MOMTA-HN: A Secure and Reliable Multi-Objective Optimized Multipath Transmission Algorithm for Heterogeneous Networks

Abstract

With the rapid development of heterogeneous network technologies, such as mobile edge computing, satellite communications, self-organizing networks, and the wired Internet, satisfying users’ increasingly diversified and complex communication needs in dynamic and evolving network environments has become a critical research topic. Ensuring secure and reliable information transmission is essential for stable network operation in these complex environments. Addressing this challenge, this study proposed a secure and reliable multi-objective optimized multipath transmission algorithm for heterogeneous networks to enhance security and reliability during data transmission. The core principle of this algorithm was that multipath transmission can provide additional protection through redundant paths. This redundancy ensured that even if one path is attacked or fails, alternative paths can maintain data integrity and reachability. In this study, we employed the Optimized Non-dominated Sorting Genetic Algorithm II (ONSGA-II) to determine the range of the initial population and filter suitable paths by optimizing them according to different demand objectives. In the path selection process, we introduced an innovative deletion graph method, which ensures that redundant paths do not share any common links with the original paths, except when there are unique links. This approach enhances the independence of transmission paths and improves the security of the transmission process. It effectively protects against security threats such as single points of failure and link attacks. We have verified the effectiveness of the algorithm through a series of experiments, and the proposed algorithm can provide decision-makers with high-reliability and low-latency transmission paths in heterogeneous network environments. At the same time, we verified the performance of the algorithm when encountering attacks, which is superior to other classical algorithms. Even in the face of network failures and attacks, it can maintain a high level of data integrity and security.

1. Introduction

Heterogeneous networks, a significant research direction in the field of networking, have demonstrated a vigorous development momentum. These networks are composed of various types of devices, communication technologies, and network structures [1]. The research scope is broad, encompassing mobile edge networks [2,3], satellite networks [4,5], self-organized networks [6,7], and the wired Internet [8,9]. The objective of constructing heterogeneous networks is to integrate diverse network resources to provide users with more flexible, efficient, and reliable communication services, thereby meeting increasingly diverse and complex communication needs. Despite the significant advantages of heterogeneous networks, their security still faces serious challenges. For instance, replay attacks, distributed denial-of-service (DDoS) attacks, and privacy breaches can lead to network disruptions, transmission failures, or even more severe consequences. Therefore, security management in heterogeneous networks remains a critical research area, with the secure transmission of network information being a primary focus.

To address security issues in heterogeneous networks, researchers have proposed various approaches, including strategies such as mobile target defense, privacy protection, and malicious traffic detection to counter complex network threats. Data encryption techniques are most commonly employed to secure data transmission. According to a Google report, encrypted data accounted for more than 80% of total network traffic as of 2024. Despite this high percentage, data breaches have become more frequent, primarily due to security vulnerabilities in network data transmission [10]. The main reasons for these vulnerabilities include the following: encryption and decryption algorithms typically require substantial computational resources, leading to high computational complexity and significant operational costs for nodes [11]; the rise of intelligent algorithms, such as semantic recognition, enables attackers to infer the overall content by obtaining only part of the data [12]. Clearly, avoiding malicious nodes during transmission is an effective method to prevent data leakage. Thus, there is a need to develop secure, resilient, and efficient detection techniques to manage malicious nodes within the network to defend against network attacks [13].

However, existing detection solutions are not yet adequate for defending against the latest internal and external threats. These models typically require monitoring both potential internal and external attacks [14,15,16] and heavily rely on the accuracy of malicious node detection. Existing studies indicate that the best malicious node detection methods achieve an accuracy of up to 80%, leaving a 20% uncertainty [17]. While it is feasible to develop algorithms that compute secure transmission routing paths to avoid data eavesdropping or interception by malicious nodes, these paths often require significantly more hops than optimal routes, reducing transmission efficiency and increasing costs. Additionally, the destination node must collect all transmitted packets to reconstruct the original data, which imposes very high reliability requirements on the network [18].

Over time, there has been a growing interest in the introduction of dynamic parameters in cyber adversarial environments, an approach that has allowed cybersecurity protection techniques to evolve from static protection to dynamic active defense. For example, Moving Target Defense (MTD) serves as a defense paradigm aimed at minimizing the inherent advantages of attackers over defenders [19,20]. MTD protocols increase the cost of an attack, limit the exposure of susceptible components, and deceive adversaries by developing mechanisms to continuously and unpredictably change system parameters [21,22]. However, even active defense techniques such as MTD still face significant challenges [23]. These methods have a high probability of escape failure because the dynamic scheduling links of such approaches and the system execution body itself can still be “bypassed or short-circuited” by exploiting high-risk vulnerabilities. Additionally, the diversity and dynamism introduced by MTD do not change the logical nature of software and hardware vulnerability backdoors, nor can they prevent coordinated attacks from internal and external sources [24].

Indeed, packet routing and communication security are two energy-consuming and critical network functions, making secure and reliable communication in heterogeneous networks a challenging task [25,26]. Many current approaches primarily detect threats and respond to them from a policy perspective. However, a more technical response from a network function perspective can also be effective. For example, the receiver could make sender know that the receiver has successfully received each packet or group of packets through an acknowledgment packet sent by the receiving node. However, this technique is impractical in a lossy environment—such as when the network is under attack from physical or information domains—because the acknowledgment messages themselves are at risk of being lost. Additionally, transmitting a large number of acknowledgment messages or waiting for their reception can significantly increase network overhead and communication delay [27]. Therefore, proposing path redundancy and path backup schemes from a transport perspective is particularly important to enhance reliability and protect against multiple network threats, such as Denial of Service (DoS) attacks, through multipath routing. However, in severely constrained environments, even multipath routing techniques may be difficult to implement, especially if their traditional principles remain unchanged (i.e., the involvement of all network nodes in the multipath routing process throughout the network lifecycle). Achieving secure and reliable data transmission in heterogeneous networks is thus a crucial and complex research area that warrants in-depth exploration. In this context, our study makes several significant contributions:

