A Clustering Routing Algorithm for Wireless Sensor Networks Using Black-Kite Optimization Combined with Time of Arrival Technique

Wireless sensor networks (WSNs) have widespread applications in vital fields, including environmental surveillance, medical care, and smart urban settings. Nevertheless, the restricted battery capacity of sensor nodes renders energy consumption an ongoing hindrance, limiting both the performance and operational lifespan of a network. To mitigate this challenge, this study proposes an enhanced clustering and routing scheme, the Black-Kite Optimization–Time Of Arrival (BKA-TOA) algorithm, which jointly optimizes cluster head selection and data transmission. The proposed BKA-TOA integrates the bio-inspired Black-Kite Optimization (BKA) with relay selection based on the Time of Arrival (TOA) technique. A multidimensional fitness function is constructed by incorporating inter-node distance, energy variance, and cluster head distribution to achieve robust clustering, balanced energy consumption, and improved scalability. Extensive simulations conducted in Matlab R2024a are used to benchmark the proposed algorithm against Particle Swarm Optimization (PSO), Improved Ant Colony–minimum spanning tree (IACO-MST), and Energy-Efficient Uneven Clustering (EEUC). The experimental results indicate that BKA-TOA significantly reduces node mortality, improves residual energy preservation, and prolongs the operational lifetime of WSNs compared with competing algorithms.