Efficient Global Dynamic Optimization using Dynamic Cut Generation and Domain Reduction Techniques

动态优化是一种用于优化控制动态过程的计算方法。有效的动态优化代码已经成为许多行业的关键支持技术，在盈利能力、效率和安全性方面带来了巨大的收益。然而，动态优化问题通常会出现多个次优局部解。在许多应用中，使用这些次优解而不是理想的全局最优解会导致重大的经济损失和性能下降；这甚至会产生昂贵或危险的不可靠结论。该项目旨在开发更有效的全局优化算法，以解决化学、制药和航空航天工业中广泛应用的各种问题。本项目旨在提高全局动态优化（GDO）代码的效率，通过开发分支定界（B&amp；B）算法中的切割生成和域约简技术来解决非凸代数优化问题。切割生成广义上是指通过施加在原始模型中冗余而不是在松弛中冗余的约束来加强非凸问题的凸松弛的方法。相比之下，域约简是指使用问题约束或已知可行目标值收紧B&amp；B节点中决策变量的边界的方法。对这种GDO技术的研究很好地激发了对标准非线性规划（nlp）的类比。先前关于GDO的工作主要集中在松弛方法上，这些松弛方法可以被认为是用于nlp的最基本方法的动态扩展（特别是那些基于因子分解的方法，如McCormick松弛）。但是，仅基于这些技术的B&amp；B代码在大多数情况下效率极低。相比之下，现代B&amp；B代码通常解决数百个决策的问题，利用丰富的切割生成和域约简技术工具箱。这强烈地表明，动态问题的类似技术将深刻地影响GDO算法的效率。除了培训研究生外，拟议的研究还包括通过克莱姆森大学的创造性探究项目培训本科生研究人员，以及通过克莱姆森大学为期六周的暑期研究实习生项目培训即将毕业的高中生。该项目还包括开发一个为期半天的实践研究活动，旨在教育女性和少数族裔在STEM领域的职业机会，由克莱姆森大学科学与工程女性项目（WISE）和教育充实与保留项目（PEER）主办。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。

Dynamic optimization is a computational approach used to optimally control dynamic processes. Effective dynamic optimization codes have become a key enabling technology in many industries, leading to substantial gains in profitability, efficiency, and safety. However, dynamic optimization problems commonly exhibit multiple sub-optimal local solutions. Use of these sub-optimal solutions instead of the desired globally optimal solution can lead to significant economic loss and performance degradation in many applications; this can even produce expensive or dangerous unreliable conclusions. This project aims to develop more efficient global optimization algorithms for types of problems that arise in a broad spectrum of applications in the chemical, pharmaceutical and aerospace industries.This project aims to increase the efficiency of global dynamic optimization (GDO) codes by developing cut generation and domain reduction techniques in the branch and bound (B&B) algorithm for solving nonconvex algebraic optimization problems. Cut generation refers broadly to methods that strengthen the convex relaxation of a nonconvex problem by imposing constraints that are redundant in the original model, but not in the relaxation. In contrast, domain reduction refers to methods that tighten the bounds on the decision variables in a B&B node using the problem constraints or a known feasible objective value. Research into such techniques for GDO is very well motivated by analogy to standard nonlinear programs (NLPs). Prior work on GDO has focused on relaxation methods that can be considered dynamic extensions of the most basic methods used for NLPs (specifically those based on factorable decomposition, such as McCormick relaxations). However, B&B codes based solely on these techniques are extremely inefficient in most cases. In contrast, modern B&B codes, which routinely solve problems with hundreds of decisions, utilize a rich toolbox of cut generation and domain reduction techniques. This strongly suggests that analogous techniques for dynamic problems will profoundly impact the efficiency of GDO algorithms. In addition to training graduate students, the proposed research will involve training of undergraduate researchers through Clemson's Creative Inquiry Program and rising high school seniors through Clemson's six-week Summer Program for Research Interns. The project also includes the development of a half-day long hands-on research activity for educating women and minorities about career opportunities in STEM fields, hosted by Clemson's Women in Science and Engineering (WISE) Program and the Programs for Educational Enrichment and Retention (PEER).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.