Resource allocation method for optimizing beam-hopping delay and rate of low-orbit satellite

Through the application of low -orbital satellite jumping resources and the application of zebra optimization algorithms, the problem of delay high and insufficient throughput in existing technologies has been solved, and the system delay is reduced and the throughput is improved.

CN119155799BActive Publication Date: 2025-01-28NANJING UNIV OF POSTS & TELECOMM +1
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Patent Information

Application Number
CN202411669990.8
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-11-21
Publication Date
2025-01-28
Estimated Expiration
2044-11-21

AI Technical Summary

Technical Problem

The existing low-orbit satellite beam hopping resource allocation method fails to effectively consider the impact of the channel environment and the limitation requirements of delay, resulting in high system delay and insufficient throughput.

Method used

By dividing satellite coverage into several waves, evaluate the delay sensitivity of each user and calculate the overall weighted delay. Keep time.

Benefits of technology

Effectively reduce the delay of the system, at the same time improve the throughput of the system, adapt to the changes in business needs, and improve the resource utilization rate.

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Abstract

The present invention discloses a resource allocation method for optimizing beam hopping delay and rate of low-orbit satellites, comprising the following steps: according to the service type of the user in the wave position, evaluating the delay sensitivity of each user, and calculating the total weighted delay of the wave position; clustering all wave positions with the total weighted delay and balance of each cluster as the goal; according to the clustering result, establishing a second-order difference objective function as a beam hopping time slot allocation model, and calculating the beam hopping time slot allocated to each beam through the zebra optimization algorithm; according to the time slot allocation result, designing the beam hopping pattern with the maximum single dwell time of the beam as the goal. The present invention provides a resource allocation method for optimizing beam hopping delay and rate of low-orbit satellites, which calculates the total weighted delay of the wave position based on the user level and service type of the user and performs clustering, and obtains the optimal time slot allocation according to the zebra optimization algorithm, thereby reducing the system delay while improving the system throughput.
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Description

Technical Field

[0001] The present invention relates to the field of satellite communication technology, and in particular to a resource allocation method for optimizing beam hopping delay and rate of a low-orbit satellite. Background Art

[0002] Low-orbit satellites are small, light, and fast, but at the same time, their onboard power resources are severely limited, and their coverage area is not fixed, and the channel environment is complex and changeable. In traditional fixed multi-beam technology, the resource loss is large, and the onboard power utilization is low, and on-demand coverage cannot be achieved. With the development of phased array antennas and radio frequency technology, beam hopping technology came into being.

[0003] Beam hopping technology is a technology based on time slicing. It is driven by business needs and only some spot beams are activated at a certain time. Beam hopping technology supports the flexibility and variability of beams, matches non-uniform and time-varying needs with satellite system resources, and improves the bandwidth utilization and power utilization of satellite resources.

[0004] High-orbit satellites are far from the earth, and the round-trip time of signals is long, so the latency requirement is not high. Low-orbit satellites are close to the earth, and the round-trip time of signals is short, so some services have higher latency requirements. For example, voice and video services have high latency requirements, while some services also have higher speed requirements, such as data services, which have higher speed requirements.

[0005] Therefore, how to reduce system latency and improve system throughput at the same time becomes a key issue in resource allocation strategy. Most of the existing low-orbit satellite beam-hopping resource allocation methods adopt a proportional fairness method, which provides system capacity in proportion to the demand of each beam position to improve system throughput. However, in this resource allocation method, the influence of the channel environment and the latency restriction requirements are not taken into account. Therefore, it is necessary to design a resource allocation method for low-orbit satellite beam-hopping latency and rate optimization to achieve the joint optimization of latency and throughput. Summary of the invention

[0006] Purpose of the invention: The purpose of the present invention is to address the deficiencies in the prior art and provide a resource allocation method for low-orbit satellite beam-hopping delay and rate optimization, so as to solve the problem of low-orbit satellite beam-hopping resource allocation under multi-service requirements, thereby reducing system delay while improving system resource utilization and improving system throughput.

