HZBSO: A Hybrid Zebra–Butterfly–Snake Metaheuristic for Joint Energy-aware Clustering and Routing in Wireless Sensor Networks

Wireless sensor networks (WSNs) enable wide-area monitoring for industrial and IoT deployments, but energy depletion caused by communication overhead remains a primary barrier to long-term operation.This work introduces Hybrid Zebra-Butterfly-Snake Optimization (HZBSO), a single-stage hybrid meta-heuristic that simultaneously elects cluster heads and forms an inter-cluster relay structure using a multi-objective fitness formulation.The optimizer combines opposition-assisted zebra exploration for enhanced search diversity, butterfly-guided exploitation for convergence toward promising regions, and bi-directional snake refinement for local solution improvement.To maintain stable performance under evolving network conditions, an adaptive weight controller dynamically rebalances objective priorities in response to observed increases in energy dispersion and delay indicators.Performance is evaluated through repeated simulations over randomized network deployments, with results reported as averaged metrics to ensure statistical robustness.In a 100-node WSN configuration, HZBSO improves network survivability and quality of service compared to representative baseline schemes, achieving a last-node-death (LND) of 1740 rounds, packet delivery ratio (PDR) of 94.92%, and average delay of 166.8 ms, while reducing control overhead to 14.09% and lowering residual energy variance to 0.225.Scalability analysis further indicates controlled runtime growth with increasing network size, supporting the applicability of the proposed approach to larger WSN deployments.