Space-air-sea integrated nrmocop method based on pareto optimality

Abstract

The application proposes a space-air-sea integrated NRMOCOP method based on Pareto optimality, solves the problem that the existing space-air-sea integrated communication cannot balance spectrum efficiency, energy efficiency and time delay, and belongs to the field of communication.The application includes establishing a space-air-sea integrated network architecture, including a channel model of a communication link between satellite nodes, aircraft nodes and ship nodes; determining a multi-objective optimization function of spectrum efficiency, energy efficiency and time delay according to the channel model; solving the multi-objective optimization function; adopting a multi-objective evolutionary algorithm to approximate a set of Pareto optimal solutions, proposing an improved non-dominated sorting genetic algorithm INSGA II and a strength Pareto evolutionary algorithm ISPEA II, and obtaining a Pareto optimal set by realizing population initialization, non-dominated sorting and selection, crossover and mutation process under the space-air-sea integrated network.The application balances between solutions and has the ability to find a Pareto optimal solution for the space-air-sea integrated network.

Description

Technical Field

[0001] This invention relates to a Pareto-optimal network route multi-objective combinatorial optimization method (NRMOCOP) for integrated air-space-sea networks, belonging to the field of communications. Background Technology

[0002] The development of terrestrial networks is limited by the construction of terrestrial base stations, which can only cover 6% of the global area. Independent deployment of terrestrial and satellite communication networks cannot provide global, multi-dimensional resource management and continuous service capabilities. Non-terrestrial networks (NTNs) are a crucial technology for new application scenarios such as satellite and airborne communications in 5G networks, marking the future transition from terrestrial to space-based communications. A Space-Air-Sea Integrated Network (SASIN) will be established, consisting of satellite, airborne, and maritime layers, to address maritime network coverage issues. SASIN will become an important component of future 6G networks, providing comprehensive network coverage and large-scale terminal access.

[0003] In SASIN, communication between nodes that are often geographically distant relies on cooperative multi-hop transmission. The goal of multi-hop routing is to select a subset of intermediate nodes to construct a multi-hop path from the source node to the destination node. The design of the routing strategy is one of the most critical factors in SASIN, significantly impacting its multi-hop network performance. Therefore, effective network routing techniques should be designed to ensure optimal performance in terms of spectral efficiency, energy efficiency, and latency. All these metrics can be considered simultaneously, generating a set of Pareto optimal solutions to a multi-objective problem.

[0004] Currently, multi-hop network routing optimization mainly employs single-objective optimization methods. In integrated air-space-sea network communication, data packets transmitted from source to destination will pass through various nodes in space, air, and sea networks with various physical layer channels, thus affecting the spectral efficiency, energy efficiency, and latency of the integrated system. However, these performance indicators are often conflicting. Furthermore, designing effective routing strategies for multi-hop networks with SASIN is challenging. On the one hand, the high dynamic characteristics of nodes such as satellites, aircraft, and ships in SASIN lead to dynamic changes in network topology. On the other hand, channel characteristics such as multipath fading in the network can cause communication links to be unreliable. Summary of the Invention

[0005] To address the problem that existing integrated air-space-sea communication systems cannot balance spectrum efficiency, energy efficiency, and latency, this invention provides a Pareto-optimal multi-objective combined optimization method for integrated air-space-sea network routing.

[0006] The present invention provides a multi-objective combined optimization method for routing in an integrated air-space-sea network based on Pareto optimality, comprising:

[0007] S1. Establish an integrated air-space-sea network architecture, including channel models for communication links between satellite nodes, aircraft nodes, and ship nodes;

[0008] S2. Determine the multi-objective optimization function for spectral efficiency, energy efficiency, and time delay based on the channel model:

[0009]

[0010]

[0011] in, ,

[0012] Indicates link Spectral efficiency, Indicates link Energy efficiency, Indicates link The time delay, Indicates routing, Represents the routing space;

[0013] S3. Solve the multi-objective optimization function:

[0014] Using the integrated air-space-sea network topology as input, a genetic algorithm is employed to find the Pareto optimal solution for the multi-objective optimization function, thereby determining the routes within the integrated air-space-sea network architecture.

