An empirical study of various candidate selection and partitioning techniques in the DIRECT framework

09/30/2021 ∙ by Linas Stripinis, et al. ∙ 0

Over the last three decades, many attempts have been made to improve the DIRECT (DIviding RECTangles) algorithm's efficiency. Various novel ideas and extensions have been suggested. The main two steps of DIRECT-type algorithms are the selection and partitioning of potentially optimal candidates. However, the most efficient combination of these two steps is an area that has not been investigated so far. This paper presents a study covering an extensive examination of various candidate selection and partitioning techniques within the same DIRECT algorithmic framework. Twelve DIRECT-type algorithmic variations are compared on 800 randomly generated GKLS-type test problems and 94 box-constrained global optimization problems from DIRECTlib with varying complexity. We have identified the most efficient selection and partitioning combinations based on these studies, leading to new, more efficient, DIRECT-type algorithms.

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