Global Optimization with the DIRECT Algorithm

Abstract

This work describes theoretical results, and practical improvements to the DIRECT Algorithm, a direct search global optimization algorithm for bound-constrained problems. We rigorously show that a sub-sequence of the points sampled by the algorithm satisfy first order necessary conditions for both smooth and non-smooth problems. We show linear convergence of the algorithm for linear problems, and demonstrate why our analysis cannot be extended to more general problems.

We analyze a parameter of DIRECT, and show that it negatively affects the performance of the algorithm. A modified version of the DIRECT is introduced. Test examples are used to demonstrate the effectiveness of the modified algorithm.

We apply DIRECT to six well-field optimization problems from the literature. We collect data on the problems with DIRECT, and utilize statistical methods to glean information from the data about the well-field problems.