A new sampling method in the DIRECT algorithm

Drawing inspiration from the fact that each point sampled by the DIRECT algorithm will be a midpoint of the center subinterval, we present a one-dimensional version which considers two symmetric points, the one-third and two-third of the length of the considered interval. The center subinterval will be the region of interest. The interval is then bisected and two new points are added at every step. The two points sampled before became two-third and one-third, respectively. Two possibilities of definition of potentially optimal intervals are given. The proposed version predicts a fast convergence, and overcomes some disadvantages of the DIRECT in the case where the global minimum lies at the boundaries.