GENDIRECT: a GENeralized DIRECT-type algorithmic framework for derivative-free global optimization

The

algorithm (DIviding RECTangles) has been a cornerstone of derivative-free global optimization for three decades, inspiring numerous enhancements and adaptations. The recent toolbox consolidated over fifty of these implementations, providing users with a diverse set of tools.

In this paper, we introduce

, a generalized framework that unifies -type algorithms under a single approach. offers a flexible alternative to creating yet another similar algorithm, enabling efficient generation of both known and novel -type optimization algorithms through the assembly of different algorithmic components. This approach surpasses the flexibility of both the toolbox and individual algorithms. allows the creation of hundreds of thousands of combinations, facilitating customization and incorporation of new components for further advancements.

A preliminary experimental study highlights the potential of specific algorithmic components (such as reduced Pareto selection or infinity norm for candidate size calculation) to significantly enhance performance on certain objective functions, emphasizing the importance of tailoring algorithmic choices within the framework to suit specific problem characteristics. The obtained results also facilitate the derivation of practical default configurations for small-, medium-, and large-budget optimization scenarios.