Algorithms for Cardinality-Constrained Multi-Objective Optimization Problems

Implementation of the MOIHT/MOHyb algorithms and the SFSD methodology proposed in

Lapucci, M. & Mansueto, P., Cardinality-Constrained Multi-Objective Optimization: Novel Optimality Conditions and Algorithms. Journal of Optimization Theory and Applications (2024)

and of the MOSPD algorithm introduced in

Lapucci, M., A penalty decomposition approach for multi-objective cardinality-constrained optimization problems. Optimization Methods and Software (2022).

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

@article{Lapucci2024,
         author={Lapucci, Matteo and Mansueto, Pierluigi},
         title={Cardinality-Constrained Multi-objective Optimization: Novel Optimality Conditions and Algorithms},
         journal={Journal of Optimization Theory and Applications},
         year={2024},
         month={Mar},
         day={04},
         issn={1573-2878},
         doi={10.1007/s10957-024-02397-3},
         url={https://doi.org/10.1007/s10957-024-02397-3}
}

@article{lapucci_penaltydecomposition_2022,
         author = {Matteo Lapucci},
         title = {A penalty decomposition approach for multi-objective cardinality-constrained optimization problems},
         journal = {Optimization Methods and Software},
         volume = {37},
         number = {6},
         pages = {2157-2189},
         year = {2022},
         publisher = {Taylor & Francis},
         doi = {10.1080/10556788.2022.2060972}
}

Main Dependencies Installation

In order to execute the code, you need an Anaconda environment and the Python package nsma installed in it. For a detailed documentation of this framework, we refer the reader to its GitHub repository.

For the package installation, open a terminal (Anaconda Prompt for Windows users) in the project root folder and execute the following command. Note that a Python version 3.9 or higher is required.

pip install nsma

Gurobi Optimizer

In order to run some parts of the code, the Gurobi Optimizer (Version 9 or higher) needs to be installed and, in addition, a valid Gurobi licence is required. The code was experimented with the Gurobi-related library gurobipy v9.5.2.

Usage

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

python main.py --single_point_methods MOIHT --refiner SFSD --prob_type QP --prob_path test_QPs/QP_n25_k1_a.pkl --s 5 --max_time 2 --plot_pareto_front --general_export

Contact

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

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