RUI: Global Optimization of Chance-Constrained Programming for Reliable Process Design

对用于化工过程优化设计的数学模型的准确性的不完全了解可能会导致燃料、疫苗、制造食品和其他化学产品的质量下降，可能会产生进一步的经济、安全、健康和环境影响。当前的计算机辅助过程优化方法在处理不确定性方面存在缺陷，这是因为严格评估复杂、高度相互关联的化工厂的设计的计算成本很高，不可避免地导致保守的、次优的设计解。受美国先进化学制造技术面临的这一挑战的推动，该项目将建立全新的确定性全局优化技术，并结合灵活的数据驱动建模方法，使其能够在不牺牲安全性的情况下设计高性能的不确定化学过程。由此产生的化学产品和工艺将以可预见的概率满足质量和运营限制，同时将工厂和运营成本降至最低。本项目将开展的基础性研究将加深对如何将数据驱动的不确定性模型用于优化以简化确定真正最优解的过程的理解。这项提议将通过在工艺设计和化学工程实验室课程中增加新的内容、指导本科生研究人员以及为K-12学生组织讲习班来支持研究和教育活动的整合。这项工作将培养来自传统代表性不足群体的新一代学生使用数据分析和全局优化策略来解决过程设计问题。本项目的目标是建立和测试一个全局优化框架来求解不确定条件下的化工过程设计机会约束规划(CCP)。拟议的研究计划将侧重于推进单阶段和两阶段CCP背后的理论，该理论受制于依赖于一般不确定性的大规模联合机会约束。在单级CCP中，将研究高斯混合模型(GMM)在描述一般不确定性方面的有效性。为实现这一目标，CCP-GMM框架将被重新制定为双凸结构。在两阶段CCP中，分段线性决策规则将与GMM相结合，以便于更灵活地表示策略。然后，通过结合二阶锥体松弛、分枝定界法、重构线性化技术和基于最优性的区间约简，所得到的双凸问题可以求解到全局最优。构建了植物油调合实验，以食用油成本最小为目标，以粘度、能量和总脂肪为不确定约束条件，对所提出的优化算法进行了验证。拟议的研究方案具有变革的潜力，因为它寻求通过将确定的GMM嵌入优化过程来改进优化过程中可用数据的使用。这种创新的策略可以绕过积分对机会约束的困难，从而大大提高了全局优化的计算效率。如果证明有效，建议的CCP全局优化算法可以广泛应用于化工、石油、燃料和制药行业的复杂设计问题，以降低成本、增强安全性和减轻环境影响。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。

Incomplete knowledge of the accuracy of mathematical models used for the optimization-based design of chemical processes can lead to degraded quality of fuels, vaccines, manufactured foods, and other chemical products, potentially giving rise to further economic, safety, health, and environmental effects. Current computer-aided process optimization methods are deficient in handling uncertainties due to the high computational cost of rigorously evaluating the designs of complex, highly interconnected chemical plants, inevitably resulting in conservative, sub-optimal design solutions. Motivated by this challenge to advancing U.S. chemical manufacturing technology, this project will establish entirely new, deterministic global optimization techniques combined with flexible data-driven modeling methods that will make it possible to design high-performance chemical processes under uncertainties without sacrificing safety. The resulting chemical products and processes will meet quality and operational constraints with predictable probability while minimizing the plant and operational costs. The fundamental research to be carried out in this project will build a deeper understanding of how data-driven uncertainty models can be used in optimization to simplify the process of identifying the true optimal solution. This proposal would support the integration of research and educational activities through the addition of new content to process design and chemical engineering laboratory courses, the mentoring of undergraduate researchers, and organizing workshops for K-12 students. This work will educate a new generation of students from traditionally underrepresented groups to solve process design problems using data analytics and global optimization strategies.The objective of this project is to build and test a global optimization framework to solve chance-constrained programs (CCPs) formulated for chemical process design under uncertainties. The proposed research plan will focus on advancing the theory behind single- and two-stage CCP subject to large-scale joint chance constraints affinely dependent on general uncertainties. In the single-stage CCP, Gaussian Mixture Models (GMMs) will be investigated for their effectiveness in describing generic uncertainties. To achieve this objective, the CCP-GMM framework will be reformulated into a bi-convex structure. In the two-stage CCP, a piecewise linear decision rule will be integrated with GMM to facilitate more flexible policy representations. The resulting bi-convex problem then can be solved to the global optimum through a combination of second-order cone relaxations, branch-and-bound methods, reformulation-linearization techniques, and optimality-based interval reductions. A vegetable oil blending experiment will be constructed to validate the proposed optimization algorithms, with an objective of edible oil cost minimization subject to the viscosity, energy, and total fat constraints as uncertainties. The proposed research program has transformative potential in that it seeks to improve the use of available data in the optimization process by embedding the identified GMM into the optimization process. This innovative strategy can bypass the difficulty of integral over chance constraints and enable much improved computational efficiency of global optimization. If proven effective, the proposed global optimization algorithms for CCP can be widely applied to complex design problems in the chemical, oil, fuel, and pharmaceutical industries, to reduce cost, enhance safety, and mitigate environmental impact.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.