## 5 Conclusions  
This paper presents a novel secure and reliable multi-objective optimized multipath transmission algorithm (MOMTA-HN) for heterogeneous networks. The primary objective of the algorithm is to provide highly secure and reliable transmission services, even when network attacks occur in heterogeneous networks. The proposed algorithm optimizes network task performance metrics, including reliability and delay, by considering multiple objective functions based on task requirements. Optimizing these objective functions ensures the smooth operation of transmission tasks and enhances the overall quality of service of the network. Furthermore, the algorithm leverages the refined population selection and ranking mechanism of the optimized Non-dominated Sorting Genetic Algorithm II (NSGA-II), effectively narrowing the initial population range and improving the convergence speed and optimization efficiency. This improvement enables the MOMTA-HN algorithm to find the optimal solution in a shorter period, demonstrating higher efficiency in practical applications. A significant innovation of the MOMTA-HN algorithm is the use of the pruned graph method to compute multiple paths for redundant transmission. The application of the pruned graph method makes the MOMTA-HN algorithm more flexible and secure in path selection. Conventional multipath transmission algorithms frequently encounter the issue of path sharing, which diminishes the dependability of transmission. In contrast, the MOMTA-HN algorithm ensures that there are no common links between the redundant paths and the original paths through the deletion graph technique, thereby enhancing network resilience and transmission reliability. Finally, this paper validates the efficacy and superiority of the MOMTA-HN algorithm through comprehensive simulation experiments and attack tests. The experimental results demonstrate that the MOMTA-HN algorithm not only maintains a high transmission success rate in the face of network attacks but also significantly improves the security and quality of service of the network. These results validate the practicality and reliability of the proposed algorithm in heterogeneous network environments. In future research, we will consider the impact of transmission bandwidth on transmission strategies in multi-objective optimization, further optimize the MOMTA-HN algorithm, and further improve the strategy of deleting graphs in the multipath transmission stage. And, we will validate it in more practical physical scenarios to further promote the development of heterogeneous network transmission technology.  
Conceptualization, S.Q., L.Y., Y.Z. and G.C.; Methodology, S.Q. and S.J.; Software, S.Q.; Formal analysis, S.J. and Y.Z.; Resources, L.Y. and L.M.; Writing--original draft, S.Q.; Writing--review & editing, S.J.; Supervision, G.C.; Project administration, L.M. and G.C.; Funding acquisition, L.Y. All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by the National Natural Science Foundation of China under Grant No. 62202097, in part by the China Postdoctoral Science Foundation under Grant No. 2024T170143 and Grant No. 2022M710677, and in part by the Jiangsu Funding Program for Excellent Postdoctoral Talent under Grant No. 2022 ZB137.  
The data presented in this study are available in Topology zoo at [[http://www.topology-zoo.org/](http://www.topology-zoo.org/)]([http://www.topology-zoo.org/](http://www.topology-zoo.org/)) (accessed on 6 July 2024). These data were derived from the following resources available in the public domain: [[http://www.topology-zoo.org/](http://www.topology-zoo.org/)]([http://www.topology-zoo.org/](http://www.topology-zoo.org/)) (accessed on 6 July 2024).  
The authors declare no conflicts of interest.