UC Davis

This dissertation explores the applications of Monte Carlo and Bootstrap methods in stochasticoptimization, focusing on enhancing computational efficiency and accuracy in solution evaluation and uncertainty quantification. For the purpose of computing the expected value of a stochastic optimization problem via simulation, we propose a method to efficiently construct importance sampling distributions using surrogate modeling. This method significantly reduces the need for repeated evaluations of the objective function, which are typically computationally intensive due to the reliance on optimization algorithms. Our method outperforms traditional Monte Carlo estimation and achieves significant speed-ups with good parallel efficiency. Additionally, we explore Monte Carlo sampling algorithms that utilize known distributions to construct confidence intervals around the optimality gap in two-stage and multi-stage stochastic programs. In scenarios where the distribution of uncertainty remains unknown, we discuss bootstrap and bagging algorithms that rely solely on sampled data to provide both a consistent sample-average solution and accurate confidence interval estimates. These methods are enhanced by integrating distribution estimation into resampling techniques to improve the precision of estimations under uncertainty. We also offer open-source software implementations of these algorithms. Extensive empirical studies show the effectiveness of the smoothed bootstrap and bagging methods, particularly for constructing confidence intervals with small data sets.