Publication Type
Conference Proceeding Article
Version
publishedVersion
Publication Date
6-2023
Abstract
A disjointly constrained bilinear program (DBLP) has various practical and industrial applications, e.g., in game theory, facility location, supply chain management, and multi-agent planning problems. Although earlier work has noted the equivalence of DBLP and mixed-integer linear programming (MILP) from an abstract theoretical perspective, a practical and exact closed-form reduction of a DBLP to a MILP has remained elusive. Such explicit reduction would allow us to leverage modern MILP solvers and techniques along with their solution optimality and anytime approximation guarantees. To this end, we provide the first constructive closed-form MILP reduction of a DBLP by extending the technique of symbolic variable elimination (SVE) to constrained optimization problems with bilinear forms. We apply our MILP reduction method to difficult DBLPs including XORs of linear constraints and show that we significantly outperform Gurobi. We also evaluate our method on a variety of synthetic instances to analyze the effects of DBLP problem size and sparsity w.r.t. MILP compilation size and solution efficiency.
Keywords
Bilinear programming; Symbolic variable elimination
Discipline
Artificial Intelligence and Robotics | Operations Research, Systems Engineering and Industrial Engineering
Research Areas
Intelligent Systems and Optimization
Publication
Integration of Constraint Programming, Artificial Intelligence, and Operations Research: 20th International Conference, CPAIOR 2023, Nice, France, May 29-June 1: Proceedings
Volume
13884
First Page
79
Last Page
95
ISBN
9783031332708
Identifier
10.1007/978-3-031-33271-5_6
Publisher
Springer
City or Country
Cham
Citation
JEONG, Jihwan; SANNER, Scott; and KUMAR, Akshat.
A mixed-integer linear programming reduction of disjoint bilinear programs via symbolic variable elimination. (2023). Integration of Constraint Programming, Artificial Intelligence, and Operations Research: 20th International Conference, CPAIOR 2023, Nice, France, May 29-June 1: Proceedings. 13884, 79-95.
Available at: https://ink.library.smu.edu.sg/sis_research/8090
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Additional URL
https://doi.org/10.1007/978-3-031-33271-5_6
Included in
Artificial Intelligence and Robotics Commons, Operations Research, Systems Engineering and Industrial Engineering Commons