Over the past three decades, numerous articles have been published discussing
the renowned DIRECT algorithm (DIvididing RECTangles). These articles present
innovative ideas to enhance its performance and adapt it to various types of
optimization problems. A comprehensive collection of deterministic,
derivative-free algorithmic implementations based on the DIRECT framework has
recently been introduced as part of the DIRECTGO project. DIRECTGO empowers
users to conveniently employ diverse DIRECT-type algorithms, enabling efficient
solutions to practical optimization problems. Despite their variations,
DIRECT-type algorithms share a common algorithmic structure and typically
differ only at certain steps.
Therefore, we propose GENDIRECT -- GENeralized DIRECT-type framework that
encompasses and unifies DIRECT-type algorithms into a single, generalized
framework within this paper. GENDIRECT offers a practical alternative to the
creation of yet another ``new'' DIRECT-type algorithm that closely resembles
existing ones. Instead, GENDIRECT allows the efficient generation of known or
novel DIRECT-type optimization algorithms by assembling different algorithmic
components. This approach provides considerably more flexibility compared to
both the DIRECTGO toolbox and individual DIRECT-type algorithms. A few hundred
thousand DIRECT-type algorithms can be combined using GENDIRECT, facilitating
users' easy customization and the addition of new algorithmic components.
By modifying specific components of five highly promising DIRECT-type
algorithms found in the existing literature using GENDIRECT, the significant
potential of GENDIRECT has been demonstrated. The resulting newly developed
improved approaches exhibit greater efficiency and enhanced robustness in
dealing with problems of varying complexity.Comment: 29 pages, 6 figures, 8 table