[0007] In order to achieve the above object, the present invention provides a resource allocation method for optimizing beam hopping delay and rate of low-orbit satellites, comprising the following steps:

[0008] S1. Divide the coverage area of ​​the satellite into several beam positions according to the radius of the beam, evaluate the delay sensitivity of each user according to the service type of the user in the beam position, and calculate the total weighted delay of the beam position;

[0009] S2, clustering all wave positions with the total weighted delay and balance of each cluster as the goal;

[0010] S3. According to the clustering results, a second-order difference objective function is established as a beam-hopping time slot allocation model, and the beam-hopping time slots allocated to each beam are calculated by using a zebra optimization algorithm;

[0011] S4. According to the time slot allocation result, a beam hopping pattern is designed with the goal of maximizing the single dwell time of the beam.

[0012] A further preferred technical solution of the present invention is that, in step S1, the coverage of the satellite is divided into a number of wave positions according to the radius of the beam, and the delay sensitivity of each user is evaluated according to the service type of the user in the wave position, and the total weighted delay of the wave position is calculated; the specific method is:

[0013] S11, dividing the coverage area of ​​the satellite into a number of beam positions according to the radius of the beam;

[0014] S12: Determine the delay sensitivity according to the service type of each user in the wave position and set the delay sensitivity weight ;

[0015] Delay Sensitive Weight The definition is: For delay-sensitive services, the delay-sensitive weight Set to a value greater than 1. For non-delay-sensitive services, the delay-sensitive weight Set to a value less than 1; the higher the delay sensitivity, The larger the value;

[0016] S13, calculate the Total weighted delay within the wave position , and its calculation formula is:

[0017]

[0018] in, Indicates that it is located at Wavelength users business needs, Indicates that it is located at Wavelength users The average delay in the past, The set of all users in a wave position is .

[0019] Preferably, in step S2, all beam positions are clustered with the total weighted delay and balance of each cluster as the goal; the specific method is:

[0020] S21. Obtain the target value of the total weighted delay of each cluster ;

[0021] S22, select a cluster, traverse each wave position, find the unassigned wave position, calculate the total weighted delay sum of the cluster after adding it to the current cluster and the target value The difference between them is selected, and the wave position with the smallest difference is added to the cluster;

[0022] S23, loop step S22 until the total weighted delay of the cluster is greater than the target value When , the wave position allocation of the cluster is ended;

[0023] S24: For the remaining clusters, repeat steps S22 to S23 to obtain the final clustering result.

[0024] As a preference, in step S21, the target value of the total weighted delay sum of each cluster is obtained. The method is:

[0025] Set The total weighted delay within the wave position is ;

[0026] According to the total weighted delay of each wave position , calculate the target value of the total weighted delay of each cluster , and its calculation formula is:

[0027]

[0028] in is the number of clusters, For the The total weighted delay within the wave position, is the set of all wave positions.

[0029] Preferably, in step S3, according to the clustering result, a second-order difference objective function is established as a beam hopping time slot allocation model, and the beam hopping time slot allocated to each beam is calculated by a zebra optimization algorithm; the specific method is:

[0030] S31. According to the clustering result, a second-order difference objective function is established as a beam hopping time slot allocation model;

[0031] S32. Calculate the beam-hopping time slots allocated to each beam through the zebra optimization algorithm.

[0032] Preferably, the second-order difference objective function established in step S31 is expressed as:

[0033]

[0034]

[0035] in, Indicates Cluster The capacity required for each beam; Indicates that it is provided to Cluster The beam capacity of the beams; Indicates that the Cluster The number of time slots per beam; represents the beam hopping period length; Indicates the number of clusters; Indicates The number of beams in a cluster.

[0036] Preferably, in step S32, the beam hopping time slots allocated to each beam are calculated by using a zebra optimization algorithm, and the specific method is as follows:

[0037] First, randomly initialize the population in the optimization space:

[0038]

[0039] in Indicates Among individuals in a population The number of time slots allocated to each wave position, Indicates The minimum number of time slots allocated to each wave position, Indicates The maximum number of time slots that can be allocated to a wave position, is a random number between 0 and 1;

[0040] Then the zebra foraging strategy and defense strategy are simulated in two stages to update the time slot allocation results of the individuals in the population.

[0041] As a preferred method, the zebra foraging strategy and defense strategy are simulated in two stages to update the time slot allocation results of the population individuals. The specific method is as follows:

[0042] In the first stage, the zebra foraging strategy is simulated. The best member of the population is considered the pioneer zebra and leads other population members to its position in the search space. The position update of the zebra in the foraging stage is mathematically modeled by the following formula:

[0043]

[0044] in represents the population change control parameter, which is a random value from the set {1, 2}. represents the state of the pioneer zebra, which is obtained by calculating the second-order difference objective function value for all individuals in the population, and the individual with the smallest objective function value is The number of time slots allocated to each wave position is , Indicates Among individuals in a population The number of time slots allocated after the wave position is updated, is a random number between 0 and 1;

[0045] If the population individuals Updated time slot allocation results The value calculated by the second-order difference objective function Less than the previous calculated value , then the individuals of the population Updated to Otherwise, the population individuals unchanged, that is:

[0046]

[0047] In the second stage, the defense strategy of zebras against predator attacks is simulated to update the positions of population members in the search space; the defense strategy of zebras varies depending on the predator, and they can either flee or attack, assuming that the two situations occur with the same probability;

[0048] When the zebra adopts the escape strategy, the strategy is modeled by the C1 mode in the following formula; when the zebra adopts the attack strategy, the strategy is modeled by the C2 mode in the following formula;

[0049]

[0050] in Indicates the current iteration number, represents the maximum number of iterations, is expressed as a constant of 0.01, is a random number between 0 and 1, is a random value from the set {1, 2}, represents the switching probability of the two strategies, The state of the attacked zebra is obtained by randomly selecting an individual from the population. The number of time slots allocated to each wave position is ;

[0051] If the population individuals Updated time slot allocation results The value calculated by the second-order difference objective function Less than the previous calculated value , then the individuals of the population Updated to Otherwise, the population individuals unchanged, that is:

[0052]

[0053] Preferably, step S4 performs resource allocation based on the time slot allocation result with the goal of maximizing the single dwell time of the beam, and the specific method is:

[0054] After obtaining the number of time slots allocated to each beam, all beams are arranged in order from largest to smallest according to demand, and time slots are allocated to the beam with the largest demand first. After all hopping beams in the current time slot are allocated, the next time slot is allocated until all time slots are allocated.

[0055] Beneficial effects: The present invention provides a resource allocation method for optimizing the delay and rate of low-orbit satellite beam hopping. The total weighted delay of the beam position is calculated based on the user level and service type of the user and clustered. The optimal time slot allocation is calculated according to the zebra optimization algorithm, which reduces the system delay and improves the system throughput. The simulation results show that compared with the traditional method, the present invention can effectively reduce the system delay and improve the system throughput.

[0056] In addition, the clustering method proposed in the present invention abandons the restriction that the wave positions must be geographically close in the traditional clustering method, making the clustering more flexible and more adaptable to changes in business requirements.

[0057] In the same satellite scenario, the system latency of the beam-hopping resource allocation method optimized by the zebra algorithm is better than that of the traditional method. In the same satellite scenario, the system throughput of the beam-hopping resource allocation method optimized by the zebra algorithm is better than that of the traditional method. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 This is a flow chart of the implementation of the resource allocation method of the present invention.

[0059] Figure 2 4 is a system model diagram of an embodiment of the present invention.

[0060] Figure 3 This is a diagram comparing system delays implemented by the resource allocation method of the present invention.

