Novel Methods and Computational Studies for Global Optimization

全局优化的新方法和计算研究

• 批准号: 0827907
• 负责人: Christodoulos Floudas
• 金额: $ 37.19万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-09-01 至 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0827907&HistoricalAwards=false
• 关键词: Novel; Methods; Computational; Studies; Global

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.

CBET-0827907FLOUDASINTELLECTUAL FEARIT：该项目的目的是为全球优化问题开发新颖的理论，算法和计算技术。 计算技术将适用于各种化学工程过程设计，合成和操作问题。 PI将调查四个子区域：（i）开发一类新的紧密凸低估器，用于两次悬而未决的单变量功能，这将增强基于二次扰动的二次扰动ABB（Meyer and Floudas（2005））方法和方法和将会和将增强。构成在各种相平衡，设计和合成问题中应用的理论基础； （ii）对多变量的紧密凸低估器的理论发展是两次连续可区分的功能，并研究其双变量，多线和一般多元功能的算法发展； （iii）通过增强的拉格朗日框架确定性全球优化的一种新的理论和算法方法； （iv）开发了新的混合全局优化方法，结合了增强的ABB确定性全球优化框架和增强Lagrangian方法的紧密凸低估器的有益元素与基于随机方法的方法。 PI还将研究分布式计算实施，并将其应用于标准，扩展和广义汇总和混合应用中出现的中等和大规模的非凸优化问题。通过这项研究，PIS希望确定新的理论，理论，算法和计算结果影响全局优化和方法。 PIS期望得出的创新功能是：（a）单变量和多变量函数两次的新的紧密凸低音凸低估器； （b）通过增强拉格朗日框架确定性全球优化的新方法； （c）改进的确定性全局优化方法嵌入了凸的下限进展，并可以解决中等至大规模的全球优化问题； （d）将确定性方法的严谨性与紧密凸低估器和计算有效的随机方法结合在一起的新型混合全局优化方法； （e）顺序和分布式计算工具。 这项研究重点是通过增强过程综合，设计和过程操作来改善大型全球优化应用程序。 更广泛的影响：这项研究将开发严格的全球优化方法，以解决过程设计，综合和过程操作中的重要问题。 通过促进对市场需求的更快响应并使加工设施更有效地使用石化，化学，制药，制造业和服务/软件公司将从这些方法中受益，从而直接影响美国经济。 此外，该研究将增强教育活动。 PI将研究结果纳入以讲座和项目形式的非线性混合整数优化的选修生课程中。 PIS还将使用选择性算法工具作为Capstone高级设计课程的一部分，称为设计，合成和优化化学过程。 PI将通过招募本科生和研究生来扩大代表性不足的团体的参与。 PI将通过在国内和国际会议上的演讲，学术指导期刊出版物以及通过网页来传播研究结果。