## 2 Related Works  
To reduce the energy consumption of nodes and prolong the network lifetime, a large number of hierarchical routing protocols have been proposed by clustering or using topology control to keep the transmission distance low [13]. One of the most classical clustering routing protocols is LEACH, proposed by [PERSON] et al. [6]. In the LEACH protocol, the random selection of cluster-heads [14] it may lead to the rapid death of cluster-heads by electing the lower energy node as a cluster-head. It divided the wireless sensor network into several clusters, and one cluster-head was randomly selected in each cluster. Each node had equal opportunity to be selected as a cluster-head. A hybrid low energy adaptive clustering hierarchy protocol (H-LEACH) has been proposed [15], which added the average residual energy of all nodes in a network to the threshold formula, and the node was defined as a cluster-head when its residual energy was greater than this threshold. Selecting the nodes with higher residual energy as a cluster-head avoided the lower energy nodes becoming cluster-heads and dying too fast. In [16], a residual energy-based cluster-head selection algorithm (RCH-LEACH) was proposed. It calculates the energy threshold for selecting cluster-heads based on the 5-10% ratio range of cluster-heads. When the residual energy of nodes is greater than this threshold, nodes are selected as cluster-heads, which makes the energy between clusters more balanced in the network. An improved integrated LEACH protocol was proposed in [17]. It combines the A\({}^{\star}\) search algorithm with the integrated LEACH protocol to form a tree of sensor nodes, then selects nodes as the cluster-heads in the shortest path. This minimizes the number of deaths of sensor nodes and saves the energy of sensor nodes. In [18], a hybrid routing algorithm (HRA-NP) was proposed based on a plain Bayesian and improved particle swarm optimization algorithm (PSO). Firstly, cluster-heads (CH) are selected based on conditional probabilities, which are estimated by a plain Bayesian classifier. Then, the multi-hop routing algorithm is applied to the data delivery of the cluster-heads. It finds the optimal path from each CH to the BS using the PSO algorithm. In [19], to reduce the energy consumption of the network, the U-LEACH (Universal-Low Energy Adaptive Cluster Hierarchy) algorithm was proposed, which forms a cluster-head chain connected to the base station. In [20], we proposed a hybrid optimization routing algorithm based on improved GA and ACO in heterogeneous sensor networks. The combination of the GA algorithm and ACO algorithm is used to select better routes. The network lifetime is effectively extended. To solve the problem of the premature death of cluster-heads due to very fast energy consumption and the unbalanced energy consumption of nodes, a double cluster-head routing algorithm was proposed in [21]. The primary cluster-heads and member nodes were identified through the LEACH protocol, and the vice cluster-heads were selected among the cluster members within the same cluster based on the residual energy of the nodes. In [22], an improved energy-efficient dual cluster-head selection protocol (IEECHS-WSN) was proposed. In cluster-head election, two cluster-heads were selected in the same cluster. The election of the first cluster-head is based on a threshold approach similar to that of LEACH, and it primarily transfers data from the cluster to the base station. The second cluster-head received data from other nodes in the cluster, then fused and forwarded it to the first cluster-head. The method selected the node with the closest distance to the cluster's centroid as the second cluster-head. Therefore, the energy of the cluster-heads was not consumed too quickly, which effectively extended the network lifetime and reduced the energy consumption in IoT applications. On the other hand, a K-means clustering-based K-LEACH algorithm was proposed to extend the network lifetime by balancing the energy consumption of nodes [23].