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技术，导致盈利能力，效率和安全性的大幅提高。然而，动态优化问题通常表现出多个次优局部解。 使用这些次优解决方案而不是期望的全局最优解决方案可能导致许多应用中的显著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结论。本研究课题的目的是针对化学、制药、航空航天等领域的广泛应用，开发更有效的全局优化算法。本研究课题的目的是，在求解非凸代数优化问题的分支定界（B B）算法中，开发切割生成和区域缩减技术，提高全局动态优化（GDO）代码的效率。 割生成广义上是指通过施加在原始模型中冗余但在松弛中不冗余的约束来加强非凸问题的凸松弛的方法。相比之下，域缩减是指使用问题约束或已知可行目标值来收紧B B节点中的决策变量的界限的方法。研究这些技术的GDO是非常好的动机类比标准的非线性规划（NLP）。GDO之前的工作主要集中在松弛方法上，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子分解的方法，如McCormick松弛）。然而，仅基于这些技术的B B码在大多数情况下是极其低效的。相比之下，现代B B代码通常解决数百个决策的问题，利用切割生成和域缩减技术的丰富工具箱。这有力地表明，类似的动态问题的技术将深刻影响GDO算法的效率。除了培训研究生外，拟议中的研究还将涉及通过克莱姆森的创造性探究项目培训本科研究人员，以及通过克莱姆森为期六周的研究实习生暑期项目培训高中高年级学生。该项目还包括开展为期半天的实践研究活动，教育妇女和少数民族了解STEM领域的职业机会，由克莱姆森的妇女在科学和工程（WISE）计划和教育丰富和保留（对等）计划主办该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的评估被认为值得支持。影响审查标准。

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.