Simulation Optimization: A Martingale-based Approach

本研究项目旨在探索解决大规模仿真优化问题的新方法。该项目的最终方法将用于有效地解决离散和连续设置中的模拟优化问题家族，并应用于制造系统，供应链，医疗保健和企业系统等各种领域。该研究针对仿真优化中的两个基本挑战：1)识别特定的概率结构，使我们能够提高搜索效率；2)在提供的目标界信息很少的情况下，测量当前解的质量。目前，该领域的大部分研究工作都致力于建立启发式。然而，很少有理论结果已经建立，解决潜在的数学结构。本研究项目旨在为仿真优化算法快速收敛建立一个具体而又广泛适用的理论条件，同时在边界信息较少但置信度较高的情况下，识别全局最优解与当前解之间的距离。如果成功，新方法和产生的算法将在解决制造、供应链和企业系统等领域的大规模模拟优化问题方面具有广泛的适用性。这个项目产生的想法将通过出版物、软件开发和参加国家和国际一级的会议来传播。该研究项目也将通过将新发展纳入PI教授的本科和研究生优化课程，与工程专业学生的教育和培训紧密结合。最后，鞅方法有望通过促进模拟优化中嵌入随机过程的进一步讨论和研究，在研究界产生更广泛的影响。

This research project aims to investigate new approaches to solve large-scale simulation optimization problems. The resulting methodology of this project will be used to efficiently solve families of simulation optimization problems in both discrete and continuous settings, and have applications to a variety of domains such as manufacturing systems, supply chain, healthcare and enterprise systems. The research targets at two fundamental challenges in simulation optimization: 1) identify specific probabilistic structures that allow us to improve the search efficiency, and 2) to measure quality of the current solution obtained when little information on the objective bound is provided. Currently, the majority of the research effort in the field has been devoted to building heuristics. Very few theoretical results have been established, however, addressing the underlying mathematical structure. This research project seeks to build a specific yet widely applicable theoretical condition for simulation optimization algorithms to quickly converge, while at the same time identify, with little bounding information but a reasonably higher level confidence, the distance between the global optimum to current solution obtained.If successful, the new methodology and the resulting algorithms will have broad applicability in solving large-scale simulation optimization problems in domains such as manufacturing, supply chain and enterprise systems. The ideas resulting from this project will be disseminated through publications, software development, and conference participation at both national and international level. This research project will also be closely integrated with the education and training of engineering students by incorporating new developments into the undergraduate and graduate optimization courses taught by PI. Finally, the martingale method is expected to have a broader impact in the research community by stimulating further discussion and study of the embedded stochastic processes in simulation optimization.