[0015] Preferably, S3 includes:

[0016] S31. Using the integrated air-space-sea network topology as input, construct a set of Euclidean space optimum points. , where n represents the number of individuals. arrive Each represents a group of n individuals. This represents the optimal point of Euclidean geometry. , ,Will The population is obtained by mapping to the feasible region where the population resides. , , This indicates the lower bound of the current dimension. This represents the upper limit of the current dimension, and will be applied to the current population. As an initial population;

[0017] S32. Based on the initial population, a genetic algorithm is used to find the Pareto optimal solution for the multi-objective optimization function, and the routing in the integrated air-space-sea network architecture is determined.

[0018] As a preferred method, the method in S32 that uses the Improved Non-dominated Sorting Genetic Algorithm II (INSGA II) to find the Pareto optimal solution for the multi-objective optimization function includes:

[0019] S321. Perform fast non-dominated sorting and calculate the rank of each individual in the initial population.

[0020] S322. Calculate the fitness function value of each individual to determine the dominance relationship between individuals;

[0021] S323. Calculate the virtual crowding distance between each individual and its adjacent peers;

[0022] S324: Perform crossover, mutation, and selection operations based on sort order. And virtual congestion distance The selection process is as follows: individuals with lower ranking rank are preferred; if two individuals have the same ranking rank, the individual with a larger virtual crowding distance is selected. The individual selected from the n individuals is the optimal Pareto solution.

[0023] As a preferred option, in S324, the crossover operator in the crossover operation :

[0024]

[0025] Represents the number of generations in evolution. This represents the minimum value of the crossover operator. Indicates the maximum value of the crossover operator;

[0026] Mutation operators in mutation operations :

[0027]

[0028] This represents the minimum value of the mutation operator. This represents the maximum value of the mutation operator.

[0029] As a preferred embodiment, in S324, the crossover operation is as follows: after selecting two parental chromosomes, a crossover gene is randomly selected from all common genes of the parental chromosomes, and a multi-node crossover method is used to generate offspring chromosomes.

[0030] As a preferred method, the method in S32 that uses the Improved Strength Pareto Evolutionary Algorithm II (ISPEA II) to find the Pareto optimal solution for the multi-objective optimization function includes:

[0031] S321, Set the current population As the initial population; the initial population will be used. Divided into current population and external populations external populations Used to store non-dominated solutions discovered during the search process, while the current population... Used to participate in generative evolution;

[0032] S322, Give the current population and external populations Each individual in Assign an intensity This represents the number and intensity of individuals dominated, based on intensity. Identify individuals Original fitness ;

[0033] S323: Calculate the fitness of an individual Among them, individuals density , , , and They represent and The number of individuals, Represents an individual arrive and The distance between all individuals in the group; Represents an individual It is a non-dominant individual;

[0034] S324: Move the current population and external populations All non-dominant individuals are placed into the outer population of the next generation. middle;

[0035] S325: If End; otherwise proceed to S326.

[0036] S326: If Then the current population and external populations Medium fitness value ranked first The dominant individual is placed Otherwise, proceed to S327;

[0037] S327: If If so, a truncation strategy is adopted to reduce its size;

[0038] S328: After the iteration is completed, the individuals in the external population are the optimal Pareto solutions.

