Solving Bilevel Programs Based on Lower-level Mond-Weir Duality

This archive is distributed in association with the INFORMS Journal on Computing under the GNU General Public License v3.0.

This repository contains supporting materials for the paper Solving Bilevel Programs Based on Lower-level Mond-Weir Duality by Y. W. Li, G. H. Lin and X. Zhu.

The software and data in this repository are a snapshot of the software and data that were used in the research reported in the paper.

Cite

To cite the contents of this repository, please cite both the paper and this repo, using their respective DOIs.

https://doi.org/10.1287/ijoc.2023.0108

https://doi.org/10.1287/ijoc.2023.0108.cd

Below is the BibTex for citing this snapshot of the repository.

@article{Li2023.0108,
  author =        {Yu-Wei Li and Gui-Hua Lin and Xide Zhu},
  publisher =     {INFORMS Journal on Computing},
  title =         {Solving Bilevel Programs Based on Lower-level Mond-Weir Duality},
  year =          {2023},
  doi =           {10.1287/ijoc.2023.0108.cd},
  url =           {https://github.com/INFORMSJoC/2023.0108},
}  

Description

The goal of this repository is to provide a large number of numerical examples to illustrate the effectiveness of solving bilevel programs based on lower-level Mond-Weir duality.

Repository Structure

Code

This paper solves bilevel programs by direct and relaxation methods of four reformulations, namely, eMDP, MDP, MPCC, and WDP.

The folder code contains four types of files: generation of linear bilevel programs ( problem ), objective functions ( fun ), constraints, and main programs. An example is as follows:

• main_eMDP is the main program for solving bilevel programs by the direct method for eMDP.

• constraints_eMDP is the constraint program for solving bilevel programs by the direct method for eMDP.

• main_ReMDP is the main program for solving bilevel programs by the relaxation method for eMDP.

• constraints_ReMDP is the constraint program for solving bilevel programs by the relaxation method for eMDP.

Data

All the necessary data for replicating the experiments is included within the code.

Results

The results consist of two parts: one is the detailed numerical results in solving bilevel programs using four methods, and the other is the results in analyzing them.

Tables 1 & 2 show the analytical results of the detailed numerical results Tables 3-17, which are in the numerical experiments section of the paper.

• Table 1 shows the comparison results of three relaxation schemes for MDP.

• Table 2 shows the comparison results of four methods.

Tables 3-17 show detailed numerical results, but are not included in the paper due to their length.

• Tables 3-5 show the numerical results derived from three relaxation schemes for MDP.

• Tables 6-8 show the numerical results derived from relaxation and direct schemes for MPCC.

• Tables 9-11 show the numerical results derived from relaxation and direct schemes for WDP.

• Tables 12-14 show the numerical results derived from relaxation and direct schemes for MDP, where the relaxation scheme is the first relaxation scheme in Tables 3-5.

• Tables 15-17 show the numerical results derived from relaxation and direct schemes for eMDP.

Requirements

All optimization problems are solved using MATLAB 9.13.0.

Support

For support in using the code, don't hesitate to get in touch with the corresponding author.