Wireless sensor networks (WSNs) are the backbone of IoT-enabled smart manufacturing, environmental monitoring, and industrial automation. However, their broadcast nature makes communication links vulnerable to eavesdropping, routing manipulation, and denial-of-service attacks. Strategically placing monitor nodes to check each link is an effective approach to protect against attacks, but energy, connectivity, and capacity constraints should be considered while picking monitor nodes. In this paper, we tackle the Minimum-Weighted Connected Capacitated Vertex Cover (MWCCVC) problem, which minimizes monitoring costs, ensures backbone connectivity, and adheres to per-node capacity constraints. Unlike prior works that consider weighted vertex cover, connectivity constraints, or capacitated variants separately, the proposed MWCCVC model jointly integrates all three dimensions within a single vertex cover-based monitoring framework. We first provide a Branch-and-Bound (B&B) solver with linear programming relaxation bounds and constraint-based pruning strategies that produces optimum solutions. Three constructive greedy heuristics (GD, GR, GW) and two hybrid genetic algorithms (HGA, HGA-v2) that combine parameterized greedy decoders with evolutionary search are proposed; all methods guarantee full edge coverage, induced-subgraph connectivity, and max-flow-validated capacity feasibility. Tests on 130 small, 160 medium, and 19 large benchmark instances show that HGA matches B&B optima on every small instance, beats the time-limited B&B by 6.6% on medium instances, where the percentage is computed based on the relative difference in average total weight with respect to B&B, and stays the best on large graphs with up to 1000 nodes. The HGA-v2 tries to balance the quality and speed, with only a 3.1% difference at $10\times$ faster execution.

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 ${\chi }^2=93.05$, $p<{10}^{-4}$. 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.