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 PSD-MADS-VNS (and these two algorithms have outperformed other algorithms in prior publications).

本文介绍了一种新的基于并行全局代理的新算法，即具有代理并行的全局优化（GOPS），用于最小化可能具有多个局部最小值，计算成本高且没有可用派生信息的连续黑盒目标函数。为P选择P个新评估点的任务通过围绕多个中心点进行采样来解决每次迭代中的处理器，在这些中心点之前已经评估了目标函数。GOPS算法通过以下方式对早期算法进行了改进：（a）基于先前评估的点的双变量非主导排序选择新的中心点并附加约束，以确保目标值低于目标百分位；以及（b）随着迭代的增加，数量中心数减少，每个中心的评估点数增加。与其他全局优化算法（尤其是使用大量处理器）相比，这些策略和控制它们的超参数显着提高了GOPS在高维问题上的并行性能。对于多达14个合成黑匣子优化基准测试问题（分别在10、21和40维度上）和一个21维度参数估计问题，GOPS最多可与128个处理器并行进行测试，从而获得了昂贵的现实世界非线性湖泊水质模型，具有每次目标函数评估需要22分钟的偏微分方程。GOPS在数值上显着优于早期算法SOP和PSD-MADS-VNS（尤其是在高维问题和处理器数量较大的情况下）（并且这两种算法均优于先前出版物中的其他算法）。和40维）和一个21维参数估计问题，这是一个昂贵的真实世界非线性湖泊水质模型，带有偏微分方程，每个目标函数评估需要22分钟。GOPS在数值上明显优于早期算法SOP和PSD-MADS-VNS（特别是在高维问题和处理器数量较大的情况下）（并且这两种算法均优于先前出版物中的其他算法）。和40维）和一个21维参数估计问题，这是一个昂贵的真实世界非线性湖泊水质模型，带有偏微分方程，每个目标函数评估需要22分钟。GOPS在数值上显着优于早期算法SOP和PSD-MADS-VNS（尤其是在高维问题和处理器数量较大的情况下）（并且这两种算法均优于先前出版物中的其他算法）。