Branch and bound method for globally optimal controlled variable selection

For selection of controlled variables (CVs) in self-optimizing control, various criteria have been proposed in the literature. These criteria are derived based on local linearization of the process model and the necessary conditions of optimality (NCO) at a nominally optimal operating point. Recently, a novel CV selection framework has been proposed by Ye et al. [1] by converting the CV selection problem into a regression problem to approximate the NCO globally over the entire operation region. In this approach, linear combinations of a subset of available measurements are used as CVs. The subset selection problem is combinatorial in nature redering the application of the globally optimal CV selection method to large-scale processes difficult. In this work, an efficient branch and bound (BAB) algorithm is developed to handle the computational complexity associated with the selection of globally optimal CVs. The proposed BAB algorithm identifies the best measurement subset such that the regression error in approximating NCO is minimized. This algorithm is applicable to the general regression problem. The efficiency and effectiveness of the proposed BAB algorithm is demonstrated through a binary disdillation column case study.