A Deep Instance Generative Framework for MILP Solvers Under Limited Data Availability
arxiv(2023)
摘要
In the past few years, there has been an explosive surge in the use of
machine learning (ML) techniques to address combinatorial optimization (CO)
problems, especially mixed-integer linear programs (MILPs). Despite the
achievements, the limited availability of real-world instances often leads to
sub-optimal decisions and biased solver assessments, which motivates a suite of
synthetic MILP instance generation techniques. However, existing methods either
rely heavily on expert-designed formulations or struggle to capture the rich
features of real-world instances. To tackle this problem, we propose G2MILP,
the first deep generative framework for MILP instances. Specifically, G2MILP
represents MILP instances as bipartite graphs, and applies a masked variational
autoencoder to iteratively corrupt and replace parts of the original graphs to
generate new ones. The appealing feature of G2MILP is that it can learn to
generate novel and realistic MILP instances without prior expert-designed
formulations, while preserving the structures and computational hardness of
real-world datasets, simultaneously. Thus the generated instances can
facilitate downstream tasks for enhancing MILP solvers under limited data
availability. We design a suite of benchmarks to evaluate the quality of the
generated MILP instances. Experiments demonstrate that our method can produce
instances that closely resemble real-world datasets in terms of both structures
and computational hardness. The deliverables are released at
https://miralab-ustc.github.io/L2O-G2MILP.
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