Computational Experience with Hypergraph-Based Methods for Automatic Decomposition in Discrete Optimization

Branch-and-price algorithms based on Dantzig-Wolfe decomposition have shown great success in solving mixed integer linear optimization problems (MILPs) with specific identifiable structure, such as vehicle routing and crew scheduling problems. For unstructured MILPs, the most frequently used methodology is branch-and-cut, which depends on generation of “generic” classes of valid inequalities to strengthen bounds. There has been little investigation into the development of a similar “generic” version of branch-and-price, though this is possible in principle. One of the most important elements required for such a generic branch-and-price algorithm is an automatic method of decomposition. In this paper, we experiment with hypergraph partitioning as a means of performing such automatic decomposition. Computational results explore the potential for applying branch-and-price algorithms within generic solvers and provide insight into how to measure the quality of the decomposition and improve it.