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 (B³) 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 B³ 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 B³ algorithm. Random matrices and binary distillation column case study are used to demonstrate the computational efficiency of the proposed method.