## 1 Introduction
### Research Gaps, Our Methodology, and Contributions
The sink node broadcasts a request information message to every SN in the network. Firstly, the sink node only completes the setup phase once in an effort to minimize the number of control messages generated during DFG establishment. In response, the SNs reply with an SN's information message, which contains the SN's location and its energy. Consequently, the sink node divides the sensing area into hexagonal DFGs of equal size. This division is based on data received from each SN. Subsequently, the sink node determines a PDFH for every cluster. In essence, the innovative proposed protocol, presented in this paper, employs a data fusion strategy in which each group's best PDFH is selected using the MPA, which has clearly become more popular in the last several years, as seen by the 2029 total citations it received according to a Google Scholar survey that was conducted up to February 8, 2025. The novel aspect of the proposed protocol is figuring out the DFFF, which takes into account not only necessary parameters, such as the average distance between DFGMs, DFGMs' RE, their distance from the sink node, Average Scale of Building Occlusions (ASBO), and PDFH rotation times, but also a weight assigned to each parameter, which is determined by a trial-and-error procedure following the execution of a colossal number of assessments and the selection of values that provide the best possible outcomes for the performance of the network. Intriguingly, in order to receive optimal PDFH, this DFFF is considered to be the objective function of the MPA that has to be minimized. In other words, the DFFF with the lowest values of the aforementioned parameters is the best one. In addition to the PDFH selection, our proposed protocol is batch-based. This means the regrouping (PDFHs reselection) does not occur every round but after a batch of rounds. In order to achieve this, the RE of the selected PDFH is compared with the average RE of DFGMs (energy threshold); if the RE of PDFH falls under the threshold, regrouping (PDFH reselection) is carried out by sending a disjoin message by a PDFH to the sink node and all SNs in the networks as an indication to start the process of regrouping. For data fusion and transmission, the proposed protocol without routing is suggested in order to send data from SNs to their PDFH, and then the PDFHs aggregate the data and then send them directly to the sink node (i.e., single hop communication) by assigning a Time Slot (TS) for each SN based on a novel Time Division Multiple Access (TDMA) technique. On the other hand, the proposed protocol with multi-hop routing transmits the data from SNs to their PDFHs, and then the PDFHs gather the data and then send them directly to the sink node (i.e., single hop communication) if the distance between PDFH and the sink node is less than the crossover distance (87 m). Otherwise, the protocol utilizes a cutting-edge Relay Data Fusion Cost Function (RDFCF) to identify PRs to route the data until reaching the sink node (i.e., multi-hop communication). The distance between the PDFH and the list of PDFHs in the upper layers, their respective RE, and ASBO are the three influential factors used to create the RDFCF. Since a PDFH with the lowest RDFCF is selected as the next relay PDFH, the RDFCF should be reduced. The notion of relay PDFHs and RDFCF reduces control overhead and the distance between PDFHs and the sink node, and intelligently relieves congestion at PDFHs near the sink node by distributing the load between PDFHs. By using such an approach, SNs that are located far away from the sink node are guaranteed to preserve energy. In general, all of the techniques mentioned are liable for saving energy and effectively increasing the network's lifespan. Impressively, as per the best of our knowledge, there is no paper in the field highlighting and covering the innovative aspects of our paper so far, particularly integrating data fusion techniques within clustered IoT architectures, making it distinguishable among others.