## 1 Introduction  
In the era of big data and artificial intelligence, wireless sensor networks (WSNs) with sensing, computing and communication ability have gradually become more and more important. In general, nodes send their data to a sink which is located at the center of the network via single-hop or multi-hop transmission. However, the energy of nodes are limited and nodes nearer to the sink have more data forwarding tasks than other nodes, thus, the energy of some nodes is exhausted quickly and the energy holes inevitably appear [1, 2]. After an energy-hole appears no more data can be delivered to the sink [3, 4]. In addition, nodes near the energy-hole are required to bear the data load of those dead nodes so that their energy consumption level will increase more rapidly [5]. As a result, the network becomes disconnected and the network lifetime ends prematurely although vast amounts of residual energy may remain unused. To solve the energy hole problem, most of the existing works focus on the optimization of the network architecture. To improve the energy efficiency and enhance the stability of the network, clustering has been applied in most multi-hop networks [6]. There have been many unequal clustering approaches proposed by researchers. For example in [7], [PERSON] et al. proposed an unequal cluster-basedrouting protocol to mitigate the hot-spot problem. The cluster heads (CHs) forward data to a sink with the help of a greedy geographic and energy-aware routing protocol. However, this may aggravate the burden of some CHs. Moreover, the data is aggregated into fixed-length packets which is not suitable for networks with massive sensing data. Thus, how to further optimize the deployment of nodes as well as the data forwarding strategy are important for mitigating the energy hole problem and improving energy efficiency. Many studies have shown that energy harvesting from natural sources, such as wind, solar, vibration and thermal can effectively improve network performance and prolong network lifetimes. However, the effect of energy harvesting mainly depends on the environment. For example, in a solar harvesting system, the amount of harvested energy is determined by the duration and strength of the solar radiation. Thus, energy harvesting from the environment is not entirely practical for WSNs [8]. On the other hand, [PERSON] et al. have demonstrated that by utilizing magnetic resonant coupling technology, wireless power transfer is both feasible and practical [9]. Nowadays, with the rapid development of energy harvesting and wireless recharging technologies, the advantages of Wireless Rechargeable Sensor Networks (WRSNs) are becoming more and more obvious in extending WSNs' lifetime and improving system robustness [10; 11; 12]. In a realistic scenario, a Wireless Charging Vehicle (WCV) travels across the network and charges all the rechargeable sensor nodes [13]. The recharging sequences are often calculated in advance so that nodes can be recharged before energy depletion [14]. Each node would be charged only once by a WCV in one charging cycle [13]. After visiting all the nodes, the WCV returns to the service station to recharge. Ideally, the lifetime of a WRSN can thus be extended infinitely for perpetual operation [14]. A proof-of-concept WRSN prototype has been established by [PERSON] et al. [15], and experiments have been conducted to evaluate its feasibility as well as the energy replenishment performance in a small-scale WSN. However, the main drawback of energy harvesting is the low recharging efficiency, since the power output of energy harvesting devices is relatively low compared to the energy consumption for sensing and communications. Some serious problems will appear if these limitations are not addressed. For example, some nodes will die before the arrival of the Wireless Charging Vehicle (WCV), or the recharging burden of the WCV is so heavy that there is not enough power for it to return to the service station [14].