A Hybrid Grey Wolf Optimization Framework with Revitalized Boltzmann Distribution-Based Connectivity Modeling for Critical Node Detection in Wireless Sensor Networks

Wireless Sensor Network (WSN) underpins numerous applications, including environmental surveillance, industrial control, and smart cities, where reliable connectivity is vital for continuous sensing and data transmission. On the other hand, a small number of failed or compromised Critical Nodes (CNs) can badly fragment the network topology, interfere with communication, and impair performance. Consequently, devising effective solutions to the CN Detection Problem (CNDP) while taking connectivity, energy, and reliability into account remains a serious research endeavor. To tackle this challenge, this work proposes a Genetic Algorithm-assisted Damped Yo-Yo Grey Wolf Optimization framework with a Revitalized Boltzmann Distribution connectivity model (GA-DY-RBD-GWO). The CNDP is formulated as a node-elimination optimization problem that identifies the top-(k) CNs, where each search agent represents a candidate subset of k nodes. To realistically characterize network connectivity, a Revitalized Boltzmann Distribution (RBD)-based pairwise connectivity model is developed by jointly considering hop distance, residual path energy, and distance-based link reliability. Based on the resulting connectivity matrix, Total Pairwise Connectivity (TPC) is computed, and node criticality is quantified by the reduction in TPC after removing a candidate node set. To effectively explore the combinatorial search space, the Grey Wolf Optimization is augmented with a damped Yo-Yo control mechanism that adaptively balances exploration and exploitation during the optimization process. Furthermore, Genetic Algorithm-inspired crossover and mutation operators improve population diversity and avoid premature convergence, while elitist retention keeps the best-so-far candidate solution. By integrating realistic RBD-based connectivity modeling with an adaptive hybrid metaheuristic, GA-DY-RBD-GWO accurately identifies CNs whose deletion induces maximal TPC degradation. Extensive experiments under diverse network topologies, deployment scenarios, and spatial distributions demonstrate that the GA-DY-RBD-GWO exhibits superior performance over representative baselines, revealing that it is an efficient topology-aware solution for CNDP to improve the reliability of WSNs.