## 2 Related Works
This stimulates exploration at the start of the iteration and exploitation as it becomes closer to the end. In this way, it is feasible to significantly increase search accuracy and quickly find the global optimal solution without settling for the local optima. SNs with significant disparities in their neighbors might be chosen as CHs, resulting in excessive intra-cluster energy consumption. An Optimized Fuzzy Clustering Algorithm (OFCA) is proposed in [41] for the selection of CHs and a routing protocol for data transmission to the sink node. In the OFCA, CHs are chosen based on distance from the sink node, RE, and SN concentration using type-1 fuzzy logic system. To establish an energy-efficient routing path to the sink node, other CHs are utilized via PSO. The FF of PSO is designed to determine the local and global best of particles, thereby increasing the network lifespan. As in standard PSO, the global best solution is determined by first initializing the particles and then updating them until a particle with an optimal fitness value represents the global best solution. As a result, CHs that have higher concentration, a less than average distance to the sink node, and higher levels of RE are selected as relay SNs. The PSO-based routing scheme in OFCA selects optimal CHs to establish efficient routing paths for data forwarding, thereby minimizing the energy consumption of CHs involved in inter-cluster communication and enhancing network lifetime. However, employing a single path from the source node to the destination may not guarantee high Quality of Service (QoS) for the network. The simulation results demonstrate that OFCA achieves a longer network lifespan and facilitates the transmission of more messages to the sink node. The authors in [42] introduced a novel clustering and routing protocol named NPSOP, based on PSO, aimed at extending network lifespan while ensuring energy efficiency and load balance. NPSOP employs PSO to select CHs and determine routes for each CH simultaneously, with particle components constrained by RMs such as distance to the sink node, RE, and centrality to enhance convergence speed. An FF, considering both network load balancing and energy consumption, evaluates particle quality. Additionally, an adaptive inertial weight is utilized to update particle status, preventing trapping in local optima and facilitating convergence to the global optimal solution iteratively. Extensive experiments compare NPSOP with existing approaches across performance metrics including energy consumption, throughput, network lifetime, standard deviation of residual energy, and load. NPSOP exceeds PSO-EEC, LDIWPSO, and OFCA by 29.94%, 24.16%, and 13.67%, respectively, in the results, which show substantial increases in network lifetime. Likewise, NPSOP reduces energy consumption by 24.08%, 19.16%, and 10.95%, respectively, in comparison to PSO-EEC, LDIWPSO, and OFCA. Beyond the previous discussion, Table 1 provides a listing of protocols that are pertinent to our work (i.e., refs. [39; 40; 41; 42]) and emphasizes the unique aspects of our methodology in contrast to these earlier studies. The comparison is predicated on the significant subjects covered in these papers, including the division of the network area, CH selection techniques, the parameters of the DFFF, clustering/data fusion grouping schemes, the number of clusters/DFGs, the type of inter-cluster communication, scheduling, RDFCF parameters, and the inclusion of examples to demonstrate CH selection processes.