Cycling in a Variance Exchange Algorithm: Its Influence and Remedy

This paper introduces cycling in a variance exchange algorithm, a sequential search procedure for the construction of exact $D-$optimal designs done over a list of \(\tilde{X}\) candidate points and involves the iterative improvement of an initial $N-$trial design. Cycling occurs in this sequence at a certain step of the exchange when a point that was earlier removed from the design at the k-th step qualifies to return to the design at the (k+1)-th point with determinant of the information matrix equal to that of the k-th step or even that of the (k-1)-th step and therefore not guaranteeing the N-point exact D-optimal design. A method to overcome cycling is finally proposed