I. Introduction
Minimizing energy consumption and prolonging network lifetime have become primal design goals of next-generation wireless networks, merely because of the energy-constrained nature of wireless devices [1], [2]. Wireless energy transfer technology emerges as a key solution for addressing such issues, and has recently attracted lots of research attention [2]–[5]. Harvesting energy wirelessly offers great potential for increasing the lifetime of wireless devices. Such an ability has even greater impact when considering battery-powered wireless devices whose batteries cannot (or are difficult to) be replaced, as in the case of remote sensor nodes. The authors in [2], [3] proposed an interesting idea for transferring energy wirelessly to sensor network nodes. The idea basically consists of having a designated wireless charging vehicle (WCV) that periodically travel inside the network to wirelessly charge sensors' batteries. They formulated an optimization problem whose objective is to maximize the ratio of the WCV's vacation time over the cycle time, and proved that the optimal traveling path for the WCV is the shortest Hamiltonian cycle. This idea of relying on designated WCVs to charge nodes' batteries wirelessly has been further applied to networks with mobile base stations [4]. The authors in [4] studied the problem of whether and how the mobile base station can be co-located on the WCV to also serve as a charging vehicle. The authors formulated the co-location problem as an optimization problem while accounting for energy charging, WCV's stopping behavior, and data flow routing. Then, they proposed a formulation that depends only on location to serve as a simpler alternative for solving the same general problem.