential sampling · Particle swarm optimization
1 Introduction Optimizing complex systems often involves computationally expensive simulations (e.g., FEA) to evaluate system behavior and estimate quantities of interest. While computationally efficient alternatives are often available for system or function evaluation, for example in the form of simplified analytical models, coarse grid models, or surrogate
Responsible Editor: Nathalie Bartoli Souma Chowdhury
[email protected] Payam Ghassemi [email protected] 1
Department of Mechanical and Aerospace Engineering, University at Buffalo, Buffalo, NY, 14260, USA
2
Data Science Institute, Columbia University, New York, NY, 10027, USA
models (to name a few), they tend to compromise on the fidelity of their estimations. These low-fidelity models often mislead the search process during optimization, leading to sub-optimal or even infeasible solutions. Variable-fidelity optimization approaches seek to address these issues and offer attractive trade-offs between computational efficiency and fidelity of the optimal solutions obtained—i.e., the ability to quickly arrive at optimal solutions that can be relied u
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