AI-enabled Automated Algorithm Selection and Configuration for Mathematical Optimization Problems

数学优化是化工决策的基石。在与可再生能源相互作用的化工过程系统的设计和实时运行、弹性供应链网络的设计和化工生产设施的可持续运行等问题中，底层过程的复杂行为和多个时间和空间尺度的存在导致了大规模和复杂的优化配方。用于解决这些问题的算法已经并且还在继续被开发，但是(I)它们的实现是具有挑战性的和计算密集的，因为它们涉及许多步骤，以及(Ii)不清楚哪种算法更适合于给定的问题。在这个研究项目中，将使用最先进的人工智能(AI)和机器学习(ML)工具来选择和实现针对给定问题的最佳优化算法。这些方法将被自动化，并纳入开放源码软件，以促进行业从业者和学术研究人员解决复杂问题。在这个研究项目中，研究生将接受基础研究方面的培训，涉及化学工程、数学优化和数据科学。在明尼苏达州明尼阿波利斯、明尼苏达州农村和明尼苏达州的美国印第安人、苗族和索马里社区开展的外联活动将突出数据科学在化学工业中日益重要的地位，并将旨在激励化学工程领域的职业生涯。这项研究将利用人工智能(AI)和机器学习(ML)中的最先进方法，使最先进的优化算法能够自动选择和配置，以解决过程系统工程中出现的非线性和混合整数非线性问题。这项研究将涉及以下任务：(I)将开发一个图神经网络框架来表示一般的非线性优化问题，以捕捉关于变量和约束的详细信息；(Ii)将使用几何深度学习方法来自动选择最佳解策略和调整优化算法；(Iii)将使用可解释的人工智能方法来解码优化问题与优化求解器的计算性能之间的关系。将在开源软件中开发和实现的优化框架将通过选择最合适的求解方法和优化的求解算法，促进过程系统研究人员有效地解决复杂决策问题的能力。此外，该框架将使检测当前建模实践和/或优化算法中可能存在的性能瓶颈成为可能，并反过来指导问题的重新制定或算法改进。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Mathematical optimization is the cornerstone of decision-making in chemical engineering. In problems such as the design and real-time operation of chemical process systems interacting with renewable energy resources, the design of resilient supply chain networks, and the sustainable operation of chemical production facilities, the complex behavior of the underlying processes and the presence of multiple temporal and spatial scales lead to large-scale and complex optimization formulations. Algorithms for solving these problems have been and continue to be developed, but (i) their implementation is challenging and computationally intensive since they involve numerous steps, and (ii) it is not clear a-priori which algorithm is better suited for a given problem. In this research program, state-of-the-art artificial intelligence (AI) and machine learning (ML) tools will be employed to select and implement the best optimization algorithm for a given problem. These methods will be automated and incorporated in open-source software to facilitate the solution of complex problems by industry practitioners and academic researchers alike. In this research program, graduate students will be trained in fundamental research cutting across chemical engineering, mathematical optimization, and data science. Outreach activities to high schools in Minneapolis, rural Minnesota, and the American Indian, Hmong, and Somali communities in Minnesota will highlight the increasing importance of data science in the chemical industry and will aim to motivate careers in chemical engineering. This research will leverage state-of-the-art methods in artificial intelligence (AI) and machine learning (ML) to enable the automated selection and configuration of state-of-the-art optimization algorithms for the solution of nonlinear and mixed integer nonlinear problems that arise in process systems engineering. The research will address the following tasks: (i) a graph neural network framework will be developed to represent generic nonlinear optimization problems in a form that captures detailed information on the variables and constraints; (ii) geometric deep learning methods will be employed for the selection of the best solution strategy and the tuning of optimization algorithms in an automated manner; (iii) explainable AI methods will be employed to decode the relationship between optimization problems and the computational performance of optimization solvers. The optimization framework to be developed and implemented in open-source software will facilitate process systems researchers’ ability to solve complex decision-making problems efficiently by selecting the most appropriate solution method and optimally tuned solution algorithm. In addition, this framework will make possible detection of possible performance bottlenecks in current modeling practices and/or optimization algorithms, and in turn guide problem reformulation or algorithm improvements.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.