# Research on Joint Resource Allocation for Multibeam Satellite Based on Metaheuristic Algorithms
## 4 Results
The best average USC result of the QPSO algorithm utilizing NDBC was 0.641, representing a 67.4% improvement relative to UBUP (1.967) and a 21% improvement relative to the result reported in [20]. The NDBC method improved all USC metrics in comparison to the UBA method, with improvements of 9-36% for the USC mean and 14-38% for the execution time. For an efficient comparative analysis, we selected the ABAP algorithm, the GA(UBA) scheme from [20], the comparison algorithm GA(NDBC), and the QPSO(NDBC) algorithm, which applied NDBC most effectively. Figure 10 depicts the capacity allocation and USC outcomes for each beam based on the four previously mentioned algorithms. Using the GA algorithm, NDBC was able to achieve better allocation results for beams 6, 11, 18, 24, and 36 in comparison to UBA. QPSO was able to improve the USC results in beams 2 and 18 using NDBC in comparison to GA. Overall, NDBC reduced resource allocation for high-demand beams, improved USC, and increased allocation fairness. Figure 10: Capacity allocation and USC of each beam for the best single execution of the algorithm. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Algorithm** & **Result** & **GA** & **DE** & **PSO** & **QPSO** \\ \hline \multirow{6}{*}{UBA} & Worst run & 1.115 & 1.016 & 0.986 & 1.538 \\  & Average run & 0.958 & 0.826 & 0.807 & 1.006 \\  & Best run & 0.768 & 0.636 & 0.671 & 0.741 \\  & Standard deviation & 62.28 & 73.28 & 45.16 & 115.21 \\  & Average execution time & 5.16 & 4.39 & 4.16 & 2.77 \\  & Average iteration & 248.96 & 423.58 & 314.27 & 216.39 \\ \hline \multirow{6}{*}{NDBC} & Worst run & 1.026 & 0.912 & 0.853 & 0.798 \\  & Average run & 0.866 & 0.749 & 0.686 & 0.641 \\ \cline{1-1}  & Best run & 0.709 & 0.606 & 0.623 & 0.576 \\ \cline{1-1}  & Standard deviation & 64.53 & 65.65 & 46.74 & 46.80 \\ \cline{1-1}  & Average execution time & 4.02 & 2.66 & 3.57 & 2.23 \\ \cline{1-1}  & Average iteration & 220.02 & 292.45 & 321.13 & 214.46 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Optimal solution and execution time of the algorithm. An important aspect of satellite resource allocation, i.e., traffic demand, depends on the specific geographical location and the associated time of day; therefore, when considering a large footprint composed of multiple beams (as in this paper), with beams experiencing varying capacity requests that also vary in time (slowly, i.e., on the order of hours). In this line, resource allocation in continuous time scenarios has been researched in various studies [12; 18; 19]. Simulation experiments were subsequently conducted in order to determine whether the application of the NDBC method in the continuous time case deviated from the results in the static scenario. Assuming that the geographical characteristics that influence beam demand remain constant, the demand is primarily influenced by temporal characteristics. The demand ratio of each point beam was considered to be identical to the stationary scenario described previously, with a random deviation of 20% or less added to simulate the actual situation. Figure 11 illustrates the total demand, with a sampling interval of 10 min and a scheduling time limit of 3 s. The maximum and minimum number of iterations was 500 and 200, respectively. After 50 iterations, the algorithm terminated if the improvement in the optimized solution was less than \(5\times 10^{-5}\). As shown in Figure 12a, the USC values of NDBC for all algorithms were superior to those of UBA in the majority of instances, whereas the application of the QPSO and PSO algorithms provided superior results compared to GA and DE. In conjunction with Table 5, it is evident that the stability of PSO and QPSO utilizing NDBC is superior to that of GA and DE (the standard deviations of the average USC were 46, 46, 65, and 64, respectively).