Despite rapid advancements in sensor networks, conventional battery-powered sensor networks suffer from limited operational lifespans and frequent maintenance requirements that severely constrain their deployment in remote and inaccessible environments. As such, wireless rechargeable sensor networks (WRSNs) with mobile charging capabilities offer a promising solution to extend network lifetime. However, WRSNs face critical challenges from the inherent trade-off between maximizing the node survival rates and maximizing charging energy efficiency under dynamic operational conditions. In this paper, we investigate a typical scenario where mobile chargers move and charge the sensor, thereby maintaining the network connectivity while minimizing the energy waste. Specifically, we formulate a multi-objective optimization problem that simultaneously maximizes the network node survival rate and mobile charger energy usage efficiency across multiple time slots, which presents NP-hard computational complexity with long-term temporal dependencies that make traditional optimization approaches ineffective. To address these challenges, we propose an enhanced evolutionary multi-objective deep reinforcement learning algorithm, which integrates a long short-term memory (LSTM)-based policy network for temporal pattern recognition, a multilayer perceptron-based prospective increment model for future state prediction, and a time-varying Pareto policy evaluation method for dynamic preference adaptation. Extensive simulation results demonstrate that the proposed algorithm significantly outperforms existing approaches in balancing node survival rate and energy efficiency while generating diverse Pareto-optimal solutions. Moreover, the LSTM-enhanced policy network converges 25% faster than conventional networks, with the time-varying evaluation method effectively adapting to dynamic conditions.

翻译：尽管传感器网络技术发展迅速，传统电池供电的传感器网络仍存在工作寿命有限、维护频繁等瓶颈，严重制约其在偏远及不可达环境中的部署。为此，具有移动充电能力的无线可充电传感器网络（WRSN）为延长网络寿命提供了可行方案。然而，WRSN面临核心挑战：在动态运行条件下如何平衡最大化节点存活率与最大化充电能效之间的固有矛盾。本文研究典型场景中移动充电器通过移动为传感器充电，在维持网络连通性的同时最小化能量浪费。具体而言，我们建立了一个多目标优化问题，该问题需在多个时隙内同步最大化网络节点存活率与移动充电器能量利用效率，其具有NP难计算复杂度与长期时域依赖特性，导致传统优化方法失效。针对这些挑战，我们提出增强型进化多目标深度强化学习算法，该算法集成了基于长短期记忆（LSTM）的策略网络用于时序模式识别、基于多层感知器的前瞻增量模型用于未来状态预测，以及时变帕累托策略评估方法用于动态偏好适应。大量仿真结果表明，所提算法在平衡节点存活率与能效方面显著优于现有方法，同时可生成多样化帕累托最优解。此外，LSTM增强策略网络较传统网络收敛速度提升25%，时变评估方法能有效适应动态环境条件。