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.

智力内容：这项研究的主要目标是开发新型的理论，算法和计算技术，以解决各种化学工程过程设计，合成和操作问题中出现的全球优化问题。 PI的目的是调查（i）开发一类新的改进的凸低估器，以两次可区分的约束非线性编程问题，这将增强ABB方法，并将在各种相平衡，设计和合成问题中应用； （ii）新颖的剪切和剪接完善的理论和算法开发ABB凸起功能，这将导致新型的猛虎凸低估器； （iii）用于开发新型三角凸的理论和算法问题，用于几类非凸三角函数的低估； 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非线性混合整数优化，以及所需的顶峰高级设计课程设计，化学过程的合成和优化。 这项研究将扩大代表性不足的团体的参与，因为它将旨在吸引研究生水平和本科高级论点的女性和少数民族学生。这项工作的结果将通过国内和国际会议上的演讲，学术指导期刊出版物以及我们的网页（http://titan.princeton.edu）广泛传播给学术界和行业的研究人员，这些方法将描述方法，实施和结果。 许多石化，化学，药品和服务/软件公司将通过开发严格的全球优化方法而受益，这些方法可以解决过程设计和操作中的重要问题。这可能会导致对市场需求的更快响应，从而更有效地利用加工设施，这对美国经济具有直接的利益。