Quantum-inspired hybrid optimization framework for energy-efficient clustering and routing in wireless sensor networks

This paper proposes QIHOR-WSN, a Quantum-Inspired Hybrid Optimization Framework that jointly optimizes clustering and routing in Wireless Sensor Networks (WSNs) to address the dual challenge of energy depletion and network lifetime in large-scale, heterogeneous deployments. In resource-constrained WSNs with unevenly distributed nodes and limited battery capacity, existing methods treat clustering and routing as separate problems, yielding suboptimal global performance and insufficient adaptability to dynamic network conditions. The proposed framework integrates Quantum Particle Swarm Optimization with a Genetic Algorithm to achieve a balanced exploration–exploitation trade-off and superior convergence characteristics. An innovative multi-objective fitness criterion is developed by collectively addressing residual energy, node density, communication distance, and network stability to facilitate energy-conscious cluster-head selection and the most energy-efficient routing paths. The framework presents a density-load-aware radio energy model that extends the classical first-order radio model to account for spatial heterogeneity and communication interference. A complete algorithmic implementation is provided, accompanied by a theoretical complexity analysis establishing O(T·(N 2 + P·N)) computational cost and O(P·N) memory requirements. Comprehensive simulations over 1,000 rounds on 100-node random deployments demonstrate that QIHOR-WSN consistently outperforms all five baseline protocols. Against classical protocols (LEACH, DEEC), network lifetime improvements reach 41–120% (FND metric); against the strongest hybrid baseline (Hybrid PSO-GA), QIHOR-WSN achieves 21.5% longer FND, 10.2% lower total energy consumption at round 1,000, 27.9% extended high-PDR operation, and 22.6% lower end-to-end delay—all statistically significant over 30 independent simulation runs (CV ≤ 5.6%). These gains confirm the robustness, scalability, and practical suitability of QIHOR-WSN for next-generation WSN applications including industrial IoT, environmental monitoring, and smart city infrastructure.