An Adaptive Restart Implementation of DIRECT

DIRECT (DIviding RECTangles) [16] is an optimization algorithm designed to aggressively search for global minima of a real valued objective function over a bound-constrained domain. The algorithm does not use derivative information in its search; instead, it relies on the iteration history to determine future sample locations. The strength of DIRECT is the balanced global and local search it performs. This article describes conditions under which the balance of the algorithm becomes skewed. We observe that DIRECT is sensitive to additive scaling, and has slow asymptotic convergence. We suggest a modification to the algorithm, and present test results that illustrate the effectiveness of our modification. For this paper, we are concerned with a bound constrained optimization problem: