Studies of Global Optimization in Process Systems Engineering

优化算法的理论和算法研究及其在工艺合成、设计和控制应用中的计算测试已经花费了大量的精力。最近对全局优化及其在化学工程问题中的应用的兴趣是由于：(1)大量的工艺合成、设计和控制问题都是全局优化问题；(2)现有的局部非线性优化方法要么无法得到可行解，要么陷入与全局解值不同的局部最优解；(3)与局部解相比，全局最优解可能具有非常不同的物理解释（例如，在相平衡中，局部解可能提供不正确的平衡相类型预测，以及每个相中的组分组成）。本研究的主要目标是发展理论、算法和计算技术，以解决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分子构象问题。这些进展将补充化学过程系统的严格数学建模方面的努力，并有助于在分子、多肽和蛋白质的设计方面的研究。PI计划调查(i)将他最近开发的全局优化方法aBB扩展到过程综合中使用的一般约束非线性优化问题和混合整数非线性问题；（ii）开发了一种新的基于全局优化的方法，用于确定某些非线性约束方程组的所有解，这些方程组在具有多个稳态的过程系统（例如反应器、精馏塔）中具有重要应用；(3)非线性耳模型的参数估计问题；（iv）不确定条件下过程系统分析中出现的双层非线性优化问题；(v)寡肽、多肽和蛋白质的三维结构预测；（vi）为aBB全球优化方法开发分布式计算框架，并为(i)到(v)开发计算工具。

Floudas - Abstract - 9528150 Significant effort has been expended toward theoretical and algorithmic studies of optimization algorithms and their computational testing in applications that arise in process synthesis, design and control. Recent interest in global optimization and its application to chemical engineering problems is due to the fact that: (1) a large number of process synthesis, design, and control problems are global optimization problems; (2) existing local nonlinear optimization approaches may either fail to obtain a feasible solution or are trapped to a local optimum solution which may differ in value from the global solution; and (3) the global optimum solution may have a very different physical interpretation when it is compared to local solutions (e.g. in phase equilibrium a local solution may provide incorrect prediction of types of phases at equilibrium, as well as the components' composition in each phase). The 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 molecular conformation problems that arise in computational chemistry and biology. These advances will complement efforts in the rigorous mathematical modeling of chemical process systems and aid the search in the design of molecules, peptides, and proteins. The PI plans to investigate (i) the extension of his recently developed global optimization approach, aBB, to general constrained nonlinear optimization problems and mixed-integer nonlinear problems which are employed in process synthesis; (ii) the development of a new global optimization based approach for the determination of all solutions of certain classes of nonlinearly constrained systems of equations which has important applications in process systems that exhibit multiple steady states (e.g., reactors, distillation columns); (iii) the parameter estimation problems of nonlin ear models; (iv) the bilevel nonlinear optimization problems that arise in the analysis of process systems under uncertainty: (v) the three-dimensional structure prediction of oligopeptides, peptides, and proteins; and (vi) the development of a distributed computing framework for the aBB global optimization approach and the development of computational tools for (i) through (v).