Global Optimization Approach in Chemical Engineering Design and Science Problems

近年来，人们在非线性规划（NLP）和混合整数非线性规划（MINLP）问题的局部优化算法的理论发展、算法研究、计算测试、化学工程设计和科学应用方面付出了大量的努力。目前存在许多局部优化算法及其有效实现，可用于小型、中型和大型问题。关于全局优化方法的理论发展、算法方法、计算测试以及在化学工程设计和科学问题中的应用的系统研究要少得多。本研究的目标是开发和应用理论、算法和计算技术来解决各种化学工程设计和科学应用中的全局优化问题（GOP）。PI将使用原始松弛对偶全局优化算法研究几类全局优化问题。他将特别关注：(1)松弛对偶子问题的新性质和新公式；(2)相和化学反应平衡系统的设计；(3)分离、热回收网络和反应器系统的工艺综合；(4)过程设计和控制中出现的双层线性和非线性优化问题；(5)最优结构(s)原子和分子簇的确定；(6)发展了一种平行的原始松弛二元方法。

A lot of effort in the recent past has been expended on theoretical development, algorithmic investigation, computational testing, and chemical engineering design and science applications of the local optimization algorithms for nonlinear programming (NLP) and mixed-integer nonlinear programming (MINLP) problems. There now exist a number of local optimization algorithms and their efficient implementations that are used for small, medium, and large scale problems. There has been much less systematic study on the theoretical developments, algorithmic methodology, computational testing, and application to chemical engineering design and science problems of global optimization approaches. The goal of this research is to develop and apply theoretical, algorithmic and computational techniques for global optimization problems (GOP) that arise in a variety of chemical engineering design and science applications. The PI will investigate several classes of global optimization problems using a primal-relaxed dual global optimization algorithm. In particular, he will focus on: (1) new properties and new formulations of the relaxed dual subproblems; (2) the design of phase and chemical reaction equilibrium systems; (3) the process synthesis of separations, heat recovery networks and reactor systems; (4) bilevel linear and nonlinear optimization problems arising in process design and control; (5) optimum structure(s) determination of clusters of atoms and molecules; and (6) the development of a parallel primal relaxed dual, GOP, approach.