Optimization Under Uncertainty

• Urmila M. Diwekar
Part of the Applied Optimization book series (APOP, volume 80)

Abstract

In previous chapters, we looked at various optimization problems. Depending on the decision variables, objectives, and constraints, the problems were classified as LP, NLP, IP, MILP, or MINLP. However, as stated above, the future cannot be perfectly forcasted but instead should be considered random or uncertain. Optimization under uncertainty refers to this branch of optimization where there are uncertainties involved in the data or the model, and is popularly known as Stochastic Programming or stochastic optimization problems. In this terminology, stochastic refers to the randomness, and programming refers to the mathematical programming techniques like LP, NLP, IP, MILP, and MINLP. In the discrete optimization chapter, we came across probabilistic techniques like Simulated Annealing and Genetic Algorithms; these techniques are sometimes referred to as the stochastic optimization techniques because of the probabilistic nature of the method. In general, however, Stochastic Programming and stochastic optimization involves optimal decision making under uncertainty. For example, consider the LP example stated in Chapter 2 where, instead of having a fixed maximum supply of chemical X2, the supply can be uncertain, as shown in the following Stochastic Programming (optimization) problem.

Keywords

Master Problem Uncertain Variable Latin Hypercube Sampling Chance Constraint Stochastic Optimization Problem
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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