Influence branching for learning to solve mixed-integer programs online
Paul Strang, Zacharie Alès, Côme Bissuel, Olivier Juan, Safia Kedad-Sidhoum, Emmanuel Rachelson
TL;DR
The paper addresses online learning for solving mixed-integer programs by introducing influence branching, a graph-based variable selection heuristic applied in the early branch-and-bound iterations. It optimizes the heuristic online using Thompson sampling to pick among five (g,k) actions by evaluating speed-ups over SCIP, demonstrating results competitive with state-of-the-art online approaches. Empirical results on the MIPcc23 corpus show speed-ups across multiple instance series, though some series (notably rhs series 2) show limited or no improvement, and findings suggest the method generalizes to online settings with variations in $A$, $b$, and $c$. Overall, the work provides a practical, graph-structured approach to guiding root-node branching decisions in online MIP solving, with potential for scaling to richer action spaces and broader online frameworks.
Abstract
On the occasion of the 20th Mixed Integer Program Workshop's computational competition, this work introduces a new approach for learning to solve MIPs online. Influence branching, a new graph-oriented variable selection strategy, is applied throughout the first iterations of the branch and bound algorithm. This branching heuristic is optimized online with Thompson sampling, which ranks the best graph representations of MIP's structure according to computational speed up over SCIP. We achieve results comparable to state of the art online learning methods. Moreover, our results indicate that our method generalizes well to more general online frameworks, where variations in constraint matrix, constraint vector and objective coefficients can all occur and where more samples are available.