Deterministic Global Optimization in Systems Engineering

克里斯托杜洛斯·A·弗洛达斯研究所：普林斯顿大学提案编号：0002777这项研究的主要目标是为各种化学工程设计和合成问题中出现的全局优化问题以及计算化学和生物学中出现的核磁共振结构优化问题开发理论、算法和计算技术。这些方法将补充化学过程系统的数学建模的努力，并有助于分子、多肽和蛋白质的设计。PI计划研究(1)将他的全局优化框架ABB扩展到参数估计和控制中出现的微分代数模型；(2)开发一种新的基于全局优化的方法来处理在不确定情况下设计中出现的一般两层和多层非线性模型，以及过程综合、设计和操作之间的相互作用；(3)开发用于过程综合中出现的凸和非凸混合整数非线性优化模型的新方法；(4)利用核磁共振实验提供的稀疏约束来预测多肽的结构；(5)开发全局优化工具，研究上述(1)-(4)的ABB全局优化方法的分布式计算框架，这些将应用于几类化工过程综合、设计、控制和计算化学问题。这项工作的创新特点包括：(A)用于具有微分和代数约束的模型的新的全局优化方法；(B)用于双层和多级非线性模型的新的全局优化方法；(C)用于混合整数非线性优化问题的结合了强割平面和分枝定界原理的新方法；(D)通过计算化学和生物学中产生的核磁共振约束来确定多肽和蛋白质结构的新方法；以及(E)用于计划工作的所有任务的顺序和分布式计算工具。

ABSTRACTPI: Christodoulos A. Floudas Institution: Princeton UniversityProposal Number: 0002777The primary objective of this research is to develop theoretical, algorithmic and computational techniques for global optimization problems that arise in a variety of chemical engineering design and synthesis problems, as well as NMR structure refinement problems that arise in computational chemistry and biology. These methods will complement efforts in the mathematical modeling of chemical process systems and aid the search in the design of molecules, peptides, and proteins. The PI plans to investigate (1) the extension of his global optimization framework, aBB, to differential algebraic models that arise in parameter estimation and control; (2) the development of a new global optimization-based approach for general bilevel and multilevel nonlinear models that arise in the design under uncertainty, and the interaction of process synthesis, desing and operations; (3) the development of novel approaches for convex and nonconvex mixed integer nonlinear optimization models that arise in process synthesis; (4) the structure prediction of peptides with the presence of sparse restraints provided by NMR experiments; and (5) development of global optimization tools and the study of a distributed computing framework for the aBB global optimization approach for (1) - (4) above.These will be applied to several classes of chemical process synthesis, design, control and computational chemistry problems. The innovative features of this work consist of: (a) new global optimization methods for models with differential and algebraic constraints; (b) new global optimization approaches for bilevel and multilevel nonlinear models; (c) new approaches that combine strong cutting planes and branch and bound principles for mixed integer nonlinear optimization problems; (d) new methods for the determination of the structure of peptides and proteins through the NMR restraints that arise in computational chemistry and biology; and (e) sequential and distributed computational tools for all tasks of the planned work.