## 2 Related Work  
In the existing literature, several energy-efficient cluster-based routing protocols have been proposed to prolong the network lifetime. Low-energy adaptive clustering hierarchy (LEACH) [19], one of the pioneer cluster-based routing algorithms, focuses on the association of homogeneous nodes. Due to the random deployment of nodes and probabilistic operations to select CHs, some areas may contain closed CHs that lead to an unbalanced dense in a cluster. Thus the idea of dynamic clustering generates unintentional communication overhead. Similarly, the CHs that are located far from the BS require more energy to communicate. LEACH-centralized (LEACH-C) [20] unraveled this issue by selecting feasible CHs, by the BS, according to the network's residual energy and the location of nodes. In this algorithm, the average residual energy of all alive nodes is first calculated. Those nodes are selected as CHs with higher residual energy than the calculated average network energy and are located at the most feasible positions within their respective clusters. The performance of LEACH-C exhibits the importance of the selection of cluster heads at feasible locations. The threshold-sensitive energy efficient sensor network (TEEN) [21] introduces threshold-based techniques for communication to minimize the unnecessary transmission in energy-restricted networks. In TEEN, threshold parameters are selected by the sink node. Only those nodes are selected for communication, which can sense any change in the wireless network environment. Furthermore, most of the alive nodes are assumed dead when no change is reported for multiple consecutive rounds. Most of the homogeneous networks die smoothly due to the same energy levels of wireless nodes [19; 20; 21]. Several efforts have demonstrated that the addition of a few different initial energy nodes (heterogeneous networks) can improve network stability. In [17], a few advanced energy nodes are added to the threshold-sensitive stable election protocol (TSEP) to prolong the network stability. High-level energy nodes are most likely to be selected as CHs; therefore, two different threshold parameters are used to select the CHs in TSEP due to two-level energy nodes. Later on, multi-level energy nodes with different residual energy levels are used in threshold distributed energy-efficient clustering (TDEEC) [18]. The CHs are selected according to their initial and residual energy levels with other probabilistic and threshold parameters, such as the average energy of the network in a particular round, average distance of CHs to the BS, and the average distance between cluster members to their respective CHs, within the TDEEC. Direct delivery of data packets from CH to BS, located at far distances, affects the performance of protocols in larger networks. Resisting routing attacks and the trust security mechanism are applied in [22]. TAGA develops the node's direct and indirect trust values considering neighboring nodes. Furthermore, researchers implemented a suitability function to choose the ideal cluster heads. The selection of CHs depends upon trust, which can change dynamically for secure routing. In [23], the authors focused on the optimal location of CHs with gateway nodes to reduce energy consumption during the communication phase. After the selection of CHs, gateway nodes are selected using different parameters to find weightage. If the distance between CHs and BS is less than calculated thresholds, CHs directly forward packets to BS; otherwise, the gateway was responsible for delivering the packet to the next gateway or CHs. It requires extending the proposed model with multi-hopping to overcome the impact of scalability by selecting feasible intermediate nodes. In [24], the authors introduced a genetic analysis approach. This approach utilizes a cluster node to choose the most favored sensor node at the most feasible position. Based on its efficient fitness capability measurements, it presented high accessibility and proficiency.