Scalable Algorithms for Deterministic Global Optimization With Parallel Architectures

复杂的系统无处不在：从农业供应链、废水处理和公共供水系统，到为住宅和工业建筑供暖、制冷和照明的能源/电力基础设施。使加工工业脱碳，特别是与食品、能源和水有关的工业脱碳，具有特别和及时的重要性。工程师有一个永恒的使命，即改善这些支持和改善社会的复杂系统的健康、安全和稳健性。然而，创新本质上增加了复杂性，因此，解决复杂和相互关联的挑战的努力，包括设计新系统和改进现有系统，严重依赖于计算建模、仿真和基于优化的方法。本提案旨在解决两个主要挑战：(1)当前计算优化方法的性能限制了它们对简化、低复杂性问题的适用性；(2)大学工程项目在整个课程中往往缺乏连贯的计算思维活动。解决(1)将缓解当前的计算瓶颈，并扩大可解决的复杂问题的规模和范围。解决(2)不仅有助于培养下一代工程师的计算建模方法，而且提高他们的整体解决问题的能力。该项目的研究目标是开发可扩展的确定性全局优化（DGO）算法和开源软件实现，通过利用并行化的替代流计算架构，实现更高复杂性模型的解决方案，包括第一原理模型和涉及非线性（偏）微分和代数方程的机器学习元素。本研究的意义在于通过开发一种新的分支定界确定性搜索算法来解锁DGO图形处理单元（gpu）的大规模并行计算性能。其结果将大大加快目前的技术水平，这将使解决食品-能源-水（FEW）应用中出现的更大规模、更复杂的问题成为可能。第一个主要创新是在任意感兴趣的域上自动生成优化公式中非凸函数的凸/凹松弛的源代码表示及其子梯度的方法。第二个主要创新是可扩展的gpu兼容并行DGO算法和开源软件实现，用于保证非凸程序的解决方案。该项目将把拟议的研究与教育活动结合起来，旨在将不同的学生群体转变为熟练的计算思考者。该项目将支持培训学生从优化环境中理解系统模型的复杂性，从而更好地理解基于优化方法的实用性。该项目将提供方法、工具和培训模块，以满足工程领域当前和未来的技术劳动力培训需求，这些领域将越来越依赖于优化创新。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。

Complex systems are everywhere: from agricultural supply chains, wastewater treatment and public water systems, to the energy/power infrastructure that heats, cools, and light residential and industrial buildings. Decarbonizing process industries, especially as they relate to food, energy, and water, is of particular and timely importance. Engineers have an ever-constant mission of improving the health, safety, and robustness of these complex systems that support and improve society. However, innovation inherently increases complexity and, therefore, the efforts to solve complex and interconnected challenges, which include designing new systems and improving existing systems, rely heavily on computational modeling, simulation, and optimization-based approaches. There are two major challenges that this proposal aims to address: (1) the current performance of computational optimization approaches limits their applicability to simplified, lower-complexity problems, and (2) university engineering programs often lack cohesive computational-thinking activities throughout their curricula. Solving (1) will alleviate the current computational bottlenecks and broaden the scale and scope of complex problems that can be solved. Solving (2) will not only help train the next generation of engineers on computational modeling approaches but improve their overall problem-solving skills.The research objective of this project is to develop scalable deterministic global optimization (DGO) algorithms and open-source software implementations by exploiting alternative stream computing architectures for parallelization, to enable the solution of higher complexity models that include first-principles models and machine learning elements involving nonlinear (partial) differential and algebraic equations. The significance of the proposed work lies in unlocking the massive parallel computing performance of graphical processing units (GPUs) for DGO with the development of a new branch-and-bound deterministic search algorithm. The result will be a significant speedup over the current state of the art, which will enable the solution of larger-scale higher-complexity problems that arise in food-energy-water (FEW) applications, among others. The first major innovation is a method for automatically generating source code representations of convex/concave relaxations of nonconvex functions in the optimization formulation, and subgradients thereof, on arbitrary domains of interest. The second major innovation is a scalable GPU-compatible parallel DGO algorithm and open-source software implementation for the guaranteed solution of nonconvex programs. This project will align the proposed research with educational activities aimed at transforming a diverse cohort of students into skilled computational thinkers. This project will support the training of students to understand the complexity of systems models from an optimization context to better understand the practicality of optimization-based approaches. This project will deliver methods, tools, and training modules to serve the immediate and future technology workforce training needs of engineering fields that will increasingly depend on optimization for innovation.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.