[0039] As a preferred option, in S1, the channel model between aircraft is as follows:

[0040]

[0041] in, The path loss of the channel between aircraft. It is the carrier frequency. It is the distance between the transmitter and the receiver;

[0042] As a preferred option, in S1, the channel model between the aircraft and the ship is as follows:

[0043]

[0044] This refers to the free-space path loss of the channel between aircraft and ships. It refers to the link range. Indicates the minimum link value. It is a constant at the minimum link distance. This represents the path loss index. It is an adjustment factor. Let represent a zero-mean Gaussian random variable with standard deviation, for different directions of travel. ;

[0045] As a preferred embodiment, in S1, the channel model between ships is as follows:

[0046]

[0047] Indicates propagation loss. It's the wavelength. It is the distance between the transmitter and the receiver. This represents the difference between the two ray paths of the transmitter and receiver. It is the reflection coefficient. , and These represent the heights of the transmitter and receiver, respectively. , Indicates the carrier frequency.

[0048] Preferably, in S1, the satellite-to-aircraft channel model is the same as the satellite-to-ship channel model, both being:

[0049]

[0050] Indicates loss, It's the speed of light. It is the distance between the transmitter and the receiver. Indicates the carrier frequency.

[0051] The beneficial effects of this invention are as follows: This invention proposes a multi-objective combined optimization method for network routing in integrated air-space-sea networks. This invention proposes a multi-objective optimization method for Pareto optimal solutions in SASIN, and a Network Routing Multi-Objective Combined Optimization (NRMOCOP) method, simultaneously optimizing multiple end-to-end performance indicators in terms of spectral efficiency, energy efficiency, and latency. This invention establishes a system model for integrated air-space-sea networks, including channel models for communication links between satellites, aircraft, and ships. Furthermore, this invention uses a multi-objective optimization method to design three objective functions: spectral efficiency, energy efficiency, and latency. In addition, this invention employs a multi-objective evolutionary algorithm (MOEA) to approximate the set of Pareto optimal solutions. An improved non-dominated sorting genetic algorithm II (INSGA II) and an improved strength Pareto evolutionary algorithm II (ISPEA II) are proposed, which obtain the Pareto optimal set by implementing population initialization, non-dominated sorting and selection, crossover, and mutation processes under the integrated air-space-sea network. First, an initial population is generated using the Euclidean space optimum set, eliminating the uncertainty caused by random initialization and the problem of uneven spatial distribution of the population. To create new solutions from the existing population, crossover operations and multi-node crossover methods are used. To increase chromosome diversity, a mutation procedure is introduced. After randomly selecting a mutation point, the genes following that point undergo mutation. Chromosomes are sorted using a non-dominant sorting method. In the simulation section, the SASIN network transmission topology is constructed based on real and simulated data. This invention can weigh the trade-offs between solutions and select feasible network routing strategies according to communication requirements, demonstrating that the proposed method has the ability to find Pareto optimal solutions for integrated air-space-sea networks. Attached Figure Description

[0052] Figure 1 It is an integrated air-space-sea network architecture;

[0053] Figure 2 It is an integrated air-space-sea network topology;

[0054] Figure 3 For Pareto optimality and Pareto frontier;

[0055] Figure 4 Initialize the graph for the population;

[0056] Figure 5 A diagram showing the intersection of two points;

[0057] Figure 6 This is a mutation pathway diagram;

[0058] Figure 7 This is a mutation diagram;

[0059] Figure 8 A performance comparison of INSGA II and ISPEA II;

[0060] Figure 9 Pareto frontier obtained for INSGA II;

[0061] Figure 10 Pareto frontier obtained for ISPEA II. Detailed Implementation

[0062] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0063] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0064] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but this is not intended to limit the scope of the invention.

