Design of scenarios for constrained stochastic optimization via vector quantization

Probabilistic methods have recently emerged as an exciting new approach for dealing with uncertainty in stochastic optimization problems. These methods depend upon the selection of a set of scenarios to represent the uncertain variables. Typically these scenarios are obtained by making random drawings from the underlying probability distribution. Here we examine alternative approaches in which the scenarios are targeted at the underlying problem. In particular, we explore the use of vector quantization methods for scenario generation. Vector quantization based scenarios are more computationally intensive to generate but offer advantages for certain classes of optimization problems. Several examples are presented to illustrate the ideas.