## 1 Introduction  
In recent years, there has been significant exploitation in wireless communications because they allow great flexibility for data transmission. Wireless communications provide a combination of connectivity and mobility using air as a medium [1]. Among the various existing wireless technologies, the most popular are wireless sensor networks. They require an efficient communication establishment, from the energy and computational point of view, which is guaranteed by developing optimal algorithms for communication protocols. Wireless networks of distributed sensors are composed of a collection of electro-mechanical microdevices, scattered within a defined area. These sensors can reveal multiple information about territory. Exchanging and transmitting this data over a channel for wireless sensor networks [2]. Wireless sensors depend on the use of batteries, which generates the main problem because they contain limited energy autonomy. Thus, a base station is required to send information and process it. Hierarchical or cluster-based routing is a well-known technique with particular advantages related to scalability and efficiency in communications. The concept of hierarchical routing has also been applied to achieve energy efficiency in WSNs. In a hierarchical architecture, high energy nodes can be used to process and send information [3]. In contrast, low energy nodes can only be used for sensor work in regions close to the target. Therefore, creating clusters and assigning particular tasks to Cluster Heads (CHs) can significantly contribute to the scalability of the system, its lifetime, and its energy efficiency. Scalability is a critical factor in WSNs, which has not been well resolved in most of the protocols due to the initial assumptions. For instance, cluster-based protocols commonly assume a single sink and cluster heads within the coverage of the sink [4]. Under those assumptions, WSNs will lack scalability, making communications highly expensive in terms of the required energy. Therefore, increasing the number of nodes or the diameter of the network will cause an overload that grows exponentially and a bottleneck consisting of only one sink that can strangle the network. Hierarchical routing is an efficient way to decrease energy consumption within the cluster and perform information aggregation. It also allows merging tasks to reduce the transmitted packet number to the sink [5]. A correct protocol must have mechanisms for saving energy in the nodes since recharging their batteries is usually tough, not possible, or even dangerous. All aspects of the nodes, from the hardware to their performed operations, will help to distribute the energy load [6]. Thanks to hierarchical routing having different roles to help us to differentiate potential phases in protocol operations, the existence of two operation modes in the sensors can foresee a higher energy expenditure. However, different transmission modes, such as cluster head and normal sensor, can be beneficial if implemented in every layer [7]. Routing protocols for wireless sensor networks (WSNs) represent an engineering area that has attracted the attention of several research communities due to its rapid development and evolution. Among all approaches, the clustering routing protocol corresponds to the most effective method to manage the energy consumption of all sensor nodes. It allows efficiently increasing the working cycle of sensor networks [8; 9]. The Low Energy Adaptive Clustering Hierarchy Protocol (LEACH) [10] represents the most popular clustering routing protocol for homogeneous WSNs. Under the operation of LEACH, cluster heads (CHs) are randomly determined while all the sensor nodes are constantly interchanged as CHs. The energy expenditure is uniformly assigned to each node in order to enlarge the network performance. Several protocols that consider the LEACH scheme as a basis have been introduced in the literature with different performance levels [11; 12; 13; 14; 15].