A GNN-Guided Memetic Algorithm for Critical-Node-Aware Scheduling in Networked Systems

In wireless rechargeable sensor networks (WRSNs), relay-critical sensors support multihop data delivery, so their energy depletion can disrupt traffic from other nodes. We propose a GNN-guided memetic algorithm for critical-node-aware mobile charging. First, a composite structural-importance metric identifies the critical set, and a deterministic topology-and-energy heuristic supplies node-value labels for GNN training. Next, the GNN combines communication links with energy and location features to predict charging priorities that guide population initialization, genetic variation and value-aware local search. Finally, a constrained simulator evaluates visit orders and charging amounts with a bounded lexicographic objective that prioritizes critical-node deaths, total node deaths and travel distance. On 240 random and clustered networks with 50–200 nodes, GNN-guided search lowers mean critical-node death ratio (CDR) relative to plain memetic search in all six 100–200-node scale/topology groups (Holm-adjusted p ≤ 0.0400). At 200 nodes, it also lowers CDR relative to topology-aware greedy by 12.93 and 10.00 percentage points on random and clustered networks, respectively (adjusted p = 0.0112 in each case). Optimized partial charging further lowers CDR and overall dead ratio relative to full charging at 100 and 200 nodes. These results demonstrate advantages in critical-node protection and charging-policy allocation under the tested conditions.