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成为许多行业的关键使能技术，从而大幅提高了盈利能力、效率和安全性。然而，动态优化问题通常表现为多个次优局部解。在许多应用中，使用这些次优解而不是期望的全局最优解可能会导致严重的经济损失和性能下降；这甚至可能产生昂贵或危险的不可靠的结论。该项目旨在开发更高效的全局优化算法，以解决化工、制药和航空航天工业中广泛应用的各种问题。该项目旨在通过开发分支定界(B&amp；B)算法中的割集生成和域缩减技术来提高全局动态优化(GDO)代码的效率。割生成泛指通过施加在原始模型中冗余但在松弛中不存在的约束来加强非凸问题的凸松弛的方法。相比之下，域缩减指的是使用问题约束或已知可行的目标值来收紧B&A；B节点中决策变量的界限的方法。类似于标准的非线性规划(NLP)，GDO技术的研究受到了很好的推动。以前关于GDO的工作集中在松弛方法上，这些方法可以被认为是用于NLP的最基本方法的动态扩展(特别是那些基于可因式分解的方法，如McCormick松弛)。然而，在大多数情况下，仅基于这些技术的B&A；B代码的效率极低。相比之下，现代的B&A；B代码利用了丰富的割集生成和域缩减技术工具箱，它们通常通过数百个决策来解决问题。这有力地表明，动力学问题的类似技术将深刻地影响GDO算法的效率。除了培养研究生，这项拟议的研究还将通过克莱姆森的创造性探究计划培训本科生研究人员，并通过克莱姆森为期六周的研究实习生暑期计划培养高三学生。该项目还包括开发一个为期半天的实践研究活动，教育妇女和少数民族在STEM领域的职业机会，由克莱姆森的女性科学和工程(WISE)计划和教育丰富和保留计划(PEER)主办。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。

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.