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

对用于化学工艺优化设计的数学模型的准确性的不完全了解可能导致燃料、疫苗、制成品和其他化学产品的质量下降，从而可能引起进一步的经济、安全、健康和环境影响。目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，这是由于严格评估复杂的高度互连的化工厂的设计的高计算成本，不可避免地导致保守的次优设计解决方案。在推动美国化学制造技术发展的挑战下，该项目将建立全新的确定性全局优化技术，结合灵活的数据驱动建模方法，使人们能够在不确定性的情况下设计高性能的化学工艺，而不会牺牲安全性。由此产生的化学产品和工艺将以可预测的概率满足质量和操作限制，同时最大限度地降低工厂和运营成本。该项目中进行的基础研究将更深入地了解数据驱动的不确定性模型如何用于优化，以简化识别真正最佳解决方案的过程。该提案将通过在工艺设计和化学工程实验室课程中增加新内容、指导本科研究人员以及为K-12学生组织研讨会来支持研究和教育活动的整合。这项工作将教育新一代的学生，从传统上代表性不足的群体，解决过程设计问题，使用数据分析和全局优化策略。该项目的目标是建立和测试一个全局优化框架，以解决机会约束规划（CCP）制定的化学过程设计下的不确定性。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，受到大规模联合机会约束，影响依赖于一般的不确定性。在单阶段CCP中，将研究高斯混合模型（GARCH）在描述一般不确定性方面的有效性。为了实现这一目标，CCP-GMM框架将被重新表述为双凸结构。在两阶段CCP中，分段线性决策规则将与GMM集成，以促进更灵活的策略表示。由此产生的双凸问题，然后可以解决的全局最优解，通过二阶锥松弛，分支定界方法，重构线性化技术，和基于最优性的区间减少的组合。植物油调配实验将被构造来验证所提出的优化算法，与食用油成本最小化的目标受到的粘度，能量，和总脂肪的约束作为不确定性。拟议的研究计划具有变革性的潜力，因为它旨在通过将识别的GMM嵌入到优化过程中来改善优化过程中可用数据的使用。该方法克服了随机积分约束的困难，提高了全局优化的计算效率。如果证明是有效的，提出的CCP全局优化算法可以广泛应用于化学，石油，燃料和制药行业的复杂设计问题，以降低成本，提高安全性，并减轻环境影响。该奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

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.