[0065] This implementation method establishes an integrated air-space-sea network architecture consisting of a satellite layer, an airspace layer, and an ocean layer, such as... Figure 1As shown. The air layer consists of aeronautical networks (AANETs) formed by aircraft, capable of exchanging information with the satellite and ocean layers. In space-air-sea communications, data packets transmitted from source to destination are passed through various nodes in space, air, and sea networks with various physical layer channels, thus affecting the latency, spectral efficiency, energy efficiency, and reliability of the integrated system. However, these performance metrics are often conflicting; therefore, this implementation method balances multiple objectives based on MOCOP. Satellites, aircraft, and ships in the system are represented as a set of nodes. This implementation primarily considers modeling under a single satellite beam. Satellites can establish communication links with aircraft and ships via satellite-to-aircraft (S2A) and satellite-to-ship (S2P) channels. Aircraft can communicate with other aircraft and ships via aircraft-to-aircraft (A2A) and aircraft-to-ship (A2P) links. Ships can transmit signals to other ships and aircraft via ship-to-ship (P2P) and ship-to-aircraft (P2A) links. Different links are expected to have different distances and throughputs, and different transceivers have different transmit powers. Therefore, it can be concluded that there are trade-offs between different routing capacities, energy efficiency, and latency. The integrated air-space-sea network topology is as follows: Figure 2 As shown.

[0066] A. Channel Model

[0067] 1) A2A Channel: The path loss of the A2A air traffic channel can be modeled as...

[0068] (1)

[0069] in, It is the carrier frequency. This is the distance between the transmitting and receiving antennas. Furthermore, small-scale fading in the A2A link is modeled with a Rician factor. The decline of the Rician.

[0070] 2) A2P Channel: The A2P channel is modeled, where the free space path loss is given as a single logarithmic distance model, as shown below:

[0071] (2)

[0072] in, It refers to the link range. It is a constant at the minimum effective link distance. This represents the path loss index. It is a small adjustment factor for the direction of travel. It is a zero-mean Gaussian random variable with standard deviation for different directions of travel (orientation and distance). Furthermore, the K-factor of the Rician fading distribution of the A2P link is given as:

[0073] (3)

[0074] 3) P2P Channel: Based on the modified 2-ray model proposed in the model, the propagation loss of the P2P channel can be expressed as:

[0075] (4)

[0076] in, It's the wavelength. and These represent the distance between the transmitter and receiver, and the difference between the two ray paths, respectively. It is the reflection coefficient, where when the roughness is zero, .also, It can be represented as:

[0077] (5)

[0078] in, and It is the height of the transmitter and receiver, in (4), It can be expressed as a function of frequency.

[0079] (6)

[0080] in, The frequency is measured in GHz. Similar to the link above, the P2P channel can be modeled as a Rician fading channel.

[0081] The P2A channel model is the same as the A2P channel model;

[0082] 4) S2A and S2P channels: The propagation of S2A and S2P channels can be represented as:

[0083] (7)

[0084] in, It's the speed of light. It is the distance between the transmitter and the receiver. Indicates frequency.

[0085] B. Problem Formulation

[0086] 1) Spectral efficiency

[0087] link The spectral efficiency can be expressed as:

[0088] (8)

[0089] in, Represents a node The transmission power, and These are nodes and The gain of the transmit or receive antenna at the node. Represents a node and Channels between nodes This indicates channel noise. Composed of propagation fading, and due to the use of decoding and forward schemes, the spectral efficiency of each link is independent. Therefore, maximizing the minimum spectral efficiency of network routing is:

[0090] (9)

[0091] 2) Energy efficiency: Link Energy efficiency can be expressed as:

[0092] (10)

[0093] Similar to spectral efficiency, this implementation maximizes the minimum energy efficiency of a route, which can be expressed as:

[0094] (11)

[0095] 3) Delay:

[0096] In this section, total latency includes propagation latency related to link distance. Transmission delay determined by packet size and link capacity and latency dependency The objective function for time delay can be expressed as:

[0097] (12)

[0098] in Indicates whether to select a link in the route. .

[0099] In summary, the three objective functions cannot simultaneously achieve their target values; therefore, it is difficult to obtain a route with maximum spectral efficiency, energy efficiency, and minimum latency. This implementation uses a multi-objective optimization method to solve this problem:

[0100] (13)

[0101] (14)

[0102] in Let N represent the route and N represent the route space. To address the optimization problem, this implementation method will... Transform into:

[0103] (15)

[0104] (16)

[0105] in:

[0106] (17)

[0107] C. Solution method proposed in this embodiment

[0108] To obtain the optimal solution, Pareto optimization is used. This implementation uses a graph to describe Pareto dominance and Pareto front as follows.

