Development of a New Adaptive Ordinal Approach to Continuous-Variable Probabilistic Optimization

摘要

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 report 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 trade-off 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 uniquely has mechanisms for quantifying and controlling error likelihood in design-space stepping decisions. The method is asymptotically convergent to the true probabilistic optimum, 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.