Design optimization of stochastic flexibility

Abstract

This paper addresses the problem of how to evaluate and optimize the probability of feasible operation for a design that is described by a nonlinear model. This property, which is denoted as the stochastic flexibility, represents the cumulative distribution over a feasible region in the space of the uncertain parameters. It is shown that the evaluation problem, which requires a sequence of optimization problems, can be formulated as a single nonlinear programming model which can be extended to design optimization problems for maximizing the stochastic flexibility subject to a cost contraint. A solution method based on Generalized Benders Decomposition is proposed to effectively solve this problem. A comparison with Taguchi's method for minimizing quadratic loss is also presented to point out that the use of a reward function can lead to designs that not only have consistent outputs, but are also feasible to operate over larger parameter ranges. Finally, several process design examples are presented to illustrate the determination of trade-offs between flexibility and cost.