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

TL;DR

This paper empirically compares various candidate selection and partitioning techniques within the DIRECT algorithm framework, identifying the most efficient combinations for global optimization tasks.

Contribution

It provides an extensive empirical analysis of different DIRECT-type algorithm variations, leading to the development of more efficient algorithms included in DIRECTGO v1.1.0.

Findings

Identified the most effective selection and partitioning combinations.

Compared 12 algorithm variations on 896 test problems.

Developed new, more efficient DIRECT-type algorithms.

Abstract

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 selecting and partitioning potentially optimal rectangles. 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 96 box-constrained global optimization problems from DIRECTGOLib v1.1 with varying complexity. Based on these studies, we have identified the most efficient selection and partitioning combinations leading to new, more efficient, DIRECT-type algorithms. All these algorithms are included in the latest version of DIRECTGO v1.1.0 and are publicly available.