Simulation-based retrospective optimization of stochastic systems
Abstract
We consider optimizing a stochastic system, given only a simulation model that is parameterized by continuous decision variables. For any specified values of the decision variables, the model is assumed to produce unbiased point estimates of the system performance measure(s), which must be expected values. The performance measures may appear in the objective function, in equality constraints, and in inequality constraints. The research goal is to develop methodologies, algorithms, and computer codes that yield close-to-optimal solutions with computational efficiency and no requirement for algorithm “tuning”. We develop a general retrospective-optimization (RO) algorithm based on a sequence of sample-path approximations to the original problem. Such approximation problems are obtained by substituting point estimators for each performance measure and using common random numbers over all values of the decision variables. The sequence of approximation problems is obtained by increasing the number of simulation replications. We assume that these approximation problems, which are deterministic, can be solved to within a specified error in the decision variables, and that this error is decreasing to zero. The computational efficiency of RO arises from being able to solve the next approximation problem efficiently based on knowledge gained from the earlier, easier approximation problems. We analyze RO algorithms analytically and empirically. Sufficient conditions are obtained for strong consistency. A probability model is developed to gain insight about good RO algorithm parameter values. Monte Carlo simulation experiments are run to verify the probability model conclusions and to test the robustness of the resulting default RO parameter values. The implementation used in these experiments uses Nelder-Mead simplex search with flexible-tolerance logic for the deterministic constrained optimization.
Degree
Ph.D.
Advisors
Schmeiser, Purdue University.
Subject Area
Operations research|Systems design
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