• A generic secure and reliable multi-objective optimized multipath transmission algorithm for heterogeneous networks is proposed: We propose an algorithm capable of constructing multiple redundant transmission paths in heterogeneous networks composed of various sub-networks. By considering the unique characteristics and task requirements of heterogeneous networks, multiple optimization objectives are introduced into the path selection process. This allows the computation of multiple optimal paths that not only meet performance requirements such as delay and reliability but also effectively avoid potential security threats, ensuring efficient and secure transmission across different types of network environments.
• Optimization of path planning decisions: Path planning decisions in this context represent a mixed-integer programming problem (MIPP), an NP-hard problem. Additionally, there are trade-offs between optimization objectives, and the dimensionality of the solution is variable, making it difficult for traditional algorithms to solve these problems in polynomial time. To address this, we propose optimizing the initial population range using the Optimized Non-dominated Sorting Genetic Algorithm II, which considers multiple objective functions, such as task reliability and delay. This approach filters out the optimal combination of paths to satisfy different demand objectives, ultimately obtaining the Pareto-optimal solution set for the optimization problem.
• Innovative application of the deletion graph method: After calculating the primary path, we propose simplifying the topological map using the deletion graph method. Unless no other links are available, this method ensures that any redundant paths do not share common links with the original path. This approach enhances the security of the transmission process and improves transmission reliability. The deletion graph technique searches for redundant paths on the new pruned graph by gradually deleting all links on the original paths, ensuring that these paths are physically independent from the original paths.
• Experimental validation and evaluation: We further validate the effectiveness of the proposed method through comparative analysis and experimental demonstration. The adaptability and robustness of the algorithm in complex and changing network environments are highlighted. The flexibility of the proposed algorithm in terms of optimization strategy is demonstrated by adopting a soft update strategy to dynamically adjust network weight parameters. This strategy allows for the collaborative optimization of the multi-objective problem under different priorities. Experimental results show that the proposed algorithm exhibits significant advantages in the face of malicious attacks and network failures, maintaining a high transmission success rate and low latency.

This study highlights the potential of multi-objective optimized multipath transmission algorithms in addressing the challenges of secure and reliable communication in heterogeneous networks. By leveraging advanced techniques like NSGA-II and the deletion graph method, the proposed solution offers a robust and adaptable framework capable of maintaining high levels of data integrity and security even in the face of network failures and attacks. The rest of this paper is organized as follows. Section 2 details the specific methods for achieving multi-objective optimization in multipath transmission for heterogeneous networks. In Section 3, we demonstrate the effectiveness of our proposed method through experimental validation. In Section 4, we review the state of the art in research on multi-objective optimization and multi-objective transmission. Finally, Section 5 provides a summary and discusses future research directions.

2. Methodology

2.1. System Model

This paper proposes a dual-network architecture for secure and reliable transmission in heterogeneous networks. The system model comprises heterogeneous transmission network resources, including satellite networks, the Internet, mobile networks, and self-organized networks, as illustrated in Figure 1. The network architecture employs a layered decoupling design to separate the transmission control layer from the network resource layer. This separation forms a flexible dual-network structure, corresponding to the transmission control network and the network resource network. The network resource layer is designed to ensure stability and reliability while allowing for network flexibility, scalability, and programmability of the forwarding plane. It provides redundant physical transmission channels, enhancing the robustness of the network. The transmission control layer is responsible for the reliable transmission of information. It utilizes innovative lightweight sharing algorithms, Delay Tolerant Networking (DTN), and other technological means to flexibly address diverse information transmission needs. The transmission control layer constructs a logically independent overlay network, with virtual nodes abstracted from the transmission control system. These virtual links correspond to the heterogeneous network access points in the network resource layer. Neighboring nodes are connected by multiple virtual links, forming redundant and reliable transmission paths.

By covering the network, the overall information of the network is shared with each other through lightweight consensus algorithms, and the transmission path is pre-calculated in the stacked network for information transmission in the physical network. The business system issues tasks and instructions at the upper level, while the transmission control layer encapsulates transmission-related functions into service-oriented entities, forming corresponding transmission control service entities. With the help of transmission control interfaces, resource collection and synchronization, path strategy control, and information transmission control are completed. We establish an identification system in the resource network layer to achieve automatic conversion of heterogeneous access protocol systems and consensus broadcasting between nodes, forming a unified resource status table for the entire network and providing support for transmission control services.

For the resource network layer, to address the characteristics of physical transmission network resources, such as heterogeneity and mobility, an overlay network based on overlay technology is constructed. This overlay network leverages various heterogeneous network resources to build a transmission control system, thus enabling the unified management and utilization of these diverse resources. By employing heterogeneous multi-means connections between disparate resource networks, the system ensures that at least two or more independent transmission channels are linked, thereby enhancing communication reliability and robustness.

The transmission control layer is the fundamental component of the system, responsible for establishing and managing physical information transmission channels across heterogeneous networks to support the operation of the secure transmission control overlay network. By interconnecting multiple heterogeneous network resources and utilizing dynamic networking functions, the transmission control system can effectively establish physical information transmission channels across heterogeneous networks. A consensus algorithm is used between transmission control systems to achieve information synchronization among distributed transmission control systems, thereby establishing a unified node resource and link state information table across the network. 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 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. (7) The final output comprises two paths that satisfy the optimization objectives.

Algorithm 1: Secure and Reliable Multi-Objective Optimization Multipath Transmission Algorithm for Heterogeneous Networks

Input: heterogeneous network $G\left(V,E\right)$, source node $v_s$, target node $v_t$, optimization parameters

Output: Multiple optimal transmission paths

1 Initial: the current network topology data and optimization parameters.

2 Obtain network topology information: the link status and connectivity status of each node.

3 Path search:

4        a. Run a variant algorithm based on Depth First Search (DFS) to recursively search for all feasible paths in the network.

5        b. Ensure that each path in the path set does not contain duplicate vertices.

6        c. When the path length exceeds the known maximum path length, stop further search.

7 Path filtering:

8        a. Using NSGA-II for multi-objective optimization, select the best path to maximize path reliability and minimize transmission delay.

9        b. The global search capability of NSGA-II avoids getting stuck in local optima during the iteration process.

10 Topology simplification:

11        a. Delete the network topology based on the first optimal transmission path.

12        b. Ensure that there is no common link between the new path and the original path.