[0109] (1) A multi-objective combined optimization method for network routing based on Pareto optimality

[0110] Given a decision vector The value of the objective function can be expressed as Due to the conflicting nature of the objective functions, it is rare for the global optimum of all individual objective functions to simultaneously occur at a single point. Therefore, this implementation finds a set of trade-off solutions. Although the solution Of all the goals, none is more important than the solution. Poor, and the solution Strictly superior to the solution in at least one objective. However, this implementation defines a solution. leading This means the solution Superior Solution If there is no better solution This means that for all feasible solutions, there is no solution that can improve certain target performance without degrading other performance aspects. Therefore, this implementation will... Defined as Pareto optimization, and the solutions contained in the Pareto optimal set are called non-dominated solutions. The objective function value of a non-dominated solution is the Pareto front, such as... Figure 3 As shown.

[0111] (2) INSGA II and ISPEA II algorithms

[0112] In this section, this implementation proposes the INSGA II and ISPEA II algorithms based on the NSGA II and SPEA II methods to solve the NRMOCOP problem.

[0113] I. INSGA II Algorithm Based on Network Topology

[0114] Using the air-space-sea network topology as input, an INSGA II algorithm based on network topology is proposed to achieve multi-objective optimization.

[0115] Step 1: First, population initialization is performed. The traditional SPEA-II algorithm uses random generation for population initialization. Randomness represents uncertainty, and a randomly generated population exhibits uneven distribution across the entire space. To eliminate the uncertainty and uneven spatial distribution of the population caused by random initialization, this implementation introduces a new population initialization method: defining a dimension of... Euclidean geometry ,and ,So . Indicates the number of individuals. This represents the optimal set of European-style spaces. This represents the optimal point of Euclidean geometry. , Constructing the optimal set of European-style spaces ,Will The population is obtained by mapping to the feasible region where the population resides. , , This indicates the lower bound of the current dimension. This represents the upper limit of the current dimension, and will be applied to the current population. As an initial population;

[0116] Step 2: Perform quick non-dominated sorting and calculate the rank of each individual. .

[0117] Step 3: Calculate the fitness function value of each individual, and determine the individual's fitness function value. With individuals The relationship of dominance between them.

[0118] Step 4: Virtual congestion distance The calculation of virtual crowding. To maintain population diversity and prevent premature maturation, INSGA-II proposed the concept of "virtual fitness." This refers to the solution Two adjacent solutions of the same level and The crowding distance between them. Represent each solution in the target space with a point, the solution... crowded distance This is the sum of the lengths of the long and short sides of the dashed rectangle. This technique can automatically adjust niches to ensure that the solution set is evenly distributed in the target space, preventing "clustering" and guaranteeing global optimization of the algorithm.

[0119] Step 5: Crossover. A crossover operation is used to create a new solution from an existing population defined as offspring. This implementation employs a multi-node crossover method. After selecting two parental chromosomes, a crossover gene is randomly selected from all common genes on the parental chromosomes. The crossover operation is as follows: Figure 5 As shown. Among them and It is a cross-gene, and this implementation method will and Chromosomes are exchanged to produce offspring.

[0120] Step 6: Mutation. Mutations are introduced to increase chromosome diversity. For example... Figure 6 As shown, after randomly selecting a mutation point, the gene following that mutation point mutates. Note that mutations can introduce illegal paths that do not satisfy the network topology; therefore, this implementation requires replacing illegal paths (i.e., paths consisting of unconnected nodes and nodes considered multiple times).

