Using a division procedure to predict and preserve potential optimality in the DIRECT algorithm

Abstract

In this paper, we are concerned with the DIRECT algorithm. The performance of this algorithm is affected if the smallest hypercube containing the lowest function value is not considered for further subdivision. In this work, we take a little modification to the division procedure such that the modified division provides a sufficient decrease in the slope from the previous potentially optimal hyper-rectangle (POH). This property depends on the location of the sampled points. We illustrate this problem with some numerical examples and show how this situation can be avoided.

Keywords and phrases:

• DIRECT algorithm
• Global optimization
• division procedure