Novel Methods and Computational Studies for Global Optimization

CBET-0827907Floudas智能优点：该项目的目标是为全局优化问题开发新的理论、算法和计算技术。计算技术将应用于各种化工过程的设计、合成和操作问题。PIS将研究四个子领域：(I)两次连续可微函数的一类新的紧凸低估估计的发展，这将增强基于分段二次摄动的ABB(Meyer和Floudas(2005))方法，并将形成应用于各种相平衡、设计和综合问题的理论基础；(Ii)多元两次连续可微函数的紧凸低估估计的理论发展，并研究其针对二元、多线性和一般多元函数的算法发展；(Iii)基于增广拉格朗日框架的确定性全局优化的新的理论和算法方法；以及(Iv)发展新的混合全局优化方法，将改进的ABB确定性全局优化框架和增广拉格朗日方法的紧凸低估估计的有益元素与基于随机的方法相结合。PI还将研究分布式计算的实现，并将其应用于标准、扩展和通用的池化和混合应用中出现的中型和大规模非凸优化问题。通过这项研究，PI有望确定影响全局优化和方法的新的理论、算法和计算结果。PI期望得到的创新特征是：(A)对单变量和多变量函数的两次连续可微约束非线性优化模型的新的紧凸低估估计；(B)通过增广的拉格朗日框架用于确定性全局优化的新方法；(C)改进的确定性全局优化方法，它嵌入了凸下界改进，并且可以解决中到大规模的全局优化问题；(D)新的混合全局优化方法，它结合了确定性方法的严密性、紧凸低估估计和计算高效的随机方法；以及(E)顺序和分布式计算工具。这项研究致力于通过加强工艺综合、设计和工艺操作来改进中到大规模的全局优化应用。更广泛的影响：这项研究将开发严格的全局优化方法，解决工艺设计、综合和工艺操作中的重要问题。通过促进对市场需求的更快响应和更有效地使用加工设施，石化、化工、制药、制造和服务/软件公司将从这些方法中受益，因此，研究将直接影响美国经济。此外，这项研究还将促进教育活动。PIS将以讲座和项目的形式将研究成果纳入一门关于非线性混合整数优化的选修研究生课程。PI还将使用选择性算法工具作为名为化学过程设计、合成和优化的顶尖高级设计课程的一部分。私人投资促进机构将通过为该项目招募本科生和研究生，扩大代表性不足群体的参与。PIS将通过在国内和国际会议上的陈述、学术评论期刊出版物和网页来传播研究成果。

CBET-0827907FloudasIntellectual Merit: The goal of this project is to develop novel theoretical, algorithmic and computational techniques for global optimization problems. The computational techniques will apply to a variety of chemical engineering process design, synthesis and operations problems. The PIs will investigate four sub-areas: (i) the development of a new class of tight convex underestimators for twice-continuously differentiable univariate functions which will enhance the piecewise quadratic perturbation-based aBB (Meyer and Floudas (2005)) approach and will form the theoretical basis for applications in a variety of phase equilibrium, design and synthesis problems; (ii ) the theoretical development of tight convex underestimators for multivariate twice continuously differentiable functions and study its algorithmic development for bivariate, multilinear and general multivariate functions; (iii) a new theoretical and algorithmic approach for deterministic global optimization via an Augmented Lagrangian framework; and (iv) the development of new, hybrid global optimization methods combining the beneficial elements of the tight convex underestimators of the enhanced aBB deterministic global optimization framework and the augmented Lagrangian approach with stochastic based approaches. The PIs will also study the distributed computing implementations and apply them to medium- and large-scale non-convex optimization problems that arise in standard, extended, and generalized pooling and blending applications.Through this research, the PIs expect to identify new theoretical, algorithmic, and computational results affecting global optimization and methodologies. The innovative features the PIs expect to derive are: (a) new tight convex underestimators for twice-continuously differentiable constrained nonlinear optimization models for both univariate and multivariate functions; (b) new methods for deterministic global optimization via an Augmented Lagrangian framework; (c) improved deterministic global optimization methods that embed the convex lower bounding advances and can address medium to large scale global optimization problems; (d) novel hybrid global optimization methods that combine the rigor of deterministic methods with the tight convex underestimators and computationally efficient stochastic approaches; and (e) sequential and distributed computational tools. This research focuses on improving medium- to large-scale global optimization applications by enhancing process synthesis, design and process operations. Broader Impact: This research will develop rigorous global optimization methods addressing important problems in process design, synthesis and process operations. By facilitating faster response to the market demands and enabling the more efficient use of the processing facilities, petrochemical, chemical, pharmaceutical, manufacturing, and services/software companies will benefit from these methods, and thereby, the research will directly impact the US economy. Additionally, the research will enhance educational activities. The PIs will incorporate the research results into an elective graduate course on Nonlinear Mixed Integer Optimization in the form of lectures and projects. The PIs will also use selective algorithmic tools as part of a capstone senior design course called Design, Synthesis and Optimization of Chemical Processes. The PIs will broaden the participation of underrepresented groups through recruiting undergraduate and graduate students for the project. The PIs will disseminate the research results through presentations at domestic and international meetings, scholarly refereed journal publications and through a web page.