[0121] Step 7: Selection Operation. The main goal of selection is to choose chromosomes with better performance and diversity. Its function is equivalent to the gradient vector, ensuring the algorithm iterates towards the Pareto optimal solution. Based on sorting... and crowding distance The selection method is as follows: when ,or and Then the individual Superior to individuals ,choose In other words: priority selection The smaller individual; if two individuals If they are the same, then select. Larger individuals are those that are sparsely distributed around them. The selection mechanism shows that the principle of non-dominated selection is based on dominance relationships and crowding levels; that is, selecting individuals that are significantly better for the objective and also for the algorithm's convergence. The individual selected from among n individuals is the optimal Pareto solution.

[0122] II. ISPEA II Algorithm Based on Network Topology

[0123] Using air-space-sea network topology as input, this paper proposes the ISPEA II algorithm based on network topology to achieve multi-objective optimization. The proposed ISPEA II adopts a fine-grained assignment strategy and incorporates density information.

[0124] Step 1: First, population initialization is performed. The traditional SPEA-II algorithm uses random generation for population initialization. Randomness represents uncertainty, and a randomly generated population exhibits uneven distribution across the entire space. To eliminate the uncertainty and uneven spatial distribution of the population caused by random initialization, this implementation introduces a new population initialization method: defining a dimension of... Euclidean geometry ,and ,So . Indicates the number of individuals. This represents the optimal set of European-style spaces. This represents the optimal point of Euclidean geometry. , Constructing the optimal set of European-style spaces ,Will The population is obtained by mapping to the feasible region where the population resides. , , This indicates the lower bound of the current dimension. This represents the upper limit of the current dimension, and will be applied to the current population. As the initial population; the initial population will be used. Divided into current population and external populations external populations Used to store non-dominated solutions discovered during the search process, while the current population... Used to participate in generative evolution;

[0125] Step 2: Before calculating the fitness of individuals, the ISPEA II algorithm first assigns a fitness value to the current population. and external populations Each individual in Assign an intensity This represents the number and intensity of the individuals it controls, according to... Value, Individual Original fitness Defined as , Indicates Pareto dominance. The smaller the value, the more individual the value. The more individuals it controls.

[0126] Step 3: However, when most individuals have the same initial fitness, Pareto dominance becomes difficult to determine. Therefore, it is necessary to introduce information on crowding levels between individuals to further distinguish differences. ISPEA II uses the k-nearest neighbor method to assess density among individuals. Each individual... arrive and Distances to all other individuals are sorted in ascending order. The density estimation formula defined by the k-th nearest neighbor method is as follows: Under normal circumstances ,in and They represent and The number of individuals, then individuals density Defined as ,but ,individual Fitness is expressed as: , Represents an individual It is a non-dominant individual.

[0127] Step 4: Execute the environmental selection strategy, which is carried out when generating a new generation of population, to select the current population. and external populations Which individuals are preserved in the next generation of external populations? Go to the middle. First, put the population... and external populations All non-dominant individuals are placed into the outer population of the next generation. In the middle, there is .

[0128] Step 5: Set the size of the external population to... ,like If the environment selection process ends, proceed to step 6; otherwise, proceed to step 6.

[0129] Step 6: If Then and Medium fitness value ranked first The dominant individual is placed If not, proceed to step 7.

[0130] Step 7: If If so, a truncation strategy is adopted to reduce its size.

[0131] After the iteration is complete, the individuals in the external population are the optimal Pareto solutions.

[0132] The proposed ISPEA II algorithm based on network topology can obtain a high diversity of non-dominated solution sets, and has a good advantage in solving high-dimensional multi-objective optimization problems in integrated air-space-sea networks.

[0133] Figure 7 Displays the positions of aircraft and ships based on real-world data, where the ship's altitude is... Randomly generated within the specified area. System simulation parameters are shown in Table 1. The maximum communication distance between nodes is defined.

