Accounting for Randomness in Heuristic Simulation Optimization

Research on the optimization of stochastic systems via simulation often centers on the development of algorithms for which global convergence can be guaranteed. Applications of optimization via simulation, on the other hand, typically involve search heuristics that have been successful in deterministic settings. Search heuristics give up on global convergence in order to be more generally applicable and to yield rapid progress toward good solutions. Unfortunately, most commercial implementations do not formally account for the randomness in simulation responses, meaning that their progress may be no better than a random search if the level of randomess is high. In addition, they do not provide statistical guarantees about the goodness of the nal results. In this paper, we report on the work we have done to uncouple the error control for the search from the error control for the nal solution. We also report on our implementation of this work in software developed for JGC Corporation of Japan. Like many organizations, JGC, a Japanese construction management company, uses simulation to evaluate and compare proposed designs for facilities such as pharmaceutical plants, oil reeneries and automobile manufacturing plants. A JGC research supervisor noticed that his engineers spent a great deal of time adjusting model decision variables (such as buuer size) and comparing the output results (such as work-in-process inventory). Furthermore, he recognized that the conclusions drawn from these comparisons were not guaranteed to be statistically valid. To remedy these shortcomings, JGC approached Northwestern University, asking for a simulation-optimization package that could provide good results on a broad range of problems in a reasonable amount of time, and provide statistical guarantees on those results. From an optimization viewpoint, several diicul-ties emerge. First, the optimization approach needs to handle simulation models that may combine integer decision variables (such as the number of drills in a machine shop), continuous decision variables (such as conveyor speed in an assembly plant or ow rate in a pharmaceutical plant) and categorical decision variables (such as queue discipline or scheduling rules). This means that some traditional simulation-optimization techniques, such as gradient-search, cannot always be applied. Second, the response properties of the problems are unknown. That is, no exploitable properties, such as convexity or continuity, can be assumed. Not surprisingly , this makes the task of nding the best design much more diicult because it prevents us from inferring anything about solutions that are not explicitly evaluated. Third, the responses …