CAREER: Optimization and Sampling in Stochastic Simulation

这个教师早期职业发展（CAREER）计划项目的目标是开发新的方法，用于优化和预测由随机模拟模型描述的复杂系统的性能。这样的系统出现在各种领域，如金融，工程设计，系统生物学和制造业，并往往具有复杂性，非线性和不确定性的动态。系统性能的优化和预测的主要挑战是昂贵的系统模型的评估，缺乏结构的性能测量，巨大的搜索空间，并需要解决效率和准确性之间的平衡。本研究旨在通过开发新的理论和方法来应对这些挑战。所提出的方法将用于从实验数据中建立一类生物系统的模型，研究这些系统的行为模式，有助于揭示生物系统的功能机制和设计原则。该项目还支持PI的教育目标，将研究与课程开发和课堂教学相结合，让更多女性和代表性不足的少数民族参与工程，并让高中生和初中女生接触工业工程和运筹学领域。本研究将提供一套新的算法，具有上级的实际性能和严格的收敛保证，为以下两个问题：（i）仿真优化;以及（ii）系统模型的响应空间的表征。对于模拟优化，将通过无缝地将确定性非线性优化的基于模型的方法的中心思想与经典的基于梯度的搜索相结合来开发算法框架。为了有效地探索响应空间，提出了一种新的方法，即在响应空间和参数空间中迭代采样，利用参数空间结构简单的优点来规避模型的非线性，同时利用响应空间的信息来加快参数空间的搜索。

The objective of this Faculty Early Career Development (CAREER) Program project is to develop new methods for optimizing and predicting performance of complex systems that are described by stochastic simulation models. Such systems arise in various areas such as finance, engineering design, systems biology, and manufacturing, and are often characterized by complexities, nonlinearities, and uncertainties in their dynamics. The major challenges in the optimization and prediction of the system performance are the expensive evaluation of system models, lack of structure in the performance measure, huge search space, and the need to address the balance between efficiency and accuracy. This research aims to make strides towards these challenges by developing new theory and methodologies. The proposed methods will be applied to modeling of a class of biological systems from experiment data and studying modes of behaviors of these systems, helping to reveal functional mechanisms and design principles of biological systems. This project also supports the PI's educational objective to integrate research with course development and in-classroom teaching, engage more females and underrepresented minorities in engineering, and expose high-school students and middle-school girls to the field of industrial engineering and operations research.If successful, this research will provide a set of new algorithms that possess both superior practical performance and rigorous convergence guarantees for the following two problems: (i) simulation optimization; and (ii) characterization of the response space of a system model. For simulation optimization, an algorithmic framework will be developed by integrating the central idea of model-based methods from deterministic nonlinear optimization with classical gradient-based search in a seamless way. To efficiently explore the response space, a new approach is proposed to sample from the response space and the parameter space iteratively, which takes advantage of the simple structure of the parameter space to circumvent the nonlinearity of the model while using the information on the response space to expedite the search in the parameter space.