Refinements in a new adaptive ordinal approach to continuous-variable probabilistic 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 effects. 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. However, in this paper, we demonstrate correct decision-making in a continuous-variable probabilistic optimization problem despite extreme vagueness in the statistical characterization of the design options. We present a new adaptive ordinal method for probabilistic optimization in which the tradeoff between computational expense and vagueness in the uncertainty characterization can be conveniently managed in various phases of the optimization problem to make cost-effective stepping decisions in the design space. Spatial correlation of uncertainty in the continuous-variable design space is exploited to dramatically increase method efficiency. Under many circumstances, the method appears to have favorable robustness and cost-scaling properties relative to other probabilistic optimization methods, and it uniquely has mechanisms for quantifying and controlling error likelihood in design-space stepping decisions. The method is asymptotically convergent to the true probabilistic optimum, and so could be useful as a reference standard against which the efficiency and robustness of other methods can be compared, analogous to the role that Monte Carlo simulation plays in uncertainty propagation.