## Appendix A A Comprehensive Example of PDFH, FSDFH, and SSDFH Selection Utilizing the MPA  
In this exemplary demonstration, we provide an in-depth and comprehensive elucidation of the MPA's operation within our proposed protocols to ascertain the optimal PDFH for DFG 5. Our focus is on DFG 5, which comprises six nodes grouped together, as depicted in Figure A1. Accordingly, the number of search agents in MPA is configured to be six. It is pertinent to mention that Section 5.2.1 delineates the initial parameters utilized in MPA. To initiate the process, during the setup phase of the proposed protocol, the sink arranges the nodes within each DFG into a matrix containing essential information such as the SN's ID, location, type, initial RE level, distance to the sink, and the DFG number. These details are presented in Table A1. For a more comprehensive understanding, the MPA comprises two primary phases: initialization and iteration. The initialization phase establishes initial conditions to prepare for the subsequent iterative process. Conversely, the iterations involve running the algorithm multiple times to determine the optimal PDFH, FSDFH, and SSDFH. Fundamentally, MPA employs a nested loop structure. The outer loop dictates how many times the entire algorithm runs to maintain the best solution among all values. Within this outer loop, a second loop iterates based on the number of SAs, which, in this case, is six times. This nested structure allows the algorithm to thoroughly explore various PDFH options and refine its decision-making process to select the best PDFH. The detailed and precise steps of the initialization phase, along with a few iterations of the iteration phase, are outlined below. Commencing the initialization phase involves constructing \(\xrightarrow{\longrightarrow}\) matrix, which incorporates the metrics \(D_{\text{CDFH}_{i}\to\text{Sink}}\), \(Inv(RE_{\text{CDFH}_{i}})\), \(AvgDis_{\text{CDFH}_{i}\to\text{DFGMs}}\), \(X_{\text{CDFH}_{i}}\), and \(ASBO_{\text{CDFH}_{i}}\), as specified in Equation (18). \[ \begin{array}{c}D_{\text{CDFH}_{i}\to\text{Sink}}\quad Inv\big{(}RE_{\text{CDFH}_{i }}\big{)}\quad\quad Avg\big{(}D_{\text{CDFH}_{i}\to\text{DFGMs}}\big{)}\quad X _{\text{CDFH}_{i}}\quad ASBO_{\text{CDFH}_{i}}\\ \text{CDFH}_{1}\quad\quad\left[\begin{array}{ccccc}66.245&1.000&29.332&0&0.4 \\ 41.087&1.000&52.171&0&0.5\\ \text{CDFH}_{3}&179.706&1.000&31.279&0&0.3\\ \text{CDFH}_{4}&108.394&1.000&29.279&0&0.7\\ \text{CDFH}_{5}&81.424&1.000&34.303&0&0.1\\ \text{CDFH}_{6}&40.069&1.000&27.110&0&0.7\end{array}\right]\end{array} \]  
\[\begin{array}{c}\overrightarrow{\text{Prey}}\left(after\ norm\right)= \begin{array}{c}D_{\text{CDFH}_{i}\to\text{Sink}}\quad Inv\big{(}RE_{\text{ CDFH}_{i}}\big{)}\quad\quad Avg\big{(}D_{\text{CDFH}_{i}\to\text{DFGMs}}\big{)}\quad X _{\text{CDFH}_{i}}\quad ASBO_{\text{CDFH}_{i}}\\ \text{CDFH}_{1}\quad\quad\left[\begin{array}{ccccc}0.1875&0.0208&0.0886&0&0.4 \\ 0.0073&0.0006&1.0000&0&0.5\\ 1.0000&1.0000&0.1663&0&0.3\\ \text{CDFH}_{4}&0.4893&0.1219&0.0866&0&0.7\\ 0.2962&0.0375&0.2870&0&0.1\\ 0&0&0&0&0.7\end{array}\right]\end{array} \]  
After completing the initialization phase, we proceed to the iterative process. This phase involves executing the MPA through a series of iterations outlined as follows:  
1. The first iteration \((Iter=0)\): Step 1: Fitness assessment and top predator detection (fitness and position): In the initialization phase, the following variables are set to the following: \[Top\_predator\_pos= [0\ \ 0\ \ 0\ \ 0\ \ 0],\ Top\_predator\_fit=\infty\]\[ \begin{array}{c}\text{CDFH}_{1}\\ \text{CDFH}_{2}\\ \text{CDFH}_{3}\\ \text{CDFH}_{4}\\ \text{CDFH}_{5}\\ \text{CDFH}_{6}\end{array}\begin{bmatrix}0&0&0&0&0\\ 0&0&0&0&0\\ 0&0&0&0&0\\ 0&0&0&0&0\\ 0&0&0&0&0\\ 0&0&0&0&0\\ 0&0&0&0&0\\ 0&0&0&0&0\end{bmatrix} ,\;\overrightarrow{Fitness}= \begin{array}{c}\text{CDFH}_{1} \\ \text{CDFH}_{2}\\ \text{CDFH}_{3}\\ \text{CDFH}_{4}\\ \text{CDFH}_{5}\\ \text{CDFH}_{6}\end{array}\begin{bmatrix}\infty\\ \infty\\ \infty\\ \infty\end{bmatrix}