13 Repeat path search and filtering:

14        a. Re input the deleted new topology map into the path search and multi-objective optimization module.

15        b. Obtain the second path.

16 Return multiple transmission paths that meet optimization objectives.

2.2. Multi-Objective Optimization Strategy

In this study, to address the conflicts among different optimization objectives, we propose using an optimized Non-dominated Sorting Genetic Algorithm II (NSGA-II) to solve multi-objective constrained optimal path problems. The NSGA-II is a powerful decision space exploration engine based on Genetic Algorithm (GA), primarily used to solve multi-objective optimization problems (MOOPs) [28]. Among the branches of multi-objective optimization problems, combinatorial optimization problems (COPs) are considered some of the most challenging and complex. Since most COPs are NP-hard, their computational complexity increases significantly as the problem size grows. Consequently, approximate methods such as metaheuristics are preferred over classical methods for solving such problems [29,30]. Multi-objective optimization involves finding the best possible solutions for multiple objectives within a given domain. A MOOP consists of a set of n decision variables, k objective functions, and a set of constraints comprising m inequality constraints and p equality constraints. The optimization objective is to find solutions that satisfy all constraints while optimizing the objective functions.

$$Min/Maxy=f\left(x\right)=\left(f_1\left(x\right),f_2\left(x\right),\dots ,f_k\left(x\right)\right),k\ge 2$$

(1)

$$Subjectto{g}_i\left(x\right)\le 0,i=1,2,\dots ,m$$

(2)

$$h_j\left(x\right)\le 0,j=1,2,\dots ,m$$

(3)

Formally, $x=\left(x_1,x_2,\dots ,x_n\right)\in D$ is the n-dimensional decision vector in $X\subseteq R^n$, and y is the k-dimensional objective vector in $R^k$. f is defined as the mapping function, $g_i$ is the i-th inequality constraint, and $h_j$ is the j-th equality constraint. Thus, Equations (2) and (3) determine the set of all feasible solutions X, so it can also be written as a set of different feasible solutions $\left(x_1,x_2,\dots ,x_n\right)\in X$.

Suppose $x_1,x_2\in X$ are two feasible solutions to a multi-objective problem. A solution $x_1$ can be regarded as superior to $x_2$ if the following condition is satisfied: $x_1$ is superior to $x_2$ in at least one of the objectives and no worse than the others. In this case, $x_1$ is said to dominate $x_2$.

$$\left\{\begin{array}{c}{x}_1\prec x_2\iff f_i\left(x_1\right)\le f_i\left(x_2\right),\forall i\in \left\{1,2,\dots ,m\right\}\hfill \\ \exists j:f_j\left(x_1\right)\le f_j\left(x_2\right)\hfill \end{array}\right.$$

(4)

The j-th value of the objective function for the decision vector x is denoted by $f_j\left(x\right)$. The solution space is denoted by X, ≺ represents the dominance relation. Let $x\in \psi \subseteq X$, if all other solutions in $\psi$ do not dominate x then x is nondominated with respect to the subset $\psi$. This means that x is nondominated with respect to $\psi$. Methods for identifying Pareto-optimal solutions include NSGA-II, the Pareto Adaptive Algorithm (APA), and others, which are employed in this study.

Optimization problems frequently exhibit not a single solution but a set of solutions, where improving one objective function necessarily entails a reduction in another. Such a solution is termed a nondominated or Pareto-optimal solution, and all Pareto-optimal solutions constitute a Pareto-optimal set (PS). In this context, a Pareto-optimal solution $x\in X$ is nondominated with respect to the entire solution space $\psi$. The set of all Pareto-optimal solutions constitutes the Pareto-optimal set (PS). The objective vector corresponding to the Pareto-optimal set is defined as the Pareto frontier, as illustrated in Figure 3.

The NSGA-II is an enhanced iteration of the Non-dominated Sorting Genetic Algorithm (NSGA), widely utilized in multi-objective optimization problems due to its elitist properties, the absence of the necessity to share parameters, and its rapid computation speed [31]. NSGA-II effectively avoids falling into local optimal solutions during the iteration process through the use of the crowding distance operator as a diversity preservation mechanism and the ability to perform global searches based on the concepts of genetic algorithms and Pareto optimality. The optimization objectives proposed in this study include multiple goals, specifically maximizing reliability and minimizing delay. The objective of maximizing reliability is to optimize the reliability of the transmission path, thereby ensuring stability and resistance to interference during data transmission. The objective of minimizing delay is to optimize the delay of the transmission path, ensuring that data can be delivered to the target node rapidly and in a timely manner. Therefore, the objective function can be defined as follows:

$$minF=min\left\{{\mathrm{Rreliability}}_{max},{\mathrm{delay}}_{min}\right\}$$

(5)

$$minF=w_{1}D+w_2(-R)$$

(6)

$$\begin{array}{cc}s.t.\hfill & D=\sum t_i\\ \hfill & R=\prod r_i{v}_i\\ \hfill & r_i=\frac{\frac{1}{\lambda }{\displaystyle \sum _{j=1}^N}{A}_{j,i}{c}_e\left(v_j\right)}{E\left({\displaystyle \sum _{j=1}^N}{A}_{j,i}S\left(v_i,v_j\right)\right)}\\ \hfill & t_i=\frac{e_i}{\mathrm{v}}\\ \hfill & R\ge 0.99\\ \hfill & D\le 500\end{array}$$

(7)

The reliability of the transmission path, R is computed as the cumulative product of the reliability of each node. The reliability of each node, $r_i$, is determined by node eigenvector centrality and node similarity. Eigenvector centrality represents the global importance of a node in the network topology, while the similarity between a node and its neighboring nodes measures the local importance of the network node. The delay of the transmission path, D is calculated as the sum of the delays of each link. The delay on each link segment, $d_i$ contributes to the total path delay. In the process of multi-objective optimization, we limit the range of reliability and delay by setting optimization objective constraints. At the same time, based on the scenario in the algorithm, we prioritize reliability as the first optimization objective. When the reliability is greater than 0.99, we select paths with a delay of less than 500 as the selected object. In addition, this algorithm continuously collaborates on reliability and latency during the cross mutation screening process of offspring by using optimized NSGA-II algorithm, ultimately achieving Pareto-optimal solution. The optimization process is described as follows.

