## 2 Related Work  
Wireless energy transfer is recognized as an effective technology for extending network lifetime. A large number of studies were aimed at optimizing the efficiency of charging devices. [PERSON] [10] proposed a wireless charging scheme based on a single mobile anchor. [PERSON] [11] introduced an optimal charging algorithm based on a novel concept called \"shuttling\" in order to minimize the charger number. [PERSON] [12] set an energy replenishment strategy based on the residual energy level and moving distance of the vehicle. [PERSON] [13] studied an optimization problem whose objective was to minimize the wireless charging vehicle's moving time. [PERSON] [14] optimized charging efficiency by optimizing power allocation and considering the location of the charger. However, the mobile vehicle cannot gather data while replenishing energy in the algorithms above, which resulted in failure to fully exploit its effect. In this paper, the effect of the mobile vehicle can be fully exploited through wireless energy transfer and mobile data gathering. Another effective strategy to prolong network lifetime is to optimize multi-hop or clustering routing strategies, and several energy balance routing algorithms were proposed. A dynamic max flow-based energy balance routing was proposed by [PERSON] [15] for extending network lifetime via an energy balance strategy. [PERSON] [16] proposed an energy-aware and secure multi-hop routing algorithm based on a secret sharing scheme, which could improve the efficiency of energy balance with a multi-hop relay. A novel energy-efficient clustering algorithm was found to improve the energy efficiency by improving energy consumption equilibrium [17]. However, the significant energy consumption difference is inevitable due to large differences in upload distance in the sensor networks with a single static sink. For example, in the multi-hop routing algorithm, nodes close to the sink need to relay the traffic of the entire network, which consumes a lot of energy, resulting in them often dying first. Our algorithm can balance the distributions of traffic load and energy through adaptive dual-mode routing-based mobile data gathering. Furthermore, the network lifetime can be prolonged efficiently. In addition, some works were aimed at introducing wireless charging technology into traditional multi-hop routing algorithms for networks with a single static sink. The autonomous load regulation mechanism-based routing (ALRMR) [18] was an efficient framework of joint wireless energy transfer and multi-hop routing where the routing strategy was adapted to the charging scheme. [PERSON] [19] attempted an approach based on the shortest path algorithm and grid clustering to save and renew power in a way that minimized energy consumption and prolonged the overall network lifetime of WSNs. [PERSON] [20] proposed an optimization algorithm from the aspects of both charging and routing processes. Furthermore, a joint energy supply and routing path selection algorithm was proposed to extend the network lifetime based on an initiative power supply [21]. These algorithms could prolong the network lifetime to a certain extent. However, load imbalance is still unavoidable in the networks with a single static sink, and the algorithms also failed to fully exploit the effect of the mobile vehicle. In our algorithm, the mobile vehicle includes wireless energy transfer and data gathering functions. Due to the benefit of mobile data gathering, the average energy consumption of all nodes can be reduced significantly, and the load can be efficiently balanced. According to the observation above, many researches were aimed at integrating data gathering and the energy replenishment function in mobile vehicles. Using a mobile vehicle with a wireless charging function, [PERSON] [22] proposed a novel way of \"upgrading\" the charging efficiency of \"bottleneck\" nodes. [PERSON] [23] presented a framework that integrated wireless charging and mobile data gathering, which analyzed the causes of energy balance.