AF: Small: Parallel Global Optimization Algorithms with Asynchrony, Adaptive Re-Planning, and Response Surfaces for Costly Simulations

AF：小型：具有异步、自适应重新规划和响应面的并行全局优化算法，用于昂贵的模拟

• 批准号: 1116298
• 负责人: Christine Shoemaker
• 金额: $ 49.99万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-09-01 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1116298&HistoricalAwards=false
• 关键词: AF; Small; Parallel; Global; Optimization

Optimization can be used for designing lower cost or more efficient strategies and selecting model parameters so that models can accurately predict system behavior. However, for computationally expensive simulation models, conventional optimization can require infeasibly long computation times (months or years) The focus of this research is to develop a method (called POARS) to use parallel processors to find the global minimum of a function with relatively few simulations. Examples of such computationally expensive simulation models are systems of nonlinear partial differential equations used to describe fluid flow and reactive chemistry transport that arise in many applications including groundwater and atmospheric modeling. Because such models can take hours or even days to complete a single simulation, it is important to have algorithms that find good optimal solutions with few simulations, which the proposed research achieves by integrating surrogate response surfaces into the optimization. The algorithm will be applied to real models (based on field data) including a groundwater model (partial differential equations) and two watershed models (spatially distributed difference equations). The POARS algorithm incorporates multiple novel features including Ensembles, Asynchronous Parallelism with Adaptive Re-planning and the use of multiple optimization methods on the response surface, where many evaluations can be made cheaply. The asynchronous aspect enables new simulations to start before simulations on other parallel processors are complete. The response surface is based on an ensemble of response surfaces including mixture models based on Dempster-Schafer theory. A proof of almost sure convergence of POARS will be given. The research will couple the optimization method on M processes with parallel simulations each on N processes to efficiently use MN processors.

优化可以用于设计成本更低或效率更高的策略和选择模型参数，使模型能够准确地预测系统行为。然而，对于计算昂贵的仿真模型，传统的优化可能需要不可行的长计算时间（数月或数年）。本研究的重点是开发一种方法（称为POARS），使用并行处理器在相对较少的模拟中找到函数的全局最小值。这种计算代价昂贵的模拟模型的例子是用于描述流体流动和反应化学输运的非线性偏微分方程系统，这些系统出现在许多应用中，包括地下水和大气模型。由于这样的模型可能需要数小时甚至数天才能完成一次模拟，因此重要的是要有能够在很少的模拟中找到良好最优解的算法，本研究通过将代理响应面集成到优化中来实现这一目标。该算法将应用于实际模型（基于现场数据），包括一个地下水模型（偏微分方程）和两个流域模型（空间分布差分方程）。POARS算法结合了多个新特性，包括集成、异步并行和自适应重新规划，以及在响应面上使用多种优化方法，可以便宜地进行许多评估。异步方面允许在其他并行处理器上的模拟完成之前开始新的模拟。响应面是基于基于Dempster-Schafer理论的混合模型的响应面集合。给出了POARS几乎肯定收敛的证明。本研究将M个进程的优化方法与N个进程的并行模拟相结合，以有效地利用MN个处理器。