The algorithmic process effectively solves the multi-objective optimization problem in heterogeneous networks, ensuring the reliability and timeliness of information transmission (Algorithm 2). The elitist strategy of NSGA-II optimization retains the best individuals from the previous generation, allowing the algorithm to avoid local optimal solutions and improve global search capability. Additionally, the algorithm maintains population diversity by calculating the crowding distance of individuals in the objective space, enhancing the stability and convergence of the algorithm. By performing the non-dominated sorting of the population, the algorithm effectively identifies superior solutions. These characteristics enable the algorithm to excel in multi-objective optimization problems, improving computational efficiency while ensuring the diversity and comprehensiveness of the optimization results. Generating the initial population using heuristics accelerates the convergence process of the algorithm and enhances the quality of the solutions, thereby achieving efficient, secure, and reliable multipath information transmission.

Algorithm 2: Multi-objective optimization process of MOMTA-HN algorithm

Input: heterogeneous network $G\left(V,E\right)$, source node $v_s$, target node $v_t$, optimization parameters

Output: Optimal transmission paths

1 Initial: The network with the input parameters.

2 Initialize population: After determining the objective function, use heuristic methods to obtain a simple path between the source and destination to generate the initial population.

3 Non dominated sorting and selection: Perform non dominated sorting and selection on the initial population obtained from the path planning module.

4 Cross and mutation: Performing cross and mutation operations on the selected population to generate the next generation population.

5 Constraint check and repair: Check whether the generated population meets the constraint conditions and make necessary repairs.

6 Generate subpopulation: Generate the first generation subpopulation and update the evolutionary algebra.

7 Fast non dominated sorting: Perform fast non dominated sorting on each generation of population.

8 Repeat the above steps until the maximum evolutionary number is reached.

9 Return Pareto frontier solution.

2.3. Multipath Transmission Algorithm

This paper proposes a framework for multipath transmission algorithms based on hierarchical culling. The core operation involves performing three different types of simplification on the network topology graph. After the NSGA-II-based multi-constraint optimal path algorithm determines the first path that satisfies the multi-constraint requirements, the framework performs different simplification operations based on varying situations to obtain the second path.

2.3.1. The First Type of Simplification Operation

The core idea of the first type of simplification operation is to ensure the independence of the new paths by fine-grained management and deletion of the heterogeneous subnetworks where the source and destination nodes are located. As illustrated in Figure 4, new links are obtained by deleting different subnetworks and links. The red, yellow, blue, and purple clouds on the left represent different heterogeneous networks. The source and destination nodes are node S and node D, respectively. The first calculated path is S-E-I-K-N-D. Through the first type of graph deletion operation, we deleted the nodes and links that the purple heterogeneous network and the first path in the red and yellow heterogeneous networks passed through. Therefore, the second calculated path is S-A-B-G-L-D. The specific steps are as follows:

Subnetwork lookup: Identify the subnetworks where the source and destination nodes are located separately. This step ensures that the network locations of the source and destination nodes are identified.

Path node subnetwork identification: Identify the subnetwork in which each node (other than the source and destination nodes) on the first path that satisfies the multi-constraint requirement is located. This step provides the basis for subsequent simplification operations by identifying the network locations of the intermediate nodes on the path.

Subnetwork compare and delete: Determine if the subnetwork where each node on the path is located is the same as the subnetwork where the source or destination node is located. If it is the same, delete the node and its associated links. Otherwise, delete all nodes within the subnetwork where the node is located and the links associated with each node in the subnetwork.

These operations result in a new network topology graph. At this point, the NSGA-II-based multi-constraint optimal path algorithm is used again to find a second path that satisfies the multi-constraint requirement. If the second path exists, the search is successful; otherwise, the second type of simplification operation is used.

2.3.2. The Second Type of Simplification Operation

The core idea of the second type of simplification operation is to delete every link on the first path that satisfies the multi-constraint requirement in the network topology. As illustrated in Figure 5, new links are obtained by deleting different subnetworks and links. The red, yellow, and purple clouds on the left represent different heterogeneous networks. The source and destination nodes are node S and node D, respectively. The first calculated path is S-E-I-K-N-D. Through the second type of graph deletion operation, we removed the nodes and links that the first path passed through in the red, yellow, and purple heterogeneous networks. Therefore, the second calculated path is S-B-J-L-D. The specific steps are as follows:

Link deletion: In the network topology, delete each link on the first path that satisfies the multi-constraint requirement. This ensures that the new path does not intersect the first path in terms of physical links, thus improving the independence of the paths and the overall reliability of the system.

Path computation: After performing the second type of simplification operation, obtain a new network topology map. At this point, the NSGA-II-based multi-constraint optimal path algorithm is used again to find a second path that satisfies the multi-constraint requirement. If the second path exists, the search succeeds; otherwise, the third type of simplification operation is used.

2.3.3. The Third Type of Simplification Operation

The core idea of the third type of simplification operation is to find a new independent path by refining the link processing based on the link bottleneck on the first path. As illustrated in Figure 6, The red and yellow clouds on the left represent different heterogeneous networks. The source and destination nodes are node S and node D, respectively. The first calculated path is S-A-F-O-R-D. It can only go through link FO. At this point, FO is the only link of the network, and nodes O and F belong to the point cut set of the network, while link FO belongs to the edge cut set. When the link FO is deleted, the network topology will split into two disconnected subgraphs. In this situation, the first and second types of simplification methods become ineffective, necessitating the use of the third type of simplification. Based on link FO, the path is divided into two distinct subgraphs. Each subgraph will then re-determine the source and destination nodes and apply the second type of simplification again to find a second path that satisfies the multi-objective optimization requirements. Therefore, the second calculated path is S-E-F-O-T-D. The specific steps are as follows:

Identify the link bottleneck: Locate the nodes on the first path where only two links are connected, i.e., the links that may have “link bottlenecks”. These links are the weakest points in the path and require special handling.

Path splitting: Split the first path into two parts based on unique links. This step refines the path processing to ensure the new path avoids these bottleneck links.

Path computation: Apply the second simplification method again to find a second path that satisfies the multi-constraint requirements. This step ensures that a second path is found even in the presence of a link bottleneck.

The main purpose of the three types of simplification operations is to significantly improve the overall reliability of the two paths. The first type of simplification ensures that the nodes on the second path are in different subnets from the nodes on the first path. If the subnet of a node on the first path fails, the node on the second path can still transmit data normally, improving the system’s fault tolerance. The second type of simplification ensures that the two paths do not share links. If a link on the first path fails, the data on the second path can still be transmitted normally, enhancing the system’s redundancy and data transmission reliability. The third type of simplification provides an effective path scheduling scheme for cases where data can only be transmitted over specific segments of links on the first path. This operation ensures that even with a link bottleneck, a second path can be found that satisfies the multi-constraint requirements, thereby ensuring the high reliability and availability of the system.

The multipath transmission algorithm framework based on hierarchical culling, as proposed in this paper, offers an efficient and reliable multipath transmission scheme through three different types of simplification operations combined with the NSGA-II multi-objective optimization algorithm. This framework not only improves the independence of paths and the overall reliability of the system but also ensures the high efficiency and security of information transmission. It is particularly suitable for the multipath transmission requirements in complex heterogeneous network environments. By fine-grained management of the network topology graph and path planning, the algorithm effectively addresses various transmission challenges, providing robust technical support for achieving highly reliable network communication.

3. Experiment

3.1. Experiment Setup

To demonstrate the rationality and applicability of the proposed evaluation method, we selected the ChinaNet network from the Topology Zoo as the target for this experiment [32]. The Topology Zoo contains 261 real network topologies from around the world and is recognized by network researchers as a publicly available dataset for experimental testing, making it a valuable resource for network-related research and experiments, particularly for various network simulations.

As shown in Figure 7, the topology of the ChinaNet network, which we chose as the test network for this paper, contains 42 nodes and 66 edges. The topology graph reveals the presence of both centralized key nodes and edge nodes, thus allowing us to better characterize different styles within the network. When designing the experiments, we considered the connectivity between the topology nodes and the ease of operation. We chose ONOS 2.4.1 and Mininet to build the experimental environment. Mininet allows for the flexible setup of network topology based on specific requirements, while the ONOS controller can automatically disseminate flow tables and control the link relationships between nodes. In the subsequent attack experiments, we could easily select the nodes to attack. We replicated the ChinaNet network in Mininet and set various parameters such as IP address, MAC address, and bandwidth according to the actual network.

As shown in Figure 8, based on the actual network configuration, we divided the network topology into different heterogeneous sub-networks according to a ratio of 2:3:1:4. Since nodes in different sub-networks exhibit varying information transmission performance, we define the common transmission delay of different heterogeneous networks as different unit times, i.e., the time it takes for data to traverse a link of length 1 in the topology, based on data from Google. The node types and their corresponding transmission unit delays are defined as follows: Dark blue nodes represent wired interconnection networks with a unit delay of 20 ms. Light blue nodes represent the mobile Internet with a unit delay of 5 ms. Yellow nodes represent satellite networks with a unit delay of 100 ms. Orange nodes represent drone self-organizing networks with a unit delay of 5 ms. To achieve efficient transmission across different heterogeneous networks, we must address the protocol conversion problem. When transmitting data across heterogeneous networks, the protocol fields of packets need to be converted to meet the requirements of the destination network. Traditional protocol conversion methods typically rely on complex protocol cross-reference tables, requiring each network node to refer to the table when transmitting data. This approach not only increases computational overhead but also introduces potential conversion errors and transmission delays.

To address these issues, we propose a cross-layer protocol encapsulation approach. Specifically, we encapsulate the protocol fields required by different heterogeneous networks uniformly in the header of the transport system message at the application layer. This method allows a network node to parse the relevant fields in the message header to complete the protocol conversion without referring to a cross-reference table when a packet enters different heterogeneous networks. This approach simplifies the protocol conversion process, reduces computational overhead, and improves the efficiency and reliability of data transmission. Under this cross-layer protocol encapsulation architecture, data traversing different heterogeneous networks requires only one parsing operation to complete the protocol conversion, avoiding delays caused by multiple conversions. We define the uniform delay for cross-network protocol conversion as 50 ms, which includes the time for parsing message headers and performing protocol conversion. By introducing the cross-layer protocol encapsulation method, we effectively solve the protocol conversion problem between different heterogeneous networks and enhance the efficiency and reliability of data transmission.

To better evaluate the security and reliability of the MOMTA-HN algorithm under attack conditions, we designed a series of experiments to randomly attack different nodes in the network. In heterogeneous networks, attacks tend to be random and continuous, with nodes interacting and the network crashing at an accelerating rate. We used the transmission success rate as a metric to measure the performance of the algorithm. To ensure the fairness and statistical significance of the experimental results, we performed 1000 independent tests for each round of experiments.

The transmission success rate is calculated using the following formula:

$$P_{success}=\frac{N_{success}}{N_{total}}$$

(8)

where $P_{success}$ is the success rate, $N_{success}$ is the number of successful transmissions, and $N_{total}$ is the total number of trials. For multipath transmission algorithms, the transmission success rate must be calculated by its complement. Suppose there are m paths in the network and the attack occurs randomly at any node on any path. After N attempts, the event of successful transmission on the i-th path is denoted as $S_i$ , and the event of successful multipath transmission S is the case where at least one of all paths is successfully transmitted. If the success rate of each path independently is $P_1,P_2,\dots ,P_m$, then the multipath transmission success rate $P_{multi}$ can be calculated by the following formula:

$$P_{multi}=1-{\prod }_{i=1}^m(1-P_i)$$

(9)

where, $1-P_i$ denotes the probability that the transmission of the i-th path fails, and thus ${\prod }_{i=1}^m(1-P_i)$ denotes the probability that all paths fail, while its complement $1-{\prod }_{i=1}^m(1-P_i)$ is the probability that at least one path succeeds. In our experiments, we assume the existence of m independent transmission paths and evaluate the success rate of each path independently. Assuming that the number of successful transmissions of the i-th path in N experiments is $N{S}_i$, the success rate $P_i$ of the i-th path is

$$P_i=\frac{N{S}_i}{N}$$

(10)

This allows us to systematically evaluate the performance of the MOMTA-HN algorithm in heterogeneous networks, particularly its robustness against malicious attacks. The experimental results demonstrate the advantages of the algorithm in complex network environments, as shown below.

3.2. Detailed Analysis and Comparison

Figure 9 presents a comparison of the MOMTA-HN algorithm with the SPFA and Dijkstra algorithms. Figure 9a depicts the comparison of reliability, while Figure 9b illustrates the comparison of delay. In the absence of attacks, we traversed the transmission paths between all nodes and computed the path transmission delay loss and the path reliability value for the three algorithms. The path reliability value is the product of the reliability of the different nodes. Minimum reliability is represented by the positive triangles in the figure. The minimum reliability for both the MOMTA-HN algorithm and the Dijkstra algorithm is 99.182%, while for the SPFA algorithm it is 99.004%. Maximum reliability is represented by the inverted triangles. The maximum reliability for all three algorithms is 99.999%. Mean reliability is represented by the star in the center of the box. The mean reliability values for the MOMTA-HN, Dijkstra, and SPFA algorithms are 99.69%, 99.666%, and 99.654%, respectively. Median reliability is represented by the tan solid line. The median reliability for all three algorithms is 99.6%.

When calculating the path transmission delay loss, we disregarded the time required for policy formulation and focused on the transmission time, derived by multiplying the link relative value by the transmission delay loss through different media, assuming constant external environmental conditions. Minimum delay is represented by positive triangles. The minimum transmission delay for all three algorithms is 10 ms. Maximum delay is represented by inverted triangles. The maximum transmission delay for both the MOMTA-HN and Dijkstra algorithms is 495 ms, while for the SPFA algorithm it is 425 ms. Mean delay is represented by the star in the middle of the box. The average transmission delays for the MOMTA-HN, Dijkstra, and SPFA algorithms are 311.66 ms, 239.5 ms, and 250.06 ms, respectively. Median delay is represented by the tan solid line. The median transmission delay for the MOMTA-HN algorithm is 325 ms, for Dijkstra it is 270 ms, and for SPFA it is 290 ms.

We can conclude through numerical analysis and comparison that the SPFA algorithm exhibited the lowest average delay (270 ms), while the MOMTA-HN algorithm exhibited the highest reliability. The MOMTA-HN algorithm selects the path with the highest reliability at the cost of slightly increased transmission delay as a result of multi-objective optimization. The algorithm enhances transmission security by calculating multiple redundant paths and ensuring that these redundant paths do not share any common links with the original paths in non-essential situations. Although the average delay of the MOMTA-HN algorithm is slightly higher than that of the SPFA algorithm, it has significant advantages in terms of network reliability. In particular, the MOMTA-HN algorithm is capable of selecting the path with the highest reliability for data transmission among multiple paths that can reach the destination during the process of multi-objective optimization. This strategy not only ensures the stability of data transmission but also improves the overall network quality of service and user experience to a certain extent.

The following presents the results of transmission performance when encountering attacks, as evaluated by different algorithms.

As illustrated in Figure 10, this study presents the results of transmission success comparisons among the MOMTA-HN algorithm, the SPFA algorithm, and the Dijkstra algorithm when encountering attacks. The experiments comprise three scenarios to demonstrate the performance of each algorithm and their path selection strategies under different source and destination node configurations.

In Figure 10a, the source and destination nodes are node 9 and node 18, respectively. In this case, the MOMTA-HN algorithm performs the first type of simplification, which involves deleting all nodes of the sub-network where the first link transmitting node is located. This results in the generation of a new multipath for redundant transmission. The figure illustrates that the red line (MOMTA-HN) is considerably higher than the blue (SPFA) and green (Dijkstra) lines. Furthermore, the number of successful transmissions of the MOMTA-HN algorithm exceeds that of the other two algorithms at all stages of the attack. The MOMTA-HN algorithm effectively avoids single points of failure through first-class simplification, thereby enhancing the robustness and reliability of the network. In contrast, the SPFA and Dijkstra algorithms do not have the same nodes traversed by their calculated paths due to differing path computation principles. Consequently, the green and blue lines in Figure 11a do not overlap. This indicates that while all algorithms have analogous objectives in path selection, the MOMTA-HN algorithm is capable of greater flexibility in adjusting paths when the network is under attack, thus ensuring the success rate of transmission.

In Figure 10b, the source and destination nodes are node 18 and node 22, respectively. The figure shows that the red line (MOMTA-HN) is significantly higher than the blue (SPFA) and green (Dijkstra) lines. The number of transmission successes of the MOMTA-HN algorithm is superior to those of the other two algorithms, both in the pre-attack period and in the later stages when there are fewer remaining nodes. At this juncture, the initial type of simplification employed by the MOMTA-HN algorithm is rendered ineffective, necessitating the implementation of a second type of simplification, namely the deletion of all nodes belonging to the initial link. With this simplification, the MOMTA-HN algorithm can recalculate the multipath for transmission. The SPFA and Dijkstra algorithms yield identical results in Figure 11b, resulting in the two lines overlapping.

In Figure 10c, the source and destination nodes are node 1 and node 9, respectively. The experimental results demonstrate that the red line (MOMTA-HN) is significantly higher than the blue (SPFA) and green (Dijkstra) lines. Furthermore, the number of successful transmissions of the MOMTA-HN algorithm outperforms the other two algorithms in both the pre-attack period and the later period when there are fewer remaining nodes. At this point, the first transmission path used for source and destination node transmission contains unique links. When both the Type I and Type II simplification methods of the MOMTA-HN algorithm prove ineffective, the algorithm employs a multipath computation strategy for Type III simplification methods, which it then compares with the other algorithms. This advanced simplification strategy enables the MOMTA-HN algorithm to identify and utilize new redundant paths, thereby preventing transmission interruptions caused by network attacks. The experimental results demonstrate that the MOMTA-HN algorithm is still capable of effectively guaranteeing the success rate of data transmission in this complex network environment, whereas the SPFA and Dijkstra algorithms are less adept at doing so.

The results of the above comparison experiments demonstrate that the MOMTA-HN algorithm exhibits a significantly higher success rate in information transmission than the SPFA and Dijkstra algorithms, particularly in the context of network attacks. The MOMTA-HN algorithm exhibits enhanced flexibility and reliability in path selection, and its multi-objective optimization strategy enables it to adapt to diverse network environments, ensuring the successful completion of transmission tasks. In contrast, the SPFA and Dijkstra algorithms demonstrate superior path selection capabilities under specific conditions. However, they lack the flexibility and robustness of the MOMTA-HN algorithm when confronted with network attacks and complex network environments.

As illustrated in Figure 11, this study presents a comprehensive comparison experiment among the MOMTA-HN algorithm, the multipath algorithm with the first type of simplification (MOMTA-I), and the multipath algorithm with the second type of simplification (MOMTA-II). The experiment is designed to evaluate the performance of these algorithms under attack scenarios, focusing on their ability to maintain successful transmissions.

In Figure 11a, the source and destination nodes are node 9 and node 18, respectively. At this juncture, the MOMTA-HN algorithm needs to perform only the first type of simplification, which involves deleting all nodes in the sub-network where the transmission node of the first link is located. This simplification aims to derive a second path for redundant transmission. The multipath algorithm that employs only the first type of simplification can also compute the same result. The deletion method of multipath algorithms using only the second type of simplification is simpler compared to the first type. After the optimization filtering of the multi-objective optimization algorithm, the second path calculated is identical for all the algorithms mentioned, causing the three lines in the figure to overlap. This scenario demonstrates that under certain conditions, both types of simplifications can achieve similar results.

In Figure 11b, the source and destination nodes are node 18 and node 22, respectively. In this scenario, the initial simplification approach of the MOMTA-HN algorithm proves ineffective, necessitating the use of the second type of simplification. This method involves deleting all nodes associated with the initial link to derive a second path for redundant transmission. The algorithm that performs only the first type of simplification is unable to compute the second path. However, the algorithm that performs only the second type of simplification can calculate the same second path as the MOMTA-HN algorithm after the required deletions, resulting in the two lines in the figure overlapping. This demonstrates the effectiveness of the second type of simplification when the first type fails.

In Figure 11c, the source and destination nodes are node 1 and node 9, respectively. At this juncture, both Type I and Type II simplification methods of the MOMTA-HN algorithm are ineffective in deriving a second path for redundant transmission. Consequently, Type III simplification is required. This advanced method involves a more sophisticated approach to ensure a new independent path is found, thereby enhancing the system’s robustness. Both the algorithms that use only the first type of simplification and those that use only the second type are unable to compute the second path, causing the lines in the figure to overlap. This highlights the necessity of the third type of simplification in more complex scenarios where traditional methods fail.

The results of the preceding comparison experiments clearly demonstrate that the MOMTA-HN algorithm exhibits a markedly superior success rate in information transmission compared to the multipath algorithms employing only the first type of simplification (MOMTA-I) or the second type of simplification (MOMTA-II). The MOMTA-HN algorithm showcases enhanced flexibility and reliability in addressing network attacks. Its advanced multi-objective optimization strategy allows it to adapt dynamically to diverse network environments, ensuring the successful completion of transmission tasks. In contrast, while the SPFA and Dijkstra algorithms demonstrate effective path selection capabilities under specific conditions, they lack the flexibility and robustness of the MOMTA-HN algorithm when confronted with network attacks and complex network environments.

The MOMTA-HN algorithm’s ability to utilize multiple types of simplifications allows it to maintain high transmission success rates even under adverse conditions. This capability is particularly crucial in heterogeneous network environments where attacks can occur unpredictably and affect various network segments differently. By effectively managing path redundancy and ensuring that redundant paths do not share critical links with the original paths, the MOMTA-HN algorithm significantly enhances the overall network reliability and security.

In conclusion, the experimental results validate the effectiveness of the MOMTA-HN algorithm in providing robust and reliable data transmission in heterogeneous networks. Its superior performance, especially in maintaining transmission success rates under attack conditions, underscores its potential as a highly adaptable and secure solution for complex network environments. This study demonstrates that incorporating multi-objective optimization and advanced simplification techniques can significantly improve network resilience and data transmission reliability, offering valuable insights for future research and development in network security and performance optimization.

4. Related Work

In recent years, the security of network transmission has gained critical importance due to the increasing complexity and variability of network environments. Particularly in the field of heterogeneous networks, researchers have been actively exploring methods to enhance the security and reliability of network transmission. This section reviews related work from the perspectives of multi-objective optimization and multipath transmission.

4.1. Multi-Objective Optimization

In traditional wireless sensor networks, the most important performance parameters are typically selected as optimization objectives, with other parameters used as constraints for optimization. However, these single-objective optimization techniques often struggle to perform effectively in real network environments [33]. Therefore, the use of multi-objective optimization (MOO) strategies is more aligned with practical needs. MOO strategies consider multiple performance metrics simultaneously, such as maximum reliability, minimum delay, and maximum network lifetime. This approach achieves a better performance balance and meets the complex demands of practical applications. In heterogeneous networks, each subnetwork has different resources, mission objectives, and constraints due to the combination of various network resources. Multi-objective optimization strategies are particularly important to ensure that information reaches the desired destination safely and reliably. To achieve secure and reliable information transmission, researchers have proposed various multi-objective optimization strategies.

Cai et al. [34] proposed a multi-objective algorithm to address the information transmission problem when vehicles switch between different heterogeneous wireless networks while in high-speed motion. Their algorithm balances service delay and service cost of packet transmission by adding differential evolutionary variants to the multi-objective evolutionary algorithm, enhancing population diversity and promoting continuous evolution. Asha et al. [35] proposed a distributed energy-efficient cluster routing based on a clustering strategy to meet the network energy demands and maintain the quality of service (QoS) for heterogeneous wireless sensor-based IoT networks. They optimized network QoS parameters such as throughput and delay using a multi-objective squid optimization algorithm to ensure the best fitness value while optimizing these parameters. Song et al. [36] proposed a multitasking and multi-objective optimization algorithm for computational offload and relay communication in an air-ground integrated network consisting of UAVs, EVUs, and GSNs. The algorithm decomposes emergency communication message transmission into two multi-objective tasks, optimizing for maximum minimum link transmission rate and minimum weighted sum of delay and energy consumption. Federated learning and Dual Deep Q Network (DDQN) jointly optimize resource allocation to improve the model’s generalization performance.

