Improved Convex Underestimators and Hybrid Methods for Deterministic Global Optimization

用于确定性全局优化的改进凸低估器和混合方法

• 批准号: 0330541
• 负责人: Christodoulos Floudas
• 金额: --
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-11-15 至 2008-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0330541&HistoricalAwards=false
• 关键词: Improved; Convex; Underestimators; Hybrid; Methods

Intellectual Content: The primary objective of this research is to develop novel theoretical, algorithmic and computational techniques for global optimization problems that arise in a variety of chemical engineering process design, synthesis and operations problems. It is the PI's intention to investigate (i) the development of a new class of improved convex underestimators for twice-continuously differentiable constrained nonlinear programming problems which will enhance the aBB approach and will be applied in a variety of phase equilibrium, design and synthesis problems; (ii) the theoretical and algorithmic development of a novel cut and splice refinement of the aBB convex subfunctional that will result in new types of tigher convex underestimators; (iii) the theoretical and algorithmic issues for the development of novel trigonometric convex underestimators for several classes of nonconvex trigonometric functions; and (iv) the development of new hydrid global optimization methods which combine the beneficial elements of the enhanced aBB deterministic global optimization framework with stochastic based approaches, and their distributed computing implementations, and their applications to medium and large-scale nonconvex optimization problems that arise in pooling and blending applications.Broader Impact: The integration of research and education will be enhanced through the introduction of lecture material and projects in the elective graduate course on Nonlinear Mixed Integer Optimization, and the required capstone senior design course Design, Synthesis and Optimization of Chemical Processes. The research will broaden the participation of underrepresented groups since it will aim at attracting female and minority students at the graduate level and the undergraduate senior theses level. The results of the work will be broadly disseminated to researchers in academia and industry through presentations at domestic and international meetings, scholarly refereed journal publications and through our web page (http://titan.princeton.edu) which will describe the approaches, implementations and results. Many petrochemical, chemical, pharmaceutical and services/software companies will benefit by the development of rigorous global optimization methods that can address important problems in process design and operations. This can lead to faster response to the market demands, and hence more efficient use of the processing facilities, which has direct benefit on the US economy.

知识内容：本研究的主要目标是开发新颖的理论、算法和计算技术，以解决各种化学工程工艺设计、合成和操作问题中出现的全局优化问题。 PI 的目的是研究 (i) 针对二次连续可微约束非线性规划问题开发一类新型改进凸低估器，这将增强 aBB 方法并将应用于各种相平衡、设计和综合问题; (ii) aBB 凸子函数的新颖切割和拼接细化的理论和算法开发，这将产生新型更严格的凸​​低估量； (iii) 为几类非凸三角函数开发新型三角凸低估器的理论和算法问题； (iv) 开发新的混合全局优化方法，将增强的 aBB 确定性全局优化框架的有益元素与基于随机的方法相结合，及其分布式计算实现，以及它们在中型和大规模非凸优化问题中的应用更广泛的影响：通过在非线性混合整数优化选修研究生课程以及所需的高级设计课程设计中引入讲座材料和项目，将增强研究和教育的整合，化学工艺的合成和优化。 该研究将扩大代表性不足群体的参与，因为它将旨在吸引研究生和本科生高级论文水平的女性和少数族裔学生。这项工作的结果将通过在国内和国际会议上的演讲、学术参考期刊出版物以及通过我们的网页（http://titan.princeton.edu）广泛传播给学术界和工业界的研究人员，该网页将描述方法和实施和结果。 许多石化、化工、制药和服务/软件公司将受益于严格的全局优化方法的开发，这些方法可以解决工艺设计和操作中的重要问题。这可以更快地响应市场需求，从而更有效地利用加工设施，这对美国经济有直接好处。