## 3 GA Hybrid-Fog Model
### GA Hybrid-Fog Formulation
Beyond these improvements, additional evaluations demonstrated the superiority of GA Hybrid-Fog over other task-offloading architectures. The results showed that the proposed architecture achieved significantly lower delays compared to GA BS-Fog, GA UAV-Fog, and GA UAV-Edge. For instance, in specific scenarios, 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 in task-offloading delay. By varying the number of tasks, we showed that the proposed GA Hybrid-Fog algorithm consistently outperforms other task-offloading technologies. Furthermore, through the analysis of variations in range and channel conditions, we observed that by leveraging both the genetic algorithm and a hybrid architecture, the GA Hybrid-Fog algorithm delivered substantial improvements in task-offloading delay. As a future research direction, we plan to incorporate a UAV energy consumption model into our study, exploring the interplay between environmental factors and algorithm performance. Moreover, we intend to apply the proposed GA Hybrid-Fog approach to real-time experiments to validate its performance in practical scenarios. This will enable us to develop a more comprehensive framework for evaluating the sustainability and efficiency of our approach. Conceptualization, M.A.A. and S.Z. ; methodology, N.M.; software, S.Z. ; validation, M.A.A., N.M. and C.T.C. ; formal analysis, S.Z. and N.M.; investigation, M.A.A. ; resources, C.T.C. ; data curation, N.M.; writing--original draft preparation, M.A.A. and S.Z. ; writing--review and editing, C.T.C. ; visualization, N.M.; supervision, S.Z. ; project administration, M.A.A. ; funding acquisition, C.T.C. All authors have read and agreed to the published version of the manuscript. This work was partially funded by the EU project REMARKABLE (grant agreement ID: 101086387) under the program HORIZON-MSCA-2021-SE-01-01; by the project CIPROM/2023/29, funded by \"Direccio General de Ciencia i Investigacio\", Generalitat Valenciana, Spain; and by the R&D project PID2021-122580 NB-I00 from MICIU/AEI/10.13039/501100011033 and \"ERDF--A Way of Making Europe\". Not applicable. The dataset is available on request from the authors. The authors declare no conflicts of interest. ## References

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