[0061] Figure 4 This is a diagram comparing system throughputs achieved by the resource allocation method of the present invention. DETAILED DESCRIPTION

[0062] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the drawings in the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments, and they should not be understood as limitations on the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention. In the description of the present invention, it should be understood that the terms used are only for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0063] Combine the following Figure 1-Figure 4 Specific embodiments of the invention are described.

[0064] Embodiment 1: This embodiment provides a resource allocation method for optimizing the delay and rate of beam hopping of low-orbit satellites. This embodiment aims to reduce the system delay while improving the system throughput, which is a key issue in the resource allocation strategy.

[0065] The resource allocation method for optimizing the delay and rate of low-orbit satellite beam hopping includes the following steps:

[0066] S1. Divide the coverage area of ​​the satellite into several beam positions according to the radius of the beam, evaluate the delay sensitivity of each user according to the service type of the user in the beam position, and calculate the total weighted delay of the beam position;

[0067] S2, clustering all wave positions with the total weighted delay and balance of each cluster as the goal;

[0068] S3. According to the clustering results, a second-order difference objective function is established as a beam-hopping time slot allocation model, and the beam-hopping time slots allocated to each beam are calculated by using a zebra optimization algorithm;

[0069] S4. According to the time slot allocation result, a beam hopping pattern is designed with the goal of maximizing the single dwell time of the beam.

[0070] The above-mentioned resource allocation method for optimizing the delay and rate of low-orbit satellite beam hopping calculates the total weighted delay of the beam position based on the user's service type and clusters it, and obtains the optimal time slot allocation according to the zebra optimization algorithm, thereby reducing the system delay and improving the system throughput.

[0071] Specifically, the specific method of step S1 is:

[0072] S11, dividing the coverage area of ​​the satellite into a number of beam positions according to the radius of the beam;

[0073] S12: Determine the delay sensitivity according to the service type of each user in the wave position and set the delay sensitivity weight ;

[0074] Delay Sensitive Weight The definition is: For delay-sensitive services, the delay-sensitive weight Set to a value greater than 1. For non-delay-sensitive services, the delay-sensitive weight Set to a value less than 1; the higher the delay sensitivity, The larger the value;

[0075] S13, calculate the Total weighted delay within the wave position , and its calculation formula is:

[0076]

[0077] in, Indicates that it is located at Wavelength users business needs, Indicates that it is located at Wavelength users The average delay in the past, The set of all users in a wave position is .

[0078] The specific method of step S2 is:

[0079] S21. Obtain the target value of the total weighted delay of each cluster ;

[0080] Set The total weighted delay within the wave position is ;

[0081] According to the total weighted delay of each wave position , calculate the target value of the total weighted delay of each cluster , and its calculation formula is:

[0082]

[0083] in is the number of clusters, For the The total weighted delay within the wave position, is the set of all wave positions;

[0084] S22, select a cluster, traverse each wave position, find the unassigned wave position, calculate the total weighted delay sum of the cluster after adding it to the current cluster and the target value The difference between them is selected, and the wave position with the smallest difference is added to the cluster;

[0085] S23, loop step S22 until the total weighted delay of the cluster is greater than the target value When , the wave position allocation of the cluster is ended;

[0086] S24: For the remaining clusters, repeat steps S22 to S23 to obtain the final clustering result.

[0087] The specific method of step S3 is:

[0088] S31. According to the clustering result, a second-order difference objective function is established as a beam hopping time slot allocation model; the established second-order difference objective function is expressed as:

[0089]

[0090]

[0091] in, Indicates Cluster The capacity required for each beam; Indicates that it is provided to Cluster The beam capacity of the beams; Indicates that the Cluster The number of time slots per beam; represents the beam hopping period length; Indicates the number of clusters; Indicates The number of beams in a cluster.

