Simulation-based optimization

Simulation-based optimization is an emerging field which integrates optimization techniques into simulation analysis. This thesis describes a sophisticated implementation of a two-phase algorithm (WISOPT) which has been successfully applied in applications such as the calibration of a Wisconsin breast cancer simulation model and the robust design of a floating sleeve coaxial antenna for hepatic microwave ablation. The underlying problem format to which this method applies is a stochastic programming problem whose objective function is an associated (expensive) measurement of an experimental simulation, with small number of design parameters.;A key guiding principle in this thesis is the use of the distribution information from Bayesian analysis of replicated evaluations of the simulation to instrument existing optimization codes and make them more robust to noisy function evaluations. The two-phase framework contains both global and local methodologies. Phase I is a global exploration step over the entire domain. One of our methods employs classifiers to facilitate the global search process. By learning a surrogate from existing data the approach identifies promising regions for optimization. Another method is an extension of a space partitioning and exploration algorithm called DIRECT. Correct partitioning is guaranteed by Monte Carlo validation based on Bayesian posterior distributions. A phase transition module using nonparametric local regression is applied to determine the exact locations of promising subregions.;Phase II is a collection of local trust-region derivative-free optimizations. The methods apply Bayesian techniques that potentially solve multiple trust region subproblems to guide appropriate sampling strategies and obtain solutions of a desired accuracy. The statistically accurate scheme determines the number of simulation runs and guarantees the global convergence of the algorithm. The ideas in the thesis also demonstrates applicability in other optimization problems such as neuro-dynamic programming. This special type of simulation problem contains time domains with the controls being revealed in a sequential manner. We efficiently manage the simulation resources using Bayesian tools in neuro-dynamic programming to derive accurate stochastic optimal controls.