Collaborative Research: Inference, Analysis and Assessment in Simulation Optimization

这项拨款提出了模拟优化(SO)问题的三个主要工作领域，即只能通过随机模拟观察所涉及的目标函数和约束的优化问题。首先，许多SO问题具有凸性或单峰性等结构，如果检测到这些结构，可以提高S对问题本身的理解，并在选择求解算法时被利用。将开发数值方法来检测这种结构。其次，将开发性能衡量标准和有效计算它们的方法，以便能够在理论上合理地比较SO算法在测试问题上的性能。第三，将开发SO问题的试验台。如果获奖，数值检测问题结构的能力将极大地提高对S问题公式的理解，并允许更多地使用利用结构的专门算法。这也可能导致用户制定问题以遵守这些结构，结果可能会创建许多新的SO问题子类。试验台，以及适当的性能测量，应该有助于鼓励算法比较和开发。到那时，我们或许能够解决比今天可能解决的更大的问题。研究成果将在应急服务、运输物流、供应链管理、收入管理等领域得到应用，并可能在许多其他领域得到应用。

This grant proposes three main areas of work on simulation optimization (SO) problems, which are optimization problems where the objective function and constraints involved can only be observed through a stochastic simulation. First, many SO problems possess structure such as convexity or unimodality that, if detected, can improve one?s understanding of the problem itself, and be exploited in selecting solution algorithms. Numerical methods will be developed to detect such structure. Second, performance measures, and methods for efficiently computing them, will be developed to enable theoretically sound comparisons of the performance of SO algorithms on test problems. Third, a testbed of SO problems will be developed.If awarded, the ability to numerically detect problem structure will greatly improve understanding of one?s problem formulations, and allow greater use of specialized algorithms that exploit structure. This could also lead to users formulating problems to adhere to those structures, with the result that many new subclasses of SO problems might be created. The testbed, along with appropriate performance measures, should help to encourage algorithm comparisons and development. We might then be able to tackle far larger SO problems than is possible today. The results of the research will find application in areas such as emergency services, transportation logistics, supply chain management, revenue management and potentially many other fields.