## 1 Introduction  
With the development of efficient wireless communication and the progress of electronic information technology, wireless sensor networks (WSNs) have widely been used in various fields due to their low cost, miniaturization ability, and multi-functional characteristics [1]. Sensor nodes operate with limited computing, storage, and communication capabilities under severe energy constraints and are designed with minimal complexity for large-scale deployment at reduced cost. All of the sensor nodes used in WSNs are small, low-cost, possess good communication capabilities, and are assumed to have similar data processing and routing capabilities. The lifetime of a WSN is defined by either the first node or all system nodes running out of energy. The better energy utilization enhances the lifetime of all of the nodes and results in an energy-efficient WSN. However, key concerns in WSNs have always included energy usage by the sensor nodes. The sensor nodes need to achieve a long life while operating on limited battery reserves. Algorithms should be designed in such a manner that the energy is best utilized by the nodes. Distributed information processing technologies and wireless communication have enabled the rapid development and deployment of WSNs [2]. Recently, research has primarily been concentrated on various routing and clustering techniques [3, 4], where the results indicated that clustered networks are energy-efficient and long-lived sensor networks. However, key strategies including clustering methodology, network structure and division, and optimization techniques are still facing significant challenges on enhancing the performance of WSNs. Firstly, clustering should include angular distance that should facilitate optimum reforming cluster centres for efficient utilization of the energy. Secondly, boundary issues should be enhanced while considering network structure and division of WSNs. Finally, an improved optimization strategy is required to balance energy consumption throughout the whole network. In WSNs, energy is saved by applying different techniques, such as duty cycle scheduling [5], energy-efficient routing [6], node replacement [7], energy replenishment [8], energy balance [9], and energy-efficient medium access control (MAC) [10]. The first and most extensively used hierarchical routing protocol is low energy adaptive clustering hierarchy (LEACH) [11, 12], which provides data fusion through cluster formation and cluster head (CH) sensor node selection. The selection of CH plays an important role in a wireless network system that oversees data aggregation and transmission. The energy consumed by CH is higher than that in other ordinary nodes. Nodes that decide to be the CH declare their status to the rest of the network based on the received signal strength intensity (RSSI). Each sensor node in LEACH joins the cluster that requires minimal power to connect with the CH. Nodes forward information to the CH, and the CH aggregates and compresses the data and sends it directly to the BS [13]. Data aggregation is completed by the CH before it is sent to the BS. After a specific time, the network goes back into the set-up phase and enters another round of CH selection. Reforming in CH selection is crucial to compute the remaining energy of the nodes and distance to BS [14, 15, 16]. The reformist computation for CH selection enhanced energy efficiency over the traditional LEACH protocol by more than 40%. The state-of-the-art LEACH algorithms [17, 18] mostly focus on novel routing strategies by avoiding collisions and organizing data transmission. Two-level clustering is introduced in [18] for a water-saving irrigation system based on the ratio of remaining energy and distance to the BS in the local region. However, conventional LEACH algorithms fail to select regular CH due to angular distance estimation and boundary conditions between nodes and CHs. The failure in LEACH adaptations adds an additional cost to the energy consumption of all nodes in the network and the network lifetime.