The DIRECT algorithm was motivated by a modification to Lipschitzian optimization. The algorithm begins its search by sampling the objective function at the midpoint of an interval, where this function attains its lowest value, and then divides this interval by trisecting it. One of its weakness is that if a global minimum lies at the boundaries, which can never be reached, the convergence of the algorithm will be unecessary slow. We present a one-dimensional variante of the DIRECT algorithm based on another strategy of sudividing the search domain. It consists of decreasing the number of intervals and increasing the number of sampling points, by interverting the roles of dividing and sampling at some steps of the DIRECT algorithm, and thus, overcoming this disadvantage.
Citation
unpublished:Department of Mathematics, faculty of sciences. University Ferhat-Abbas, 19000 SETIF, ALGERIA.