Securing IoT-enabled wireless sensor network links requires selecting a minimum-cost set of connected monitor nodes that observes every link while satisfying capacity constraints, a problem known as the minimum weighted connected capacitated vertex cover (MWCCVC). To the best of our knowledge, this work introduces the first learning-based framework for the MWCCVC through a three-stage pipeline that combines supervised graph neural networks, feasibility repair, and local search. We compare twelve graph neural network architectures, including graph convolutional network, graph attention network, GraphSAGE, Graph Isomorphism Network (GIN), and GraphTransformer, under unified features, loss functions, and hyperparameter tuning. Throughout the evaluation on 309 benchmark instances under a 5-fold cross-validation protocol, feasibility is guaranteed by the deterministic repair module instead of being learned by the network, resulting in 100% feasible covers across all evaluated instances. At the large scale, GIN, GraphSAGE, DeeperGIN, and EdgeAwareGIN reach parity with the state-of-the-art hybrid genetic algorithm (HGA), with GIN attaining a mean gap of −0.37% (a difference of less than one percentage point) while completing in seconds instead of HGA’s hours. Statistical tests across the full 309-instance benchmark confirm significant differences between the architectures, with Friedman χ2=93.05, p<10−4. The best-performing architectures remain within about 2% of HGA on small- and medium-scale instances, where HGA is near-optimal, and become the preferred choice at the large scale, mainly because their wall-clock time is much shorter than HGA’s at the same solution quality.
Uslu et al. (2026) studied this question.