Robust Optimization

In this chapter we discuss robustness from a more general perspective, that of model building in general, without specific discussion of noise factors. This notion of robustness in the sense of lack of sensitivity of an optimal solution to variations in the model has always been a key idea in mathematical modeling, and in particular, in mathematical programming. This differs from environmental variation in the sense of Taguchi, as discussed in the previous chapter. Thus, in this chapter, no “noise factors” are assumed to exist.

In this chapter we present the “Minimax Deviation method” for robust optimization of Xu and Albin. This is a method that attempts to protect against sampling variability of the parameter estimates in the model, hence it is a frequentist method. We relate this method to confidence regions on the optimal settings (Chapter 7) and to some other proposals for process optimization from the area of Stochastic Programming.

A natural alternative to the Xu-Albin method is to employ a Bayesian approach in which the uncertainty in the model parameters, considered as random variables, is incorporated in the optimization. Such Bayesian approach to process optimization is presented in Part V of this book.