Bidirectional branch and bound for controlled variable selection. Part III: local average loss minimization

The selection of controlled variables (CVs) from available measurements through exhaustive search is computationally forbidding for large-scale processes. We have recently proposed novel bidirectional branch and bound (B-3) approaches for CV selection using the minimum singular value (MSV) rule and the local worst- case loss criterion in the framework of self-optimizing control. However, the MSV rule is approximate and worst-case scenario may not occur frequently in practice. Thus, CV selection by minimizing local average loss can be deemed as most reliable. In this work, the B-3 approach is extended to CV selection based on local average loss metric. Lower bounds on local average loss and, fast pruning and branching algorithms are derived for the efficient B-3 algorithm. Random matrices and binary distillation column case study are used to demonstrate the computational efficiency of the proposed method.