## 3 GA Hybrid-Fog Model
### GA Hybrid-Fog Formulation
The task-offloading delay of the proposed GA Hybrid-Fog approach and that of GA UAV-Edge as a function of the number of nodes (number of FUAVs or number of edge UAVs) is shown in Figure 7, with the number of offloaded tasks fixed at 100. The results show that GA Hybrid-Fog outperformed GA UAV-Edge, with a significantly lower offloading delay. Specifically, for five nodes, GA Hybrid-Fog had a delay of 1.3 s, whereas

Figure 5: Variations in task-offloading delay as a function of the number of tasks for various IoD technologies. GA UAV-Edge experienced a delay of 26.2 s, representing a 95.04% improvement. This confirms the superiority of GA Hybrid-Fog, which benefits from the combined processing capacity of both FBSs and FUAVs, unlike GA UAV-Edge, which relies solely on edge UAVs. Figure 8 presents the variations in task-offloading delay with respect to the number of tasks (TN) for various IoD technologies, including GA Hybrid-Fog, GA BS-Fog, GA UAV-Fog, and GA UAV-Edge, where the number of FUAVs and FBSs was fixed at five. GA Hybrid-Fog exhibited the lowest offloading delay compared to the other IoD technologies. For a TN of 350 tasks, GA Hybrid-Fog resulted in a delay of 3.6 s, GA BS-Fog had a delay of 4.3 s, GA UAV-Fog experienced a delay of 15.3 s, and GA UAV-Edge had a delay of 92.1 s. This is because the proposed GA Hybrid-Fog algorithm utilizes both FUAVs and FBSs, leveraging a total of 10 nodes compared to just 5 in the other configurations. Figure 6: Variations in task-offloading delay as a function of the number of nodes for GA Hybrid-Fog and GA UAV-Fog. Figure 7: Variations in task-offloading delay as a function of the number of nodes for GA Hybrid-Fog and GA UAV-Edge. In terms of improvement, GA Hybrid-Fog achieved a 16.28% improvement over GA BS-Fog, a 76.47% improvement over GA UAV-Fog, and a 96.09% improvement over GA UAV-Edge. These results highlight the significant reduction in offloading delay achieved by the GA Hybrid-Fog algorithm compared to the other IoD technologies. Figure 9 illustrates the variations in task-offloading delay as a function of the data rate (DR) for various IoD technologies, where the number of devices was fixed at five for both NFBSs and NFUAVs. The variations in the DR reflect changes in channel conditions, as shown in Equations (1) and (3), which primarily depend on range variation. The results demonstrate that the GA Hybrid-Fog method had a significantly lower offloading delay compared to other IoD technologies. This improvement is attributed to its efficient task distribution across fog BSs, fog UAVs, and edge UAVs. Figure 8: Variations in task-offloading delay with respect to the number of tasks for various IoD technologies. Figure 9: Variations in task-offloading delay as a function of the data rate for various IoD technologies. For instance, at a DR of 5 Mb/s, the GA Hybrid-Fog method achieved the best performance with a delay of 1.1 s. This represents a 15.38% improvement over the GA BS-Fog method (1.3 s), a 73.81% improvement over the GA UAV-Fog method (4.2 s), and a remarkable 95.67% improvement over the GA UAV-Edge method (25.4 s). These results highlight the superior performance of the GA Hybrid-Fog approach in minimizing offloading delays across various scenarios. ## 5 Conclusions

In this paper, we addressed the problem of task offloading in IoD networks by proposing the GA Hybrid-Fog algorithm, which integrates a genetic algorithm with a hybrid fog computing architecture. The experimental results demonstrated the effectiveness of our approach in minimizing task-offloading delay across different network conditions. We evaluated the proposed GA Hybrid-Fog algorithm by comparing it with two existing task-offloading methods, PSO and MILP. The results showed that the GA Hybrid-Fog algorithm consistently outperformed the other task-offloading methods. For instance, in specific scenarios, the GA Hybrid-Fog algorithm achieved a 46.39% improvement over PSO and a 58.73% improvement over MILP.