Efficiencies from Spatially-Correlated Uncertainty and Sampling in Continuous-Variable Ordinal Optimization

A very general and robust approach to solving continuous-variable optimization problems involving uncertainty in the objective function is through the use of ordinal optimization. At each step in the optimization problem, improvement is based only on a relative ranking of the uncertainty effects on local design alternatives, rather than on precise quantification of the effect. One simply asks "Is that alternative better or worse than this one?"-not "HOW MUCH better or worse is that alternative to this one?" The answer to the latter question requires precise characterization of the uncertainty-with the corresponding sampling/integration expense for precise resolution. By looking at things from an ordinal ranking perspective instead, the trade-off between computational expense and vagueness in the uncertainty characterization can be managed to make cost-effective stepping decisions in the design space. This paper demonstrates correct advancement in a continuous-variable probabilistic optimization problem despite extreme vagueness in the statistical characterization of the design options. It is explained and shown how spatial correlation of uncertainty in such design problems can be exploited to dramatically increase the efficiency of ordinal approaches to optimization under uncertainty.