Citation:
Yi Cao, Vinay Kariwala, Bidirectional branch and bound for controlled variable
selection. Part I: Principles and minimum singular value criterion, Computers &
Chemical Engineering, Volume 32, Issue 10, 17 October 2008, Pages 2306-2319
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.