Bidirectional Branch and Bound for Average Loss Minimization

Two algorithms for selection of controlled variables using the average loss as the criterion.

Description

This is the third part of the work to select measurements / measurement combination for selfoptimizing control. It uses aberage loss as the criterion instead of the worst case loss presented in the second part.

Bidirection branch and bound (B3) is a very efficient BAB algorithm. In the first two parts, we developed b3msv and b3wc algorithms for minimum singular value and worst case loss.

Reference:
V. Kariwala and Y. Cao, Bidirectional Branch and Bound for Controlled Variable Selection: Part III. Local Average Loss Minimization, IEEE Transactions on Industrial Informatics, Vol. 6, No. 1, pp. 54—61, 2010.

http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5378454

Acknowledgements

The author wishes to acknowledge the following in the creation of this submission:
Bidirectional Branch and Bound Minimum Singular Value Solver (V2), Bidirectional Branch and Bound Solvers for Worst Case Loss Minimization

• MATLAB release: MATLAB 7.9 (2009b)

[Yinghui Tay]

Hi Yi Cao, I have used your b3av file to select the top few candidates set for my controlled variables selection. However, a warning appears: Warning: Matrix is close to singular or badly scaled.
         Results may be inaccurate. RCOND = 1.705851e-028.
> In b3av at 103
  In CV_Wn_5percent_Juu2 at 17

I am not sure if this warning distorts or implicate my results as the top set of CVs selected is impossible to effect and hence I would like to seek your opinions on this issue.

[Yi Cao]

Hi Yinghui,

This warning is at line 103, which is before actual BAB search. The line aims to calculate the average loss if all measurements are used. Therefore, the warning suggests your matrices, G and Y are close to singular. You can send me you code to have a look.

HTH
Yi