## 2 Related Work  
Many protocols have been proposed to boost the performance of WSNs by improving data transmission within them. The majority of these protocols have achieved promising results by using multi-hop techniques to route data across the WSN. These techniques vary between static and dynamic approaches. In the literature, several multi-hop routing protocols that use a static approach have been proposed such as the Multi-Hop based on the LEACH (MH-LEACH) protocol [9]. It introduces two phases for selecting efficient paths from CHs to the BS: an initialization phase and a steady-state phase. The initialization phase is responsible for forming the clusters and follows the same procedure as the original LEACH. Therefore, the CHs broadcast announcement messages to all non-CHs, inviting them to join their clusters. Then, the non-CH nodes select the most suitable CH based on RSSI. Once the cluster formation is complete, each CH transmits its routing table to the BS, which in turn carefully checks the routing table. If the BS identifies intermediate CHs between the source CH and the BS, it rearranges the routing table accordingly and sends it back to the source CH. The design of the MH-LEACH protocol contributes to reducing the energy required for transmitting the aggregated data to the BS, thereby extending the network lifetime. Despite its ability to curb transmission energy, the MH-LEACH protocol uses a fixed route from the CH to the BS throughout each round. Furthermore, it does not support any sleep-scheduling mechanism, leaving all nodes permanently active, which leads to continuous energy drain. To address the energy imbalance issue in the original LEACH, the LEACH-TL protocol was introduced in [10]. Instead of one CH, LEACH-TL assumes that each cluster should have two CHs to mitigate energy depletion, which may occur if the selected CH has low residual energy. Accordingly, one of them, referred to as the secondary CH, is responsible for gathering data from the cluster's member nodes, while the second, known as the main CH, is used to transmit the aggregated data to the BS. If the residual energy of the main CH decreases to less than half, the secondary CH takes responsibility for transmitting the data to the BS. In certain cases, the aggregated data of the main CH can be transmitted to the BS via another main CH. LEACH-TL prolongs the overall network lifetime by improving energy balancing within the clusters. However, no sleep-scheduling mechanism is employed; the protocol relies on static routes for data delivery to the BS. Alternatively, various protocols have adopted dynamic multi-hop routing approaches in WSNs. For example, the EDMHT-LEACH protocol proposed in [11], is considered an enhanced version of the DMHT-LEACH protocol. It introduces several modifications, including adjustments to the equation used for CH selection and to the number of member nodes in each cluster. Furthermore, it defines a new type of node called an Independent Node (IN), which is not affiliated with any specific cluster. INs also participate in routing the CH data to the BS. The EDMHT-LEACH protocol achieves a better energy balance by adjusting the cluster size and controlling the number of nodes within each cluster. The use of INs reduces the load on CHs and optimizes the overall network's performance. However, the EDMHT-LEACH protocol does not employ any sleep-scheduling mechanism, leading to an increase in unnecessary energy dissipation. From another perspective, several protocols have introduced active/sleep mechanisms for the network nodes. The authors in [12] employed the K-means algorithm to modify the LEACH protocol. The algorithm contributed to the selection of the CHs. Furthermore, they proposed an active/sleep scheduling mechanism for the cluster member nodes. Accordingly, nodes in sleep mode turn off their transmitter and receiver modules to minimize energy consumption, while active nodes continue to operate normally.