Joint Energy Loss and Time Span Minimization for Energy-Redistribution-Assisted Charging of WRSNs With a Mobile Charger

The use of mobile chargers (MCs) to charge the nodes in wireless rechargeable sensor networks via wireless power transfer (WPT) has attracted much research effort. Existing works mostly concentrate on path planning whereas neglecting the opportunities to improve charging coverage and efficiency by exploiting the energy redistribution (ERD) process among nodes and an MC’s capability of charging multiple nodes simultaneously via WPT. To exploit such opportunities, we study the underlying ERD-assisted MC charge scheduling (ERAMCCS) problem, i.e., to find a charging schedule satisfying the nodes’ energy demands with minimum energy loss and minimum time span. After proving that the problem is NP-hard, we propose a charge scheduling algorithm based on the greedy idea (CSBGI), which provides a solution by decoupling the problem into two subproblems: 1) ERAMCCS-Energy and 2) ERAMCCS-Time, to minimize the energy loss and the time span, respectively. By partitioning the energy loss into transmission energy loss and moving energy loss, we solve the ERAMCCS-Energy problem by minimizing the two parts, respectively, by formulating and solving some linear programming problems and traveling salesman problem problems based on the charging position set. The charging position set is iteratively refined by identifying and removing redundant charging positions. For the ERAMCCS-Time problem, concurrent energy transmission opportunities are exploited to try to minimize the time span of the schedule. We demonstrate some key properties of CSBGI, such as its approximation ratio in terms of energy loss and its time complexity. Testbed experiments and numerical simulations confirm the superiority of CSBGI over typical algorithms.