# A practical DIRECT-type algorithm for medium-scale black-box global optimization

arXiv: https://arxiv.org/abs/2609.09796 · HTML: https://mlsanity.com/paper/2609.09796/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 83 references that are in the map.
- First posted on arXiv 9 Sep 2026.

## Builds on (most cited first, 10 of 10)

- [COCO: A Platform for Comparing Continuous Optimizers in a Black-Box Setting](https://mlsanity.com/paper/1603.08785/) (2016)
- [Automated Algorithm Selection: Survey and Perspectives](https://mlsanity.com/paper/1811.11597/) (2018)
- [IOHprofiler: A Benchmarking and Profiling Tool for Iterative Optimization Heuristics](https://mlsanity.com/paper/1810.05281/) (2018)
- [DynamoRep: Trajectory-Based Population Dynamics for Classification of Black-box Optimization Problems](https://mlsanity.com/paper/2306.05438/) (2023)
- [DIRECTGO: A new DIRECT-type MATLAB toolbox for derivative-free global optimization](https://mlsanity.com/paper/2107.02205/) (2021)
- [Impact of Training Instance Selection on Automated Algorithm Selection Models for Numerical Black-box Optimization](https://mlsanity.com/paper/2404.07539/) (2024)
- [New hard benchmark functions for global optimization](https://mlsanity.com/paper/2202.04606/) (2022)
- [Lipschitz-inspired HALRECT Algorithm for Derivative-free Global Optimization](https://mlsanity.com/paper/2205.03015/) (2022)
- [Adaptive Block Coordinate DIRECT algorithm](https://mlsanity.com/paper/1612.08786/) (2016)
- [An empirical study of various candidate selection and partitioning techniques in the DIRECT framework](https://mlsanity.com/paper/2109.14912/) (2021)

## Abstract (arXiv)

The DIRECT algorithm is a deterministic global optimization method known for its versatility and balanced exploration-exploitation strategy. However, DIRECT-type algorithms are primarily effective for low-dimensional problems and often exhibit slow convergence as dimensionality increases, limiting their applicability to more complex optimization tasks. To address this limitation, this paper introduces X-DTC-GL, a novel DIRECT-type algorithm that incorporates dynamic partitioning and hybridization techniques. The dynamic partitioning approach adaptively refines the search space based on local one-dimensional surrogate models, enabling rapid subdivision of promising hyper-rectangles. The hybridization strategy selectively employs a hill-climbing method to exploit promising regions identified by the surrogate models. Extensive experiments on four diverse benchmark suites demonstrate that X-DTC-GL significantly outperforms existing DIRECT-type baselines, achieving improvements of ~12% in solvability and ~27% in solution quality. Performance-profile analyses indicate the fastest convergence on up to ~40% of instances, the best runtime performance on ~17% of problems, and competitive overall execution times. By improving performance within the partition-based framework, these advances strengthen the algorithm's competitiveness in state-of-the-art black-box optimization.