Flexibility Index of Black-Box Models with Parameter Uncertainty through
Derivative-Free Optimization
Abstract
The existing methods of flexibility index are mainly based on
mixed-integer linear or nonlinear programming methods, making it
difficult to readily deal with complex mathematical models. In this
article, a novel solution strategy is proposed for finding a reliable
upper bound of the flexibility index where the process model is
implemented in a black box that can be directly executed by a commercial
simulator, and also avoiding the need for calculating derivatives. Then,
the flexibility index problem is formulated as a sequence of univariate
derivative-free optimization (DFO) models. An external DFO solver based
on trust-region methods can be called to solve this model. Finally,
after calculating the critical point of the model parameters, the vertex
enumeration method and two gradient approximation methods are proposed
to evaluate the impact of process parameters and to evaluate the
flexibility index. A reaction model is studied to show the efficiency of
the proposed algorithm.