G2MILP: Learning to Generate Mixed-Integer Linear Programming Instances
for MILP Solvers
Abstract
There have been significant efforts devoted to developing advanced
mixed-integer linear programming (MILP) solvers, which are powerful
tools for solving various real-world optimization problems. Despite the
achievements, the limited availability of real-world instances often
results in sub-optimal decisions and biased evaluations, which motivates
a suite of MILP instance generation techniques. However, these
approaches either rely on expert-designed formulations or struggle to
capture the rich features of real-world instances. Moreover, the task of
generating challenging MILP instances—which are valuable resources for
evaluating solvers and motivating more efficient algorithms—remains
underexplored. To tackle these problems, we propose G2MILP,
which to the best of our knowledge is the first deep generative
framework for MILP instances. Specifically, G2MILP represents MILP
instances as bipartite graphs and employs a masked variational
autoencoder to iteratively corrupt and replace parts of the original
graphs to generate new ones. We then propose a hardness-oriented scheme,
which iteratively augments the generator by learning from the hardest
instances, to enhance G2MILP to construct challenging MILP instances.
Experiments demonstrate that G2MILP can generate realistic MILP
instances to effectively facilitate downstream tasks. Moreover, G2MILP
can generate difficult instances initializing from given datasets, and
the boost of hardness can be orders of magnitude.