QPSODRL: an improved quantum particle swarm optimization and deep reinforcement learning based intelligent clustering and routing protocol for wireless sensor networks.

In wireless sensor networks (WSNs), energy-efficient clustering and adaptive routing are key to extending network lifetime and ensuring reliable communication under dynamic conditions. Although numerous metaheuristic- and learning-based schemes have been developed to address these challenges, existing methods may suffer from premature convergence, imbalanced energy utilization, and limited generalization capability when network conditions vary, which restricts their long-term effectiveness. To address these limitations, an intelligent clustering and routing protocol called QPSODRL (Quantum Particle Swarm Optimization and Deep Reinforcement Learning), that integrates an enhanced Quantum Particle Swarm Optimization (QPSO) and Deep Reinforcement Learning (DRL), is proposed in this paper. In the clustering phase based on QPSO, an entropy-guided activation strategy is introduced to dynamically switch between global exploration and local exploitation, based on the network's energy distribution entropy. Additionally, an elite-guided quantum perturbation mechanism is adopted to drive particles toward promising regions while maintaining diversity, significantly improving convergence quality. In the routing phase, a modified Dueling Double Deep Q-Network (D3QN) is extended with an advantage entropy regularization term, which encourages policy diversity and avoids overfitting, thereby increasing robustness against topology variations. Furthermore, an Enhanced Prioritized Experience Replay (E-PER) strategy is integrated to adjust sampling priorities based on temporal-difference errors, residual energy, and communication cost, accelerating policy convergence in energy-constrained environments. Extensive simulation results demonstrate that QPSODRL outperforms four state-of-the-art protocols in terms of network lifetime, load balancing, throughput, and energy consumption, validating its superiority in optimization accuracy, learning efficiency, and environmental adaptability.