## 1 Introduction
The entire network's operation is jeopardized if the base station malfunctions or is compromised. This limitation is particularly concerning in critical applications such as military or disaster recovery, where network reliability is paramount. The common issue with classic clustering protocols in WSN is finding an optimal solution to achieve uniform energy consumption across the sensor nodes. To overcome this, recent research has turned to metaheuristic algorithms for CH selection and routing optimization in WSN. Metaheuristics such as the genetic algorithm (GA) [4; 5], particle swarm optimization (PSO) [6; 7], ant colony optimization [8], gray wolf optimization [9; 10], firefly optimization [11; 12], wild geese optimization algorithms [13], and their respective variations offer flexibility, scalability, and superior search capabilities. These algorithms are particularly well suited for dynamic and large-scale WSN environments. Unlike traditional deterministic approaches, metaheuristics can explore the solution space more thoroughly, thereby improving the chances of finding an optimal or near-optimal solution for energy-efficient clustering and routing. They have become popular due to their flexibility, scalability, and searchability in finding the optimal solution to many engineering problems, such as in WSN. Similar advanced routing protocols and cluster head selection algorithms based on metaheuristic algorithms have also been proposed in the literature to achieve optimal WSN performance [13; 14; 15; 16; 17; 18; 19; 20; 21; 26]. For instance, in [14; 15; 16; 19; 21; 26], different optimization techniques were proposed by improving existing optimization algorithms such as the gray wolf optimization, sine-cosine algorithm, ant swarm foraging algorithm, or incorporating factors such as distance in the selection of cluster heads to improve the energy efficiency of WSNs. For instance, the algorithm proposed in [14] called EECHIGOWO successfully improved the stability, energy efficiency, and stability of the WSN, but their approach was ineffective for heterogeneous nodes. The DUCISCA method proposed in [15] successfully reduced the overhead of nodes, effectively minimizing energy consumption, but their method had a higher death speed for the sensor nodes. The DE-SEP technique introduced in [19] was also successful in improving the death rate of each node and equally effective in improving energy efficiency as the WSN size increased. Still, their method suffered from degraded stability as the separation between the CH and other nodes and base station members increased. Lastly, the E-CERP method in [21] optimized the routing path, resulting in reliable communication between nodes, but in their study, only static nodes were considered. Aside from these limitations, these methods failed to incorporate other performance metrics like trust, delay, and distance in their evaluation. These different metrics are critical in ensuring the overall network reliability and efficiency. Furthermore, they are primarily designed for static sensor networks, limiting their applicability to dynamic environments where sensor nodes can move. Other papers in the literature [14; 15; 16; 17; 19; 20; 21; 22; 23; 24; 25; 26] also failed to evaluate their research across different wireless technologies. They primarily optimize energy efficiency and cluster head selection but do not consider performance across wireless technologies like Bluetooth, Wi-Fi, LoRa, and ZigBee. Limiting their assessment to a single wireless entity diminishes its relevance for broader WSN applications and implementations. Our previous research utilized the chronological wild geese optimization (CWGO) algorithm [13], which optimally selects routing paths and cluster heads in a WSN. We evaluated the CWGO algorithm against E-CERP, EECHIGOWO, DUCISCA, and DE-SEP based on distance, delay, trust, and energy metrics. However, these comparisons focus solely on static sensor nodes and assess individual metrics rather than a unified measure of overall network performance.