Simulation Optimization: A Martingale-based Approach

University Of Wisconsin-Madison, Madison WI

Investigators

Abstract

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.