Computing Bipath Multicommodity Flows with Constraint Programming–Based Branch-and-Price-and-Cut

Abstract

We propose a constraint programming (CP)–based branch-and-price-and-cut framework to exactly solve bipath multicommodity flow (MCF): an MCF problem with two paths for each demand. The goal is to route demands in a capacitated network under the minimum cost. The two paths must have disjoint arcs, and the delays accumulated along the two paths must be within a small deviation of each other. CP is used at multiple points in this framework: for solving pricing problems, for cut generation, and for primal and branching node heuristics. These modules use a CP solver designed for network routing problems and can be adapted to other combinatorial optimization problems. We also develop a novel, complete, two-level branching scheme. On a set of diverse bipath MCF instances, experimental results show that our algorithm significantly outperforms monolithic CP and mixed integer linear programming models and demonstrate the efficiency and flexibility brought by the tailored integration of linear programming and CP methodologies. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: This work was supported by the Natural Sciences and Engineering Research Council of Canada; Huawei Technologies. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0128 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0128 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .