## 2 Methodology
### System Model
Based on this table, the system can execute redundant dynamic path calculations and path policy control through identification, ensuring the routing of heterogeneous networks is reachable and guaranteeing highly reliable information transmission. The business system, as the user side, adapts to various types of service terminals and accepts operation and maintenance management. When accessing the transmission control system, the business system can perform encryption and decryption operations on the data as needed to enhance the security and reliability of system transmission. Concurrently, the business system can interact with the transmission control system to dynamically adjust the transmission strategy according to system demand and business requirements, guaranteeing the timely transmission and effective management of information. The preceding network architecture proposes a secure and reliable multi-objective optimized multipath transmission algorithm for heterogeneous networks, aimed at safely and reliably delivering information from the source to the destination. The algorithm's framework is depicted in Figure 2. Firstly, the data acquisition module is responsible for obtaining the topological state of the network, the link state of each node, and the connectivity state of the links from the heterogeneous network. Then, this information will be fed into the path planning module, which generates a solution set of all feasible paths from the source to the destination. And the multi-objective optimization module processes this solution set to determine Path 1, which is then passed to the multipath computation module. This module generates a simplified topological graph and updates node states. The newly generated graph and updated node states are subsequently re-evaluated by the path planning module and the multi-objective optimization module to determine Path 2. Ultimately, the system outputs a multipath transmission solution from the source to the destination, ensuring secure and reliable data delivery. The specific implementation process is depicted in Algorithm 1. This algorithm computes multiple redundant transmission paths that satisfy the optimization objectives, utilizing network topology information and task requirements. The process involves the following steps: (1) Initialize the current network topology data and optimization parameters. (2) Obtain network topology information from the heterogeneous network, including the link status of each node and the connectivity status of the links. (3) Execute a variant of the algorithm based on depth-first search. This step recursively searches all feasible paths in the network, ensuring there are no duplicate vertices in each path within the set of paths. During the search, the algorithm records the length of the current path and ceases further  
Figure 2: Algorithm framework diagram. searching when the path length exceeds the known maximum path length. This is achieved by optimizing the initial population size to reduce unnecessary computation. (4) Actively screen suitable paths using a multi-objective optimization algorithm to obtain the initial path. The objective is to maximize path reliability and minimize transmission delay. This study employs the optimized NSGA-II algorithm, which is based on the concepts of genetic algorithms and Pareto optimality, widely used in multi-objective optimization problems. The global search capability of the optimized NSGA-II algorithm helps circumvent the pitfall of local optimal solutions during the iteration process. (5) Utilize the multipath computation module to simplify the topology based on the first optimal transmission path. The core operation involves performing three distinct types of simplifications to the network topology graph to ensure that the newly generated path has no common links with the original path. (6) Re-run the depth-first search variant and multi-objective optimization steps with the pruned new topology graph to obtain the second path.