[0134] Table 1 System Simulation Parameters

[0135] Simulation parameters numerical values Side length of the square region 2000 Number of aircraft nodes 10 Number of satellite nodes 1 Number of ship nodes 10 Maximum communication distance between aircraft 2000 Maximum communication distance between ships 2000 Maximum communication distance between aircraft and ships 2100 Satellite altitude 35786 Aircraft altitude 2000 Ship height 2 Launch power of each satellite 60dBm The transmission power of each aircraft 40dBm The launch power of each ship 40dBm Number of iterations 500

[0136] Given a network transmission topology, the INSGA II and ISPEA II algorithms are used to find solutions to multi-objective problems.

[0137] Figure 8 A performance comparison of the two algorithms is presented. It can be seen that the INSGA II and ISPEA II algorithms provide optimized routes with different performance levels. However, it is difficult to say which solution is the best. For example, the INSGA II algorithm finds a solution with high spectral efficiency and low latency but low energy efficiency, while the ISPEA II algorithm provides a solution with higher spectral efficiency and energy efficiency but higher latency. The difference in simulation results between the two algorithms is due to their different mutation and selection methods, resulting in different chromosomes in the parents and offspring. However, the ISPEA II algorithm tends to find solutions with lower latency.

[0138] exist Figure 9 This implementation presents the three-dimensional Pareto front of the INSGA II algorithm, with network routing performance also shown in the figure. It exhibits the highest energy efficiency. The solution also has the highest latency of 307.1 ms, while the solution with the best latency performance has the worst spectral efficiency performance, at only 0.2486 bps / Hz.

[0139] and Figure 9 Similarly, this implementation method Figure 10 Simulation results for the Pareto front in ISPEA II are presented, showing that the solution with the best energy efficiency has the largest delay, while the solution with the best delay performance has the lowest energy efficiency. This implementation allows for the selection of feasible routing schemes based on communication requirements.

[0140] Simulation results show that NSGAINSGA II finds a solution with high spectral efficiency and low latency but low energy efficiency, while ISPEA II provides a solution with higher energy efficiency and spectral efficiency but higher latency. The difference in simulation results between the two algorithms is due to different mutation and selection methods, resulting in different chromosomes in the parents and offspring. This implementation allows for trade-offs between solutions, but it cannot find a solution with optimal energy efficiency, spectral efficiency, and latency performance. Therefore, this implementation can select feasible routes based on communication requirements, i.e., latency-tolerant or energy-tolerant networks.

[0141] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A space-air-sea integrated NRMOCOP method based on Pareto optimality, characterized in that, The method comprises; S1, establishing a space-sea-air integrated network architecture, including a channel model of a communication link between a satellite node, an aircraft node and a ship node; S2, determining a multi-objective optimization function of spectrum efficiency, energy efficiency and time delay according to the channel model: min [f1, f2, f3] wherein C i→j Indicates link l i,j Spectral efficiency, E i→j Indicates link l i,j Energy efficiency, D i→j Indicates link l i,j The time delay, N represents the route, and N represents the route space; S3, solving the multi-objective optimization function: Taking the space-sea-air integrated network topology as input, a genetic algorithm is used to solve the Pareto optimal solution of the multi-objective optimization function to determine the route in the space-sea-air integrated network architecture; In S1, the channel model between the aircraft and the ship is: L A2P R1 is the link range, R min denotes the minimum link value, A0 is a constant at the minimum link distance, n A denotes the path loss exponent, F A is an adjustment factor, X A denotes a zero-mean Gaussian random variable with standard deviation, for different directions of travel, In S1, the channel model between the ship and the ship is: L 2-ray represents the propagation loss, λ is the wavelength, d is the distance between the transmitter and the receiver, Δd represents the difference between the 2-ray paths of the transmitter and the receiver, R2 is the reflection coefficient, h t and h r respectively represent the height of the transmitter and the receiver, α = 1.019exp(-0.06256f) + 0.06982, f representing the carrier frequency; S3 includes: S31. Using the integrated air-space-sea network topology as input, construct the Euclidean space optimum set Q. n =(k1i1,k2i2,...,k n i n ), where n represents the number of individuals, i1 to i n Let each represent n individuals, and k represent k. i k represents the optimal point in Euclidean geometry. i =2cos(2πi / 7), i=1,2,...,N, change Q n Mapping to the feasible region of the population yields the current population P. s P s =a j +Q n (b j -a j ), a j b represents the lower bound of the current dimension. j This represents the upper limit of the current dimension, and sets the current population P. s As an initial population; S32, according to the initialized population, a genetic algorithm is used to solve the Pareto optimal solution of the multi-objective optimization function to determine the route in the space-sea-air integrated network architecture; The S32 includes: S321, Set the current population P s As the initial population; the initial population P is used as the initial population. s Divided into the current population P t and external population E t External population E t Used to store non-dominated solutions discovered during the search process, while the current population P t Used to participate in generative evolution; S322, give the current population P t and each individual i in the external population E t is given a strength S(i) representing the number of individuals dominated and the strength, and according to the strength S(i), the original fitness R(i) of the individual i is determined; S323: Calculate the fitness of individual F(i) = R(i) + D(i), where the density of individual i N and M represent the number of P t and E t individuals, respectively, d k (i) represents the distance of individual i to all individuals in P t and E t ; F(i) < 1 indicates that individual i is a non-dominated individual; S324: put the current population P t and the external population E t into the external population E t+1 of the next generation; S325: If |E t+1 | = M, end, else go to S326; S326: If E t+1 <M, then put the M-E t dominant individuals with the highest fitness values in the current population P t and the external population E t+1 into E t+1 , otherwise, go to S327; S327: If E t+1 > M, then adopt a truncation strategy to reduce its size; S328: After the iteration is completed, the individuals in the external population are the optimal Pareto solutions.

