New Approaches for Simulation-Based Optimal Decision Making

从制造和供应链管理到服务系统，包括医疗保健、交通和金融服务，仿真在许多工业环境中被广泛使用。然而，由于许多这样的系统的复杂性，即使在计算能力不断提高的情况下，计算也经常成为基于模拟模型解决大规模问题的限制因素。该奖项支持产生新算法的基础研究，这些算法将提高为上述制造业和服务业的许多问题找到最佳决策的效率，从而为美国经济和社会带来直接好处。研究涉及数学模型、计算、应用概率和统计学。直接梯度估计技术，如摄动分析和似然比方法，为获得无偏梯度估计器提供了计算上有效的方法，而不需要重新模拟。这种估计器是许多模拟优化算法中使用的基于梯度的搜索过程的基础。然而，所得算法仅使用梯度，与它们在确定性优化设置中的应用一致，其中梯度是精确的，因此使用目标函数(或性能度量)值本身来执行梯度搜索不会获得任何价值。另一方面，在随机设置中，梯度估计是有噪声的，这意味着使用函数值来提供关于估计梯度的附加信息可能是有益的。该研究探索了将随机模拟的直接梯度估计与现有的模拟优化技术相结合的新方法，特别是响应面方法和随机逼近。研究的目标包括：(I)开发新的更有效的算法，(Ii)证明所得算法的收敛，(Iii)分析算法的有限时间性质，以及(Iv)基于理论和经验数值测试提供实用的实施指南。因此，除了算法的进步之外，可能还需要新的理论来指导新算法可能在哪些环境下提供额外的好处。

Simulation is widely used in many industrial settings, from manufacturing and supply chain management to service systems, including health care, transportation, and financial services. Due to the complexity of many of these systems, however, computation has often been a limiting factor in solving large-scale problems based on simulation models, even with the continuing advances in computing power. This award supports fundamental research leading to new algorithms that would improve the efficiency of finding optimal decisions for many problems in the manufacturing and service industries mentioned above, and thus lead to direct benefits to the U.S. economy and society. The research involves mathematical models, computing, applied probability, and statistics. Direct gradient estimation techniques such as perturbation analysis and the likelihood ratio method provide computationally efficient methods for obtaining unbiased gradient estimators without the need for resimulation. Such estimators are the basis for gradient-based search procedures used in many simulation optimization algorithms. However, the resulting algorithms use only the gradients, consistent with their application in the deterministic optimization setting, where the gradients are exact so there is no value gained in using the objective function (or performance measure) values themselves for performing gradient search. On the other hand, in the stochastic setting, the gradient estimates are noisy, which means that using the function values to provide additional information on estimating the gradient may be beneficial. The proposed research explores new methods for incorporating direct gradient estimates from stochastic simulation into existing simulation optimization techniques, specifically response surface methodology and stochastic approximation. The goals of the research include: (i) developing new more effective algorithms, (ii) proving convergence of the resulting algorithms, (iii) analyzing finite-time properties of the algorithms, and (iv) providing practical implementation guidelines based on both theory and empirical numerical testing. Thus, in addition to algorithmic advances, new theory will likely be needed to provide guidance as to the settings in which the new algorithms are likely to provide additional benefit.