Collaborative Research: A New Paradigm for Simulation Optimization: Marriage between Expectation-Maximization and Model-Based Optimization

协作研究：仿真优化的新范式：期望最大化与基于模型的优化的结合

• 批准号: 1130761
• 负责人: Jiaqiao Hu
• 金额: $ 19.73万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-09-01 至 2015-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1130761&HistoricalAwards=false
• 关键词: Collaborative; Research; New; Paradigm; Simulation

The research objective of this award is to create new simulation optimization algorithms that combine rigorous theoretical performance guarantees with the robust empirical behavior of a class of random search techniques called the model-based methods. The research approach is based on integrating the principle of the well-known Expectation-Maximization (EM) algorithm from the field of statistics into model-based methods. In particular, through exploiting a novel connection to the EM algorithm, this research will investigate a unifying framework to design and implement new model-based algorithms for solving a broad class of simulation optimization problems with very modest computational effort. These algorithms will be studied in terms of their properties (such as convergence and convergence rate) using a fusion of theories and tools from EM, stochastic approximation, and Quasi-Newton methods. A variety of applications from biostatistics to electric power systems will also be tested for the purposes of evaluating the practical utility of the developed techniques and algorithms. If successful, the resulting techniques will have applicability in a wide array of industry and science sectors. Through collaboration with bio-statisticians, the developed algorithms will be applied to optimal drug dose-response experimental designs, with potential benefits to health care. In addition, the intended applications to electric power systems will also promote synergy among different disciplines. The research resulting from this project will be disseminated through publications, software development, and participation at national and international conferences. This award will also be closely integrated with the education and training of students in mathematical science and engineering by incorporating new developments into the advanced courses taught by investigators at different institutions, and promoting the participation of female students in research.

该奖项的研究目标是创建新的模拟优化算法，将严格的理论性能保证与一类称为基于模型的方法的随机搜索技术的稳健经验行为相结合。该研究方法基于将统计学领域著名的期望最大化（EM）算法的原理集成到基于模型的方法中。特别是，通过利用与 EM 算法的新颖连接，本研究将研究一个统一的框架来设计和实现基于模型的新算法，以非常少量的计算量解决广泛的模拟优化问题。将使用 EM、随机逼近和拟牛顿方法的理论和工具的融合来研究这些算法的属性（例如收敛性和收敛速度）。还将测试从生物统计学到电力系统的各种应用，以评估所开发的技术和算法的实际效用。如果成功，所得技术将适用于广泛的工业和科学领域。通过与生物统计学家的合作，开发的算法将应用于最佳药物剂量反应实验设计，这对医疗保健具有潜在的好处。此外，在电力系统中的预期应用也将促进不同学科之间的协同作用。该项目的研究成果将通过出版物、软件开发以及参加国内和国际会议进行传播。该奖项还将与数学科学与工程专业学生的教育和培养紧密结合，将新进展融入到不同院校研究者所讲授的高级课程中，并促进女学生参与研究。