Search and selection for large-scale stochastic optimization

This dissertation studies optimization of unstructured stochastic simulation problems. Computer simulation is widely used to model proposed designs, or improve existing designs, of industrial, retail, computer, telecommunications and service systems. In most of these complex systems, the output performance measures, such as work in progress, time in queue, or average throughput, are stochastic in nature. This stochastic variation makes it more difficult to compare alternative designs. Simulation is an evaluative tool; it does not naturally suggest or generate new solutions. Optimization, on the other hand, is used to seek out the best design from a possibly large number of different combinations of controllable decision variables. Most traditional optimization methods, such as linear or integer programming, assume deterministic (as opposed to stochastic) outputs, as well as an underlying mathematical model that can be exploited. In a computer simulation of a complex system, however, neither of these assumptions typically hold. Researchers have succeeded in adapting a few traditional optimization techniques, such as gradient search, to a simulation setting, but in most cases the simulation model must adhere to a restrictive set of assumptions; in other words, the problem must have a particular structure, such as convexity or continuity. We have developed theory that allows a heuristic search procedure—a deterministic optimization procedure that does not rely heavily on problem structure—to function in a stochastic environment. We also developed theory that allows us to select the true best system from among a large number of stochastic systems. This theory is used after the search procedure has run its course. We implemented both the search and selection theory into software.