  Current state-of-the-art solvers for mixed-integer programming (MIP) problems
are designed to perform well on a wide range of problems. However, for many
real-world use cases, problem instances come from a narrow distribution. This
has motivated the development of specialized methods that can exploit the
information in historical datasets to guide the design of heuristics. Recent
works have shown that machine learning (ML) can be integrated with an MIP
solver to inject domain knowledge and efficiently close the optimality gap.
This hybridization is usually done with deep learning (DL), which requires a
large dataset and extensive hyperparameter tuning to perform well. This paper
proposes an online heuristic that uses the notion of entropy to efficiently
build a model with minimal training data and tuning. We test our method on the
locomotive assignment problem (LAP), a recurring real-world problem that is
challenging to solve at scale. Experimental results show a speed up of an order
of magnitude compared to a general purpose solver (CPLEX) with a relative gap
of less than 2%. We also observe that for some instances our method can
discover better solutions than CPLEX within the time limit.
