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-0827907Floudas智力优点：该项目的目标是为全局优化问题开发新颖的理论、算法和计算技术。 该计算技术将适用于各种化学工程工艺设计、合成和操作问题。 PI 将研究四个子领域：(i) 开发用于两次连续可微单变量函数的新型紧凸低估器，这将增强基于分段二次扰动的 aBB（Meyer 和 Floudas (2005)）方法，并将形成在各种相平衡、设计和综合问题中应用的理论基础； (ii) 多元两次连续可微函数的紧凸低估器的理论发展，并研究其针对二元、多线性和一般多元函数的算法发展； (iii) 通过增强拉格朗日框架进行确定性全局优化的新理论和算法方法； (iv) 开发新的混合全局优化方法，将增强型 aBB 确定性全局优化框架的紧凸低估器的有益元素和基于随机方法的增强拉格朗日方法结合起来。 PI 还将研究分布式计算实现，并将其应用于标准、扩展和广义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 期望确定影响全局优化和方法的新理论、算法和计算结果。 PI 期望获得的创新功能包括： (a) 新的紧凸低估器，用于单变量和多元函数的两次连续可微约束非线性优化模型； (b) 通过增强拉格朗日框架进行确定性全局优化的新方法； (c) 改进的确定性全局优化方法，嵌入凸下界进步并可以解决中到大规模全局优化问题； (d) 新颖的混合全局优化方法，将确定性方法的严格性与紧凸低估量和计算高效的随机方法相结合； (e) 顺序和分布式计算工具。 这项研究的重点是通过增强工艺合成、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、合成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并更有效地利用加工设施，石化、化学、制药、制造和服务/软件公司将从这些方法中受益，因此，该研究将直接影响美国经济。 此外，该研究将加强教育活动。 PI 将以讲座和项目的形式将研究成果纳入非线性混合整数优化研究生选修课程中。 PI 还将使用选择性算法工具作为名为“化学工艺的设计、合成和优化”的高级设计课程的一部分。 PI 将通过招募本科生和研究生参与该项目来扩大代表性不足群体的参与。 PI 将通过在国内和国际会议上的演讲、学术参考期刊出版物和网页来传播研究成果。