Globally convergent optimization for data-dependent systems enabled through a novel data-driven branch-and-bound framework

复杂工程系统的决策取决于基于高保真仿真和/或实验生成的数据的数据驱动优化算法的发展。尽管数据驱动优化具有很大的潜力，但目前还缺乏能够为一般类型的数据依赖问题提供高质量解决方案的高效且可扩展的方法。越来越多的应用程序可以从数据驱动的优化和控制中受益，包括化学过程合成、提高石油采收率、二氧化碳封存、建筑物的能源效率等等，这是提出这项工作的动机。提出的研究重点是将传统的过程系统工程与机器学习和不确定性量化概念相结合，以克服数据依赖优化的关键挑战，这些挑战目前阻碍了它们在具有大量维度和约束的应用中的效率和可扩展性。提出的研究目标是(a)识别有效的空间和变量分解策略，以创建可处理的优化子问题；(b)利用数据和模型不确定性，从理论上制定数据依赖相关性的高估和低估近似函数；(c)针对大量具有挑战性的基准问题，以及油田作业、提高石油采收率、建筑设计和效率等具有挑战性的案例研究，研究数据驱动分支优化的收敛率和最优性界限。这项工作的中心思想是制定新的估计不足/过高的近似值，这将被纳入一个新的定制分支界搜索中，以系统地识别具有可处理的样本数量和改进的收敛率的最佳解决方案。可扩展的数据驱动优化工具和基准库将被创建，并公开提供来自著名领域的示例，如机械和结构设计、化学流程图设计、油田控制、参数估计和蛋白质折叠。还有一项计划，将数据科学概念以教学模块的形式纳入化学工程教育，这些模块将提供给整个学术界。垂直整合项目（VIP）计划也被提出，旨在吸引来自理工科的本科生作为跨学科团队的成员，解决具有挑战性的数据驱动优化问题。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Decision-making for complex engineering systems depends on the development of algorithms for data-driven optimization based on data generated either by high fidelity simulations and/or experiments. Despite the high potential of data-driven optimization, there is currently a lack of efficient and scalable methods that can provide high quality solutions for a general class of data-dependent problems. The proposed work is motivated by the increasing number of applications that can benefit from data-driven optimization and control, including chemical process synthesis, enhanced oil recovery, carbon dioxide sequestration, energy efficiency of buildings, and many more.The proposed research is focused on the integration of traditional process systems engineering with machine learning and uncertainty quantification concepts to overcome key challenges of data-dependent optimization which currently hinder their efficiency and scalability in applications with a high number of dimensions and constraints. The objectives of the proposed research are (a) the identification of efficient space and variable decomposition strategies for creating tractable optimization sub-problems, (b) the formulation of theoretically overestimating and underestimating approximating functions for data-dependent correlations by leveraging data and model uncertainty, and (c) the study of convergence rates and optimality bounds of data-driven branch-and bound optimization for a large set of challenging benchmark problems, as well as challenging case studies for oil-field operations, enhanced oil recovery and building design and efficiency. The central idea of this work is the formulation of novel under/over-estimating approximations, which will be incorporated within a novel customized branch & bound search to systematically identify optimal solutions with a tractable number of samples and improved convergence rates. Scalable data-driven optimization tools and a benchmarking library will be created and made publicly available with examples drawn from prominent fields, such as mechanical and structural design, chemical flowsheet design, oilfield control, parameter estimation, and protein folding. There is also a plan to incorporate data-science concepts into the chemical engineering education in the form of teaching modules that will be made available to the academic community at large. A Vertically Integrated Projects (VIP) program is also proposed aimed at attracting undergraduate students from science and engineering disciplines to work as members of interdisciplinary teams towards solving challenging data-driven optimization problems.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.