Collaborative Research: Combining Gradient and Adaptive Search in Simulation Optimization

“结合梯度和自适应搜索的仿真优化”这一研究项目的目的是在仿真优化方面取得重大的理论和实践进展。具体地说，我们计划做以下工作：(I)在最近发展的一种称为模型参考自适应搜索的方法中，基于不同的参考分布序列开发新的模拟优化算法，以及结合局部梯度搜索和问题结构的新的全局-局部混合搜索算法；以及(Ii)对所得到的算法进行严格的理论分析，包括使用自适应搜索框架的有限时间行为和使用与随机逼近方法的新连接的渐近行为。我们还将开发高效的计算选择方法来在模拟优化中实现这些算法，其中目标函数需要多次模拟重复，这是计算昂贵的，以便估计系统性能。为了研究特定的梯度搜索算法和问题结构，并根据经验行为评估有效性，将测试从供应链管理到金融工程的各种应用程序。美国整个行业都在使用模拟，因此如果成功，由此产生的优化算法将具有广泛的实用适用性。要解决大型、复杂的随机离散事件仿真模型中出现的难题，将需要重要的新方法，从而导致算法开发和收敛分析方面的研究进展。在理论方面，严格的分析将探索与随机逼近和随机自适应研究中丰富的结果之间的联系，这些结果以前从未以这种方式使用过，从而对有限时间性能和渐近收敛速度产生了新的见解。在实践方面，这一系列研究填补了“分析”计算工具包的一个重要部分，该工具包提高了美国企业的竞争力，从拥有全球供应链的制造商和零售商，到管理复杂风险因素的金融服务。

"Combining Gradient and Adaptive Search in Simulation Optimization" This research project aims to make significant theoretical and practical advances in simulation optimization. Specifically, we plan on doing the following: (i) develop new simulation optimization algorithms based on different sequences of the so-called ``reference distributions" in a recently developed approach called model reference adaptive search, and new hybrid global-local search algorithms integrating local gradient search and problem structure; and (ii) conduct rigorous theoretical analysis of the resulting algorithms, both finite-time behavior using an adaptive search framework and asymptotic behavior using a novel connection to stochastic approximation methods. We will also develop efficient computational selection methods for implementing these algorithms in simulation optimization, where the objective function requires multiple simulation replications, which are computationally expensive, in order to estimate system performance. A wide variety of applications from supply chain management to financial engineering will be tested for the purposes of investigating specific gradient search algorithms and problem structure, and evaluating the effectiveness in terms of empirical behavior. Simulation is used throughout the US industry, so if successful, the resulting optimization algorithms will have broad practical applicability. To attack difficult problems arising from large, complex stochastic discrete-event simulation models will require significant new methodologies, leading to research advances in both algorithmic development and convergence analysis. In terms of theory, the rigorous analysis will explore connections to a rich body of results in stochastic approximation and stochastic adaptive research that have never been employed in this manner before, yielding new insights into both finite-time performance and asymptotic rates of convergence. In terms of practice, this line of research fills an important part of the "analytics" computational tool kit that has led to increased competitiveness for US businesses from manufacturers and retailers with global supply chains to financial services managing complex risk factors.