Seminal Concepts for a New Approach to Continuous-Variable Optimization Under Uncertainty: Probabilistic Ordinal Optimization*

A very general and robust approach to solving optimization problems involving probabilistic uncertainty is through the use of Probabilistic Ordinal Optimization. At each step in the optimization problem, improvement is based only on a relative ranking of the probabilistic merits of local design alternatives, rather than on crisp quantification of the alternatives. Thus, we simply ask: "Is that alternative better or worse than this one?" to some level of quantified statistical confidence, not: "HOW MUCH better or worse is that alternative to this one?". The latter answer strictly implies asymptotically converged statistics (and corresponding expense of sampling/integration) associated with complete certainty (i.e., 100% confidence in the statistics). Looking at things from an ordinal optimization perspective instead, we can begin to quantify and utilize the tradeoff between computational expense and vagueness in the uncertainty characterization. This paper introduces fundamental ordinal optimization concepts using a low-dimensional probabilistic optimization problem as a vehicle. Advanced implementational possibilities are discussed, along with merits versus non-ordinal approaches to optimization under uncertainty.