Algorithm 1: The Charging Time Scheduling Strategy

Input: the initial energy $E_0$, the residual energy $e_{i,t}$, the estimated energy consumption rate ${\widehat{c}}_{i,t}$, the charging duration $T_c$ of WCD, the charging rate ${\mathsf{\Lambda }}_c\eta$, the location of each node. Output: each node’s charging time $t_i^{\prime }$ and the travel path of mobile charger. $t_i\leftarrow (E_0-e_{i,t})/{\mathsf{\Lambda }}_c\eta$     /*the maximum charging time for each node*/ $t_i^{\prime }\leftarrow (t_i/{\displaystyle {\sum }_{i=1}^N{t}_i})\ast T_c$    /*the original charging time of each node*/ $l_{i,t}\leftarrow e_{i,t}/{\widehat{c}}_{i,t}$         /*the estimated remaining lifetime of each node*/ Calculate the charging schedule cycle $T$ according to $T_c$ and the maximum travel time. Sort the remaining lifetime from small to large to obtain the element set $M={\{(N_i,t_i^{\prime })\}}_{i=1}^n$. $k\leftarrow 1,m\leftarrow n$ Calculate the shortest travel path for visiting nodes selected to be charged. return $t_i^{\prime }$ and the shortest travel path.