## 1 Introduction  
In recent decades, wireless sensor networks (WSNs) have attracted a lot of attention, mostly as a result of their diverse applications across a wide range of fields. Many military and civilian applications (for example, intelligent transportation systems) integrate tasks such as detection, classification, plus the localization and tracking of events or targets in sensor fields [1; 2; 3; 4]. Wireless sensor nodes communicate with each other to collect data, process them, and then transmit the sensed data to a base station (BS). Apart from their miscalleanous applications, energy efficiency in a WSN is still a vital issue. Wireless sensor nodes are identified as major energy-consuming sources in WSNs [5; 6; 7]. Generally, wireless sensors are limited in terms of their size and battery lifetime. In addition, in most cases it is difficult to replace or recharge the sensors, hence, limitations on energy resources in WSNs specify energy consumption is a major problem. For the efficient conservation of energy in WSNs, various mechanisms have been used by researchers, including single-hop, multi-hop, and cluster-based transmission. Briefly, important parameters such as the distance between the source and the destination, as well as path loss, are inevitable factors in multi-hop transmission [8]. Additionally, the efficiency of multi-hop transmission will be influenced by the correlation between the power costs of receiving and transmitting [9]. If the nodes are communicating with the minimum amount of power necessary to reach the destination, and if that is considered to be the total power transmitted along the path, then single-hop communication [10] would be the most energy-efficient strategy [11]. In the sensor network, there are two different routing protocols: flat routing and hierarchical routing. In the flat routing protocol, the nodes directly communicate with the base station (BS) to send data packets. Therefore, the energy of the nodes rapidly drains out due to direct interaction with the BS. To improve the lifetime and performance, the sensor network must utilize the least amount of energy. For extending the network's lifespan, scalability, and load balancing, various cluster-based routing methods have developed [12]. The hierarchical routing models provide both single-hop and multi-hop routing through the formation of several clusters by considering CH in the network for improving the performance of WSN. So, cluster head selection is important to handle the limited energy in the best possible way to uplift the network lifetime. However, for efficient data transmission and energy management, clustering is one of the most effective methods in WSNs [13; 14; 15; 16; 17; 18]. Typically, sensor nodes in networks are organized into several clusters, as shown in Figure 1, and each cluster has a cluster head (CH) that collects information from each member node (sensor) in the cluster and transmits data to the BS. There are numerous clustering protocols focused on transmission power control or network topology. EECS, HEED, UCR, EECF, and others are energy-based. LEACH, C-LEACH, I-LEACH, P-LEACH, and PEGASIS are protocols in homogeneous networks. Low-Energy Adaptive Clustering Hierarchy (LEACH) was the first cluster-based hierarchical routing protocol. The probability of selecting the CH in LEACH and LEACH-based clustering networks is a totally random process with no guarantee of the number of CHs, which adversely affects the overall performance of the network [19]. On the other hand, transmission-power-based protocols such as EECS and HEEDS use residual energy as a rudimentary factor, as well as intra-cluster communication cost as a secondary factor. However, multi-hop inter-cluster communications increases the network overhead and costs. To control the network topology, transmission power control has been widely explored by the research community [20; 21], but the interactions of transmission power with clustering algorithms are still uninvestigated.