Mini courses > Scenario Generation and Sampling Methods

Güzin Bayraksan                                       Tito Homem-de-Mello

Ohio State University, USA                  University Adolfo Ibáñez, Chile

From May 9th to May 13th, 2016

We review methods for generating scenarios to approximate stochastic optimization problems. General methods such as Monte Carlo, Latin hypercube sampling and quasi-Monte Carlo methods will be discussed.  We will provide an overview of properties of such methods, in terms of asymptotic convergence and behavior for finitely many samples. We will also review a number of specialized sequential sampling algorithms to solve stochastic optimization problems and methods to assess solution quality. In the context of multi-stage stochastic programs, we will pay particular attention to methods for generating scenario trees, such as moment-matching, clustering, and probability-based metrics. We will discuss applications of the methods studied in the course, especially  in the areas of energy and finance.

Material

Homem-de-Mello, T. and Bayraksan, G., “Monte Carlo Sampling-Based Methods for Stochastic Optimization,” Surveys in Operations Research and Management Science, 19(1): 56–85, 2014 [www]

 Session 1: pdf,  Session 2: pdf , Session 3: pdf, Session 4: pdf, Session 5: pdf 

Videos: available upon request