Graph Neural Networks are Heuristics
This reframes learning in combinatorial optimization by enabling graph neural networks to act as direct heuristics, potentially impacting researchers and practitioners in optimization and AI.
The paper tackles the problem of using graph neural networks for combinatorial optimization without supervised training or search, showing that a single model can generate solutions for the Travelling Salesman Problem via forward passes, reducing optimality gaps through dropout and ensembling.
We demonstrate that a single training trajectory can transform a graph neural network into an unsupervised heuristic for combinatorial optimization. Focusing on the Travelling Salesman Problem, we show that encoding global structural constraints as an inductive bias enables a non-autoregressive model to generate solutions via direct forward passes, without search, supervision, or sequential decision-making. At inference time, dropout and snapshot ensembling allow a single model to act as an implicit ensemble, reducing optimality gaps through increased solution diversity. Our results establish that graph neural networks do not require supervised training nor explicit search to be effective. Instead, they can internalize global combinatorial structure and function as strong, learned heuristics. This reframes the role of learning in combinatorial optimization: from augmenting classical algorithms to directly instantiating new heuristics.