Integration and computational issues in stochastic design and planning optimization problems

In stochastic process design and planning optimization problems, the expected value of the objective function in face of uncertainty is typically evaluated through an n-dimensional integral, where it is the number of uncertain parameters. In this paper, suitable integration techniques are presented and computational issues are discussed in relation to the number of uncertain parameters and the uncertainty model considered. A specialized cubature technique, suitable to integrate normally distributed uncertainties, is introduced, which for n < 10 can reduce significantly the computational effort required when compared to other strategies, such as product Gauss rules or efficient sampling techniques. The computational performance of the different integration techniques and their applicability are discussed through two process-engineering examples.