A-Optimality Orthogonal Forward Regression Algorithm Using Branch and Bound

In this brief, we propose an orthogonal forward regression (OFR) algorithm based on the principles of the branch and bound (BB) and A-optimality experimental design. At each forward regression step, each candidate from a pool of candidate regressors, referred to as
S
, is evaluated in turn with three possible decisions: 1) one of these is selected and included into the model; 2) some of these remain in
S
for evaluation in the next forward regression step; and 3) the rest are permanently eliminated from
S
. Based on the BB principle in combination with an A-optimality composite cost function for model structure determination, a simple adaptive diagnostics test is proposed to determine the decision boundary between 2) and 3). As such the proposed algorithm can significantly reduce the computational cost in the A-optimality OFR algorithm. Numerical examples are used to demonstrate the effectiveness of the proposed algorithm.