2. The space-air-sea integrated NRMOCOP method based on Pareto optimality according to claim 1, characterized in that, The S32 includes: S321, performing fast non-dominated sorting to calculate the sorting level of each individual in the initialized population; S322, calculating the fitness function value of each individual to determine the dominance relationship between the individuals; S323, calculating the virtual crowding distance between each individual and the adjacent individuals of the same level; S324: cross operation, mutation operation, selection operation, based on ranking level i rank and virtual crowded distance i d Selection: prefer to select the individual with smaller ranking level; if the ranking levels of two individuals are same, select the individual with larger virtual crowded distance, the selected individual in n individuals is the optimal Pareto solution.

3. The space-air-sea integrated NRMOCOP method based on Pareto optimality according to claim 2, characterized in that, In S324, the crossover operator P in the crossover operation c (i): P c (i) = minP c +(maxP c -minP c )*i / Gen Gen represents the evolution number, minP c represents the minimum value of the crossover operator, maxP c represents the maximum value of the crossover operator; Mutation operator P in the mutation operation m (i): P m (i) = minP m +(maxP m -minP m )*i / Gen minP m denotes the minimum value of the mutation operator, maxP m denotes the maximum value of the mutation operator.

4. The space-air-sea integrated NRMOCOP method based on Pareto optimality according to claim 3, characterized in that, In S324, the crossover operation is: after selecting two parent chromosomes, a crossover gene is randomly selected in all common genes of the parent chromosomes, and a multi-node crossover method is used to generate offspring chromosomes.

5. The Pareto-optimal based space-sea-air integrated NRMOCOP method according to claim 1, wherein, In S1, the channel model between the aircraft and the aircraft is: L A2A [dB] = -145.06 + 20 log 10 (f) + 20 log 10 (d) where L A2A [dB] is the path loss of the channel between aircraft and aircraft, f is the carrier frequency, and d is the distance between the transmitter and the receiver.

6. The space-air-sea integrated NRMOCOP method based on Pareto optimality according to claim 1, characterized in that, In S1, the channel model of the satellite to the aircraft is the same as the channel model of the satellite to the ship, both of which are: L represents the loss, c is the speed of light, d is the distance between the transmitter and the receiver, and f represents the carrier frequency.

Images