  In many operational applications, it is necessary to routinely find, within a
very limited time window, provably good solutions to challenging mixed-integer
linear programming (MILP) problems. An example is the Security-Constrained Unit
Commitment (SCUC) problem, solved daily to clear the day-ahead electricity
markets. Previous research demonstrated that machine learning (ML) methods can
produce high-quality heuristic solutions to combinatorial problems, but proving
the optimality of these solutions, even with recently-proposed
learning-enhanced branching methods, can still be time-consuming. In this
paper, we propose a simple modification to improve the performance of
learning-enhanced branching methods based on the key observation that, in such
operational applications, instances are significantly similar to each other.
Specifically, instances typically share the same size and problem structure,
with slight differences only on matrix coefficients, right-hand sides and
objective function. In addition, certain groups of variables within a given
instance are also typically similar to each other. Therefore, unlike previous
works in the literature which predicted all branching scores with a single ML
model, we propose training separate ML models per variable or per groups of
variables, based on their similarity. We evaluate this enhancement on realistic
large-scale SCUC instances and we obtain significantly better gap closures than
previous works with the same amount of training data.
