Machine Learning for Optimization-Based Separation of Mixed-Integer Rounding Cuts

Arnaud Deza, Elias Boutros Khalil, Aleksandr M. Kazachkov, Oscar Guaje

Abstract:

Mixed-integer rounding (MIR) cutting planes (cuts) are effective at improving
the strength of a linear relaxation for mixed-integer linear programming (MIP)
problems. The cuts in this family are derived by aggregating constraints then
rounding coefficients, but finding the strongest MIR cuts requires optimizing
a costly MIP for the aggregation step, so in practice, heuristic strategies for
separating fractional points are employed. We propose to improve MIR cut generation in the context of a common scenario in applications, where constraints
remain fixed but costs are varied. We present a hybrid cut generation framework
in which we train a machine learning (ML) model to classify which constraints
are involved in useful MIR cuts based on fractional points from relaxations of
the problem. At test time, the predictions of the ML model create a reduced
MIP-based generator of MIR cuts. In our experiments, we create an instance
family from each of three benchmark MIP instances by performing a careful and
costly perturbation of objective coefficients to build a dataset of 1,000 fractional
points to be separated over the same constraint set. The results indicate that the
reduced separator better strengthens the bound in each round of cut generation,
particularly for instances in which the full separator failed to find strong cuts.