Pan et al. [37] addressed the resource scheduling problem for device-to-device (D2D) networks with UAV clusters. They considered the number of UAVs, their locations, transmit power, flight speed, communication channels, and device assignments to maximize D2D network capacity, minimize the number of deployed UAVs, and minimize the average energy consumption of all UAVs. Given the mixed integer programming problem (MIPP) and NP-hard nature of the problem, they proposed a non-dominated sorting genetic algorithm-III (NSGA-III-FDU) with a flexible solution dimensionality mechanism, a discrete part generation mechanism, and an adjustment mechanism for the number of drones. Guo et al. [38] discussed the use of multiple reconfigurable intelligent surface (RIS)-assisted satellite-UAV-terrestrial integrated network (IS-UAV-TN) heterogeneous network communication with co-optimization performance. They posed a multi-objective optimization problem for the collaborative UAV concerning obstacles and dynamic environments in the transmission path to maximize the system’s achievable rate and minimize the UAV’s energy consumption during a given mission. To facilitate online decision-making, they utilized Deep Reinforcement Learning (DRL) algorithms to achieve real-time interaction with the communication environment. Seifhosseini et al. [39] proposed a multi-objective cost-aware optimization algorithm for task scheduling in heterogeneous Internet of Things, which optimizes indicators such as execution time, cost, and reliability. They also verified the effectiveness of the algorithm through experiments in different scenarios. Seifhosseini et al. [40] considered the propagation cost in heterogeneous networks and solved the multi-objective key entity recognition problem by optimizing the maximum propagation scale and minimizing the heterogeneous propagation cost. By selecting strategies and hierarchical crossover operators, more complete Pareto solutions among candidates can be selected during the evolution process.

The above studies demonstrate that applying multi-objective optimization in heterogeneous networks not only improves the security and reliability of transmission but also offers new solutions for efficient transmission in complex network environments. Combining evolutionary algorithms, federated learning, and deep reinforcement learning, these studies have achieved efficient multi-objective optimization, thereby improving network performance and resource utilization.

4.2. Multipath Transmission

In recent years, researchers have been exploring ways to improve transmission security and reliability in heterogeneous network environments. Heterogeneous networks, such as satellite networks, the wired Internet, and mobile communication networks, face numerous challenges in data transmission due to their complex and variable characteristics. Multipath transmission protocols use multiple available paths to meet strict quality of service (QoS) constraints, achieving goals such as low latency while completing reliable transmission [41]. However, the traditional TCP protocol can only achieve single point-to-point transmission, and can only re-establish the connection after encountering threats such as attacks that cause transmission interruption. Therefore, researchers optimized TCP multipath transmission and proposed algorithms such as SCTP [42] and CMT [43] that can transmit the sender’s data concurrently through different paths. However, these algorithms still have problems such as inappropriate packet scheduling, unnecessary packet retransmission, unnecessary congestion window (CWND) reduction, and receiver buffer blocking (RBB) [44]. In order to solve these problems, researchers further optimized the traditional TCP algorithm and proposed MPTCP [45] to use multiple paths to improve the resource utilization of the transmission path. MPTCP can not only transmit data packets through different paths according to different strategies, but also has a congestion control (CC) mechanism to manage network load and avoid congestion.

Okamoto et al. [46] proposed an SCTP extension to mitigate the impact of packet loss in lossy environments and limit redundant data transmission on different paths, thereby minimizing network congestion. Silva et al. [47] proposed a selective redundant multipath transmission (SRMT) strategy that uses the primary path to transmit data and the secondary path to transmit redundant data. Shailendra et al. [48] proposed an efficient SCTP multipath scheme (MPSCTP) that transmits packets on multiple paths simultaneously. MPSCTP solves the problems of packet reordering and invalid CWND growth and improves the efficiency of multipath transmission. MPSCTP was later enhanced to include full path delay, taking into account the data rate on each channel, thereby minimizing block delays on different channels.

Similar to SCTP, MPTCP is a connection-oriented multi-host standard protocol designed to distribute traffic between different routes and provide transparency at the application layer. In MPTCP, a session to be transmitted is usually divided into multiple different data substreams for transmission, and packet loss on different paths can be detected and reordered at the receiving end. Peng et al. [49] further optimized the MPTCP algorithm to address the problem that the system often misjudges random packet loss as congestion loss, and proposed a flow-based transmission model to improve the stability of the transmission system. Cai et al. [50] proposed a packet-differentiated OLIA (D-OLIA) based on packet loss, combining the delay jitter and CWND jitter eigenvalues to determine the type of packet loss, making up for the shortcomings of simply judging by delay or CWND. Oh and Lee [51] proposed a new heterogeneous network multipath transmission algorithm, which uses the MPTCP algorithm and the receiving end buffer scheduling strategy to estimate out-of-order packets and allocate packets accordingly based on the performance differences of each sub-flow, effectively balancing network throughput and delay performance. Wang et al. [52] studied how to minimize data transmission time in time-varying networks. The authors proposed a one-time solver that can solve the MDDT problem in polynomial time and verified the effectiveness of the proposed algorithm. Ouyang et al. [53] proposed an IMPNC transmission scheme to solve the problem of traditional TCP single-path transmission delay in low-orbit satellite networks. The scheme utilizes multiple paths for end-to-end redundant transmission and improves the algorithm to adapt to limited satellite bandwidth resources.

These studies demonstrate that multipath transmission has significant potential to improve network performance and reliability, especially in complex heterogeneous network environments. In conclusion, multi-objective optimization and multipath transmission techniques play a pivotal role in enhancing the security and reliability of network transmission. The multi-objective optimization strategy effectively addresses the actual needs in complex network environments by balancing multiple performance objectives. Furthermore, multipath transmission technology achieves higher data transmission efficiency and network reliability by utilizing multiple available paths. Consequently, we propose a multi-objective optimization multipath transmission algorithm for heterogeneous networks. The objective is to enhance transmission performance and security in heterogeneous network environments, better aligning with the needs of practical applications.

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.