# On-Demand Charging Management Model and Its Optimization for Wireless Renewable Sensor Networks
###### Abstract
Periodically, the wireless mobile charging device carries out the charging techniques following a pre-optimized tour that helps to charge the sensor nodes in a short period with a small WMCD travel distance. However, when the nodes' energy consumptions are dissimilar, the TSP-based solution may result in unnecessary visits to nodes with sufficient energy. When mobile charging devices perform sensor node charging tasks, this challenge not only augments the charging device travel distance but also increases the waiting time before low-energy nodes can be charged. Unlike previous schemes [13; 14; 15], where a wireless mobile charging device (WMCD) charges all sensor nodes in a renewable cycle, in our strategy, a WMCD only visits and charges a small group of SNs in each cycle. The major goal is thus to reduce node energy consumption to keep all nodes operational, as well as to minimize the WMCD travel distance, which will increase its vacation time. This is referred to as network eternal functioning, and it is one of the key aims in the design of WRSNs. Seeking an ideal method to schedule a fleet of WMCDs for recharge is typically an NP-hard problem, whereas traditional efforts using standard optimization approaches are not cost-effective due to the WMCD's limited computing resources. Thus, in practice, heuristic algorithms are typically recommended to establish a good compromise between optimality and computing complexity. Wireless energy transfer is an energy harvesting method to address the network's lifetime bottleneck. [PERSON] et al. [11] considered the development of recharging performance in the WSN by successfully illuminating a 60 W bulb over a distance of two meters using magnetic resonance. Several models for wireless energy transfer have been proposed, each with a different specific goal. [PERSON] et al. [16] suggested a near-optimal solution to the problem of safe charging in a sensor network deployment with a static base station. The suggested scheme reduces the unexpected emission of electromagnetic radiated waves from several sinks to a predefined level. One of the challenges that must be addressed is the selection of an ideal point for electromagnetically radiated signals in a plane. They demonstrated that rechargeable sensors can harvest energy from other sources and maximize the charging efficiency. [PERSON] et al. [17] proposed a scheme called ERSVC, and, in their strategy, they prove that the traveling distance plays a large role in energy consumption. To save energy in ERSVC, they created a detailed plan for data flow, charging duration and visiting sets. Furthermore, they showed that ERSVC can theoretically ensure that the network operates forever. However, their method of charging nodes in each cycle is still a problem because they wait for their sensor nodes to approach the general minimum energy level, and this can cause the WMCD to consume more time and energy, reduce its vacation time and cause nodes to start dying in early rounds. A dynamic optimal scheme was proposed in [18] that aimed to increase the vacation time ratio of a wireless mobile charger. In their work, they offered a novel method for determining the best placement of the service station. To ensure enough coverage, not all sensor nodes in each subnetwork are chosen as active nodes. When the sensor node's remaining energy for active nodes falls below a certain threshold, the sensor node stops working and waits for charging. [PERSON] et al. [19] showed how to schedule charging and allocate charging time simultaneously by prolonging the network lifetime and improving the charging efficiency using a proposed mixed-integer optimization algorithm. According to the simulation results, the suggested algorithm may achieve a charging success rate of 100 percent in periodic and hybrid services, which is much higher than the comparison methods. However, due to the enormous number of request nodes in large-scale networks, it is difficult for a single vehicle to meet all charging requests. [PERSON] et al.