Optimization of Computer Simulation Models with Rare Events

Discrete event simulation systems (DESS) are widely used in many diverse areas such as computer-communication networks, exible manufacturing systems, project evaluation and review techniques (PERT), and ow networks. Because of their complexity , such systems are typically analyzed via Monte Carlo simulation methods. This paper deals with optimization of complex computer simulation models involving rare events. A classic example is to nd an optimal (s; S) policy in a multi-item, multi-commodity inventory system, when quality standards require the backlog probability to be extremely small. Our approach is based on change of the probability measure techniques, also called likelihood ratio (LR) and importance sampling (IS) methods. Unfortunately, for arbitrary probability measures the LR estimators and the resulting optimal solution often tend to be unstable and may have large variances. Therefore, the choice of the corresponding importance sampling distribution and in particular its parameters in an optimal way is an important task. We consider the case where the IS distribution comes from the same parametric family as the original (true) one and use the stochastic counterpart method, to handle simulation based optimization models. More speciically, we use a two-stage procedure: at the rst stage we identify (estimate) the optimal parameter vector at the IS distribution, while at the second stage we estimate the optimal solution of the underlying constrained optimization problem. Particular emphasis will be placed on estimation of rare events and on integration of the associated performance function into stochastic optimization programs. Supporting numerical results are provided as well.