🤖 AI Summary
This work investigates how graph neural networks (GNNs) can efficiently solve combinatorial optimization problems—such as the Traveling Salesman Problem—under a fully unsupervised, search-free, and non-sequential decision-making setting. The proposed non-autoregressive GNN model incorporates global structural constraints as inductive bias during training, enabling it to generate high-quality solutions in a single forward pass without requiring supervision or explicit search. By leveraging dropout at inference time together with snapshot ensembling, the model substantially narrows the optimality gap and enhances performance through solution diversity. This study presents the first demonstration that GNNs can function as internalized unsupervised heuristics, establishing a novel paradigm for learned combinatorial optimization solvers.
📝 Abstract
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.