## 1 Introduction  
Rapid advancements in wireless communication, computational intelligence, and metaheuristic optimization algorithms have allowed efficient and scalable solutions for complex problems, particularly in wireless sensor networks (WSNs). WSNs consist of small, low-power sensor nodes that transmit and receive data wirelessly using a wireless communication technology. They are widely used across numerous domains, including smart agriculture, education, telemedicine, search and rescue operations, environmental monitoring, military applications, and commercial sectors, for their ability to give timely and accurate data collection, monitoring, and communication over large areas. They are valuable in scenarios where manual data acquisition is dangerous or impractical. The sensor nodes deployed in these areas can be either static or dynamic, depending on the application requirements and the specific area where they are used. Static WSNs are primarily employed in applications where nodes remain stationary after deployment. These networks are ideal for long-term monitoring of a specific target area, such as air and water quality monitoring, soil moisture monitoring in agriculture, structural health monitoring, surveillance, and perimeter security. On the other hand, dynamic WSNs consist of mobile sensor nodes capable of changing location over time after deployment. Typical scenarios for them include search and rescue operations, wildlife monitoring and tracking, vehicular networks, and intelligent transportation systems. These applications offer greater flexibility and adaptability, making them suitable for changing environments or requiring sensor nodes to follow moving objects, people, or conditions. In both modes of WSNs, the limited energy resources of the nodes are a critical consideration during design and implementation. WSNs must be optimized to maximize energy efficiency to avoid network failure and guarantee optimal performance. One technique to achieve optimal WSN performance is using cluster-based routing protocols that can be implemented in various methods. One of the most famous clustering protocols that pioneers this concept is the low-energy adaptive clustering hierarchy (LEACH) protocol [1]. This protocol works by randomly selecting a CH from the sensor nodes, and the selected CH transmits the data coming from the cluster members to the base station. The problem with the LEACH protocol is the randomness of CH selection. It may select a CH with low residual energy or nodes at the edge of the WSN, making the transmission distance longer, which translates to more significant energy consumption. The literature also proposes variations of the LEACH protocol to improve its performance, such as the LEACH-C [2], in which they incorporated a sorting algorithm to select the nodes with the highest residual energy as the best candidate to be the CH. By selecting nodes with higher residual energy as CHs, LEACH-C addresses some of the energy inefficiencies in the original LEACH protocol. However, as mentioned, this approach assumes a uniform distribution of nodes, which is not always the case in practical WSN deployments. In real-world applications, sensor nodes are often deployed in non-uniform, unpredictable patterns, making LEACH-C's assumptions less applicable and potentially leading to inefficient cluster formation and energy consumption in irregular deployments. Another hierarchical routing protocol like LEACH is the base-station-controlled dynamic clustering protocol (BCDCP) [3], which utilizes the base station to perform energy-intensive computations such as the CH selection and routing that reduces the work allocations to individual sensor nodes. BCDCP also uses a minimum spanning tree algorithm to minimize energy consumption during inter-cluster communications, making it a more energy-efficient technique than the classical LEACH protocol. Despite these advantages, BCDCP's centralized structure introduces a significant vulnerability: the base station becomes a single point of failure.