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

该奖项的研究目标是创建新的模拟优化算法，该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。研究方法是将统计学领域中著名的期望最大化(EM)算法的原理融入到基于模型的方法中。特别是，通过利用与EM算法的一种新的联系，这项研究将研究一个统一的框架，以设计和实现新的基于模型的算法，以非常少的计算工作量解决广泛的模拟优化问题。这些算法将使用EM、随机逼近和拟牛顿方法的理论和工具的融合来研究它们的性质(如收敛和收敛速度)。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用价值。如果成功，由此产生的技术将适用于广泛的工业和科学部门。通过与生物统计学家的合作，开发的算法将被应用于最优药物剂量-反应实验设计，并可能对医疗保健产生好处。此外，电力系统的预期应用也将促进不同学科之间的协同。该项目所产生的研究成果将通过出版物、软件开发以及参加国家和国际会议来传播。该奖项还将与学生在数学科学和工程方面的教育和培训紧密结合，将新的发展纳入不同机构研究人员教授的高级课程，并促进女学生参与研究。

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.