Combinatorial optimization is a well-established area in operations research and computer science. Until recently, its methods have focused on solving problem instances in isolation, ignoring the fact that they often stem from related data distributions in practice. However, recent years have seen a surge of interest in using machine learning, especially graph neural networks (GNNs), as a key building block for combinatorial tasks, either  as solvers or as helper functions. GNNs are an inductive bias that effectively encodes combinatorial and relational input due to their permutation-invariance and sparsity awareness . This paper presents a conceptual review of recent key advancements in this emerging field, aiming at both the optimization and machine learning researcher .
Combinatorial optimization is a well-established area in operations research and computer science. Until recently, its methods have focused on solving problem instances in isolation, ignoring the fact that they often stem from related data distributions in practice. However, recent years have seen a surge of interest in using machine learning, especially graph neural networks (GNNs), as a key building block for combinatorial tasks, either directly as solvers or by enhancing exact solvers. The inductive bias of GNNs effectively encodes combinatorial and relational input due to their invariance to permutations and awareness of input sparsity . This paper presents a conceptual review of recent key advancements in this emerging field, aiming at researchers in both optimization and machine learning .
A
directly
R
as helper functions. GNNs are an inductive bias that
by enhancing exact solvers. The inductive bias of GNNs
R
permutation-invariance and sparsity awareness
invariance to permutations and awareness of input sparsity
R
both the
researchers in both
D
researcher