  Combinatorial Optimization (CO) has been a long-standing challenging research
topic featured by its NP-hard nature. Traditionally such problems are
approximately solved with heuristic algorithms which are usually fast but may
sacrifice the solution quality. Currently, machine learning for combinatorial
optimization (MLCO) has become a trending research topic, but most existing
MLCO methods treat CO as a single-level optimization by directly learning the
end-to-end solutions, which are hard to scale up and mostly limited by the
capacity of ML models given the high complexity of CO. In this paper, we
propose a hybrid approach to combine the best of the two worlds, in which a
bi-level framework is developed with an upper-level learning method to optimize
the graph (e.g. add, delete or modify edges in a graph), fused with a
lower-level heuristic algorithm solving on the optimized graph. Such a bi-level
approach simplifies the learning on the original hard CO and can effectively
mitigate the demand for model capacity. The experiments and results on several
popular CO problems like Directed Acyclic Graph scheduling, Graph Edit Distance
and Hamiltonian Cycle Problem show its effectiveness over manually designed
heuristics and single-level learning methods.
