G-DFL: Combining Gradient Information and Primitive Directions for High-Performance Mixed-Integer Optimization

Implementation of the G-DFL algorithm proposed in

Lapucci M., Liuzzi G., Lucidi S. & Mansueto P., Combining gradient information and primitive directions for high-performance Bound-Constrained mixed-integer optimization. Journal of Global Optimization (2026)

Lapucci M., Liuzzi G., Lucidi S. & Mansueto P., Combining Gradient Information and Primitive Directions for High-Performance Mixed-Integer Optimization. arXiv pre-print (2024)

and of the MISQP algorithm introduced in

Exler O. & Schittkowksi K., A trust region SQP algorithm for mixed-integer nonlinear programming. Optimization Letters (2007)

If you have used our code for research purposes, please cite the publication mentioned above. For the sake of simplicity, we provide the Bibtex format:

@Article{Lapucci2026,
author={Lapucci, Matteo
and Liuzzi, Giampaolo
and Lucidi, Stefano
and Mansueto, Pierluigi},
title={Combining gradient information and primitive directions for high-performance Bound-Constrained mixed-integer optimization},
journal={Journal of Global Optimization},
year={2026},
month={Jan},
day={12},
issn={1573-2916},
doi={10.1007/s10898-025-01583-5},
url={https://doi.org/10.1007/s10898-025-01583-5}
}

Main Dependencies Installation

In order to execute the code, you need an Anaconda environment.

Main Packages

• python v3.9.16
• numpy v1.24.3
• scipy v1.10.1
• tensorflow v2.13.0
• gurobipy v11.0.0

Gurobi Optimizer

In order to run some parts of the code, the Gurobi Optimizer (Version 11 or higher) needs to be installed and, in addition, a valid Gurobi licence is required.

Usage

In args_parser.py you can find all the possible arguments. Given a terminal (Anaconda Prompt for Windows users), two examples of execution could be the following.

python main.py --algs G-DFL MISQP --seeds 16007 --verbose --max_time 2 --type_gradient_related_direction lbfgs

python main.py --algs G-DFL MISQP --seeds 16007 --save_logs --max_time 2 --type_gradient_related_direction lbfgs

In the second case, the logs are saved in the Outputs folder. In main.py, you can find all the documentation about how they are stored.

Contact

If you have any question, feel free to contact us:

Pierluigi Mansueto
Global Optimization Laboratory (GOL)
University of Florence
Email: pierluigi dot mansueto at unifi dot it

Giampaolo Liuzzi
Dipartimento di Ingegneria Informatica Automatica e Gestionale "Antonio Ruberti" (DIAG) (DIAG)
University of Rome "La Sapienza"
Email: liuzzi at diag dot uniroma1 dot it