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Bidirectional branch and bound for controlled variable selection Part I : principles and minimum singular value criterion

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Bidirectional branch and bound for controlled variable selection Part I : principles and minimum singular value criterion

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Title: Bidirectional branch and bound for controlled variable selection Part I : principles and minimum singular value criterion
Author: Cao, Yi; Kariwala, Vinay
Copyright year: 2008
Abstract: The minimum singular value (MSV) rule is a useful tool for selecting controlled variables (CVs) from the available measurements. However, the application of the MSV rule to large-scale problems is difficult, as all feasible measurement subsets need to be evaluated to find the optimal solution. In this paper, a new and efficient branch and bound (BAB) method for selection of CVs using the MSV rule is proposed by posing the problem as a subset selection problem. In traditional BAB algorithms for subset selection problems, pruning is performed downwards (gradually decreasing subset size). In this work, the branch pruning is considered in both upward (gradually increasing subset size) and downward directions simultaneously so that the total number of subsets evaluated is reduced dramatically. Furthermore, a novel bidirectional branching strategy to dynamically branch solution trees for subset selection problems is also proposed, which maximizes the number of nodes associated with the branches to be pruned. Finally, by replacing time-consuming MSV calculations with novel determinant based conditions, the efficiency of the bidirectional BAB algorithm is increased further. Numerical examples show that with these new approaches, the CV selection problem can be solved incredibly fast.
Subject: DRNTU::Engineering::Chemical engineeringDRNTU::Engineering::Electrical and electronic engineering::Control and instrumentation::Control engineeringDRNTU::Science::Mathematics::Applied mathematics::Optimization
Type: Journal Article
Series/ Journal Title: Computers and chemical engineering
School: School of Chemical and Biomedical Engineering
Rights: Computers & Chemical Engineering Copyright © 2007 Elsevier Ltd. All rights reserved. The Journal's web site is located at http://www.sciencedirect.com/science/journal/00981354
Version: Accepted version

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