Wireless Sensor Networks Nodes Clustering and Optimization Based on Fuzzy C-Means and Water Strider Algorithms

Wireless sensor networks (WSNs) face critical challenges in energy management and network lifetime optimization due to limited battery resources and communication overhead. This study introduces a novel hybrid clustering protocol that integrates the Water Strider Algorithm (WSA) with Fuzzy C-Means (FCM) clustering to achieve superior energy efficiency and network longevity. The proposed WSA-FCM method employs WSA for global optimization of cluster-head positions and FCM for refined node membership assignment with fuzzy boundaries. Through extensive experimentation across networks of 200-800 nodes with 10 independent simulation runs, the method demonstrates significant improvements: First Node Death (FND) delayed by 16.1% ($678\pm12$ vs $584\pm18$ rounds), Last Node Death (LND) extended by 11.9% ($1,262\pm8$ vs $1,128\pm11$ rounds), and 37.4% higher residual energy retention ($5.47\pm0.09$ vs $3.98\pm0.11$ J) compared to state-of-the-art hybrid methods. Intra-cluster distances are reduced by 19.4% with statistical significance (p < 0.001). Theoretical analysis proves convergence guarantees and complexity bounds of $O(n\times c\times T)$, while empirical scalability analysis demonstrates near-linear scaling behaviour. The method outperforms recent hybrid approaches including MOALO-FCM, MSSO-MST, Fuzzy+HHO, and GWO-FCM across all performance metrics with rigorous statistical validation.