Efficient sampling technique for optimization under uncertainty

The concept of robust design involves identification of design settings that make the product performance less sensitive to the effects of seasonal and environmental variations. This concept is discussed in this article in the context of batch distillation column design with feed stock variations, and internal and external uncertainties. Stochastic optimization methods provide a general approach to robust/parameter design as compared to conventional techniques. However, the computational burden of these approaches can be extreme and depends on the sample size used for characterizing the parametric variations and uncertainties. A novel sampling technique is presented that generates and inverts the Hammersley points (an optimal design for placing n points uniformly on a k-dimensional cube) to provide a representative sample for multivariate probability distributions. The example of robust batch-distillation column design illustrates that the new sampling technique offers significant computational savings and better accuracy.