Towards Low-Cost Yet High-Performance Sensor Networks by Deploying a Few Ultra-fast Charging Battery Powered Sensors

. 2018 Aug 23;18(9):2771. doi: 10.3390/s18092771

Algorithm 1 Joint charging scheduling and routing allocation algorithm (CSRA).

Input: a set $V_{s}$ , a set V of to-be-charged sensors, the residual energy $e_{i}$ of each sensor $v_{i}$ in $V_{s}$ at some time $t_{0}$ , a small threshold $ϵ$ with $ϵ > 0$ .

Output: routing $f_{i j}$ , charging tour C.

1:
Obtain a routing $f_{i j}^{0}$ by assuming that each sensor uploads its data along its minimum energy path to the base station;
2:
for $K \leftarrow$ 1 to $K_{m a x}$ do
3:
Find a charging tour $C^{K}$ with the routing $f_{i j}^{K - 1}$ , by invoking Algorithm 2 for the charging scheduling subproblem;
4:
Obtain a routing $f_{i j}^{K}$ with the charging tour $C^{K}$ , by invoking Algorithm 3 for the routing allocation subproblem;
5:
Let $D^{K - 1}$ and $D^{K}$ be the longest sensor dead durations of solutions $(f_{i j}^{K - 1}, C^{K - 1})$ and $(f_{i j}^{K}, C^{K})$ , respectively;
6:
if $D^{K} > D^{K - 1}$ then
7:
$C \leftarrow C^{K - 1}, f_{i j} \leftarrow f_{i j}^{K - 1}$ ; /* $(f_{i j}^{K}, C^{K})$ is no better than $(f_{i j}^{K - 1}, C^{K - 1})$ */
8:
break;
9:
else
10:
$C \leftarrow C^{K}, f_{i j} \leftarrow f_{i j}^{K}$ ; /* $(f_{i j}^{K}, C^{K})$ is better than $(f_{i j}^{K - 1}, C^{K - 1})$ */
11:
end if
12:
if $D^{K - 1} - D^{K} \leq ϵ$ then
13:
/* the difference of the longest sensor dead durations $D^{K}$ and $D^{K - 1}$ of solutions $(f_{i j}^{K}, C^{K})$ and $(f_{i j}^{K - 1}, C^{K - 1})$ is smaller than $ϵ$ */
14:
break;
15:
end if
16:
end for
17:
return charging tour C, and routing $f_{i j}$ .