GOPS: efficient RBF surrogate global optimization algorithm with high dimensions and many parallel processors including
- PDF / 3,518,838 Bytes
- 37 Pages / 439.37 x 666.142 pts Page_size
- 15 Downloads / 191 Views
GOPS: efficient RBF surrogate global optimization algorithm with high dimensions and many parallel processors including application to multimodal water quality PDE model calibration Wei Xia1 · Christine Shoemaker1,2 Received: 13 December 2019 / Revised: 24 August 2020 / Accepted: 24 August 2020 © The Author(s) 2020
Abstract This paper describes a new parallel global surrogate-based algorithm Global Optimization in Parallel with Surrogate (GOPS) for the minimization of continuous black-box objective functions that might have multiple local minima, are expensive to compute, and have no derivative information available. The task of picking P new evaluation points for P processors in each iteration is addressed by sampling around multiple center points at which the objective function has been previously evaluated. The GOPS algorithm improves on earlier algorithms by (a) new center points are selected based on bivariate non-dominated sorting of previously evaluated points with additional constraints to ensure the objective value is below a target percentile and (b) as iterations increase, the number of centers decreases, and the number of evaluation points per center increases. These strategies and the hyperparameters controlling them significantly improve GOPS’s parallel performance on high dimensional problems in comparison to other global optimization algorithms, especially with a larger number of processors. GOPS is tested with up to 128 processors in parallel on 14 synthetic black-box optimization benchmarking test problems (in 10, 21, and 40 dimensions) and one 21-dimensional parameter estimation problem for an expensive real-world nonlinear lake water quality model with partial differential equations that takes 22 min for each objective function evaluation. GOPS numerically significantly outperforms (especially on high dimensional problems and with larger numbers of processors) the earlier algorithms SOP and PSDMADS-VNS (and these two algorithms have outperformed other algorithms in prior publications). Keywords PDE-constrained optimization · Surrogate models · Parallel computing · Water quality models · Global optimization · Multi-modal and black-box objective Electronic supplementary material The online version of this article (https://doi.org/10.1007/s1108 1-020-09556-1) contains supplementary material, which is available to authorized users. Extended author information available on the last page of the article
13
Vol.:(0123456789)
W. Xia, C. Shoemaker
1 Introduction Optimization of numerical simulation models is important because they are widely used in numerous real-world applications in many fields, including science and engineering. One essential category of computer simulation models is those that are computing solutions to a system of partial differential equations (PDE) on, for instance, surface water and groundwater problems (Culver and Shoemaker 1992; Gorelick et al. 1993; Hinkelmann 2006; Pinder and Gray 1977; Yeh 2015), and aerodynamics problems (Bons et al. 2019; Sóbester and Forrester
Data Loading...
