Algorithm 1 Cluster initialization based on improved K-medoids algorithm

Input: Location and energy information of T sensor node in in the monitoring sub-network area of $N\times N$

Output: T sensor nodes are allocated to K clusters in the mode of optimal energy consumption

Step 1: Determining the optimal clustering group number $k_{opt}$;

Step 2: Selecting a sensor node as the first cluster center randomly;

Step 3: Calculating the distance from each node to the selected cluster center;

repeat

for i = 1, 2, …, k

for j = 1, 2, …, T − k

$d_{Cto{C}_{ji}}=\sqrt{{\left(x\left(j\right)-x\left(i\right)\right)}^2+{\left(y\left(j\right)-y\left(i\right)\right)}^2}$

until the distances between all nodes are calculated

Step 4: Selecting the k-th ($1<k<k_{opt}$) clustering center

repeat

for j = 1, 2, …, T − k

for i = 1, 2, …, k

$d_{Cto{C}_j}=\min \left(d_{Cto{C}_{ji}}\right)$;

$\mathrm{sum}\left(d\left(x_{Cto{H}_j}\right)\right)={\displaystyle \sum }_{j=1}^{T-k}{d}_{Cto{C}_j}$

$p_j=\frac{d\left(x_{Cto{H}_j}\right)}{\mathrm{sum}\left(d\left(x_{Cto{H}_j}\right)\right)}$

until all $k_{opt}$ cluster centers had been selected

Step 5: Initialization of all clusters based on selected $k_{opt}$ cluster centers

repeat

for i = 1, 2, …,$k{}_{opt}$

for j = 1, 2, …, T − $k_{opt}$

$d_{Cto{C}_{ji}}=\sqrt{{\left(x\left(j\right)-x\left(i\right)\right)}^2+{\left(y\left(j\right)-y\left(i\right)\right)}^2}$

for j = 1,2,…,T-$k_{opt}$

for i = 1, 2, …, $k_{opt}$

$d_{Cto{C}_j}=\min \left(d_{Cto{C}_{ji}}\right)$;

until all sensor nodes are allocated to the cluster with the lowest energy consumption.