[0092] S32, calculating the beam hopping time slots allocated to each beam through the zebra optimization algorithm;

[0093] First, randomly initialize the population in the optimization space:

[0094]

[0095] in Indicates Among individuals in a population The number of time slots allocated to each wave position, Indicates The minimum number of time slots allocated to each wave position, Indicates The maximum number of time slots that can be allocated to a wave position, is a random number between 0 and 1;

[0096] Then the zebra foraging strategy and defense strategy are simulated in two stages to update the time slot allocation results of the individuals in the population.

[0097] In the first stage, the zebra foraging strategy is simulated. The best member of the population is considered the pioneer zebra and leads other population members to its position in the search space. The position update of the zebra in the foraging stage is mathematically modeled by the following formula:

[0098]

[0099] in represents the population change control parameter, which is a random value from the set {1, 2}. represents the state of the pioneer zebra, which is obtained by calculating the second-order difference objective function value for all individuals in the population, and the individual with the smallest objective function value is The number of time slots allocated to each wave position is , Indicates Among individuals in a population The number of time slots allocated after the wave position is updated, is a random number between 0 and 1;

[0100] If the population individuals Updated time slot allocation results The value calculated by the second-order difference objective function Less than the previous calculated value , then the individuals of the population Updated to Otherwise, the population individuals unchanged, that is:

[0101]

[0102] In the second stage, the defense strategy of zebras against predator attacks is simulated to update the positions of population members in the search space; the defense strategy of zebras varies depending on the predator, and they can either flee or attack, assuming that the two situations occur with the same probability;

[0103] When the zebra adopts the escape strategy, the strategy is modeled by the C1 mode in the following formula; when the zebra adopts the attack strategy, the strategy is modeled by the C2 mode in the following formula;

[0104]

[0105] in Indicates the current iteration number, represents the maximum number of iterations, is expressed as a constant of 0.01, is a random number between 0 and 1, is a random value from the set {1, 2}, represents the switching probability of the two strategies, The state of the attacked zebra is obtained by randomly selecting an individual from the population. The number of time slots allocated to each wave position is ;

[0106] If the population individuals Updated time slot allocation results The value calculated by the second-order difference objective function Less than the previous calculated value , then the individuals of the population Updated to Otherwise, the population individuals unchanged, that is:

[0107]

[0108] The specific method of step S4 is:

[0109] After obtaining the number of time slots allocated to each beam, all beams are arranged in order from largest to smallest according to demand, and time slots are allocated to the beam with the largest demand first. After all hopping beams in the current time slot are allocated, the next time slot is allocated until all time slots are allocated.

[0110] According to the above method, a simulation experiment is performed in this embodiment:

[0111] like Figure 2 As shown in the figure, in this system model, the LEO satellite altitude is 1175KM and the beam radius is 25KM. All the beam positions are divided into 8 clusters, each cluster includes 8 beam positions, and the time slot window of each cluster is W. Some simulation parameters are shown in the following table:

[0112]

[0113] In order to verify the performance of the present invention, the resource allocation method of this embodiment, method 1: traditional clustering (only looking at the wave number, such as 1-8, 9-16 wave number one cluster) + proportional fairness algorithm, and method 2: load balancing clustering + proportional fairness algorithm, are used to simulate the system delay and system throughput. The simulation results are as follows: Figure 3-Figure 4 shown.

[0114] from Figure 3 It can be seen that the system delay increases with the increase of the number of cycles, and eventually gradually stabilizes. It can be seen that the method proposed in the present invention has a significant reduction in delay compared with the other two methods. Figure 4 It can be seen that the method proposed in the present invention has a significant improvement in the throughput of non-delay-sensitive services compared to the two traditional methods, because these services have higher requirements on the rate and relatively lower requirements on the delay.

[0115] As described above, although the present invention has been shown and described with reference to specific preferred embodiments, it should not be construed as limiting the present invention itself. Various changes in form and details may be made without departing from the spirit and scope of the present invention as defined in the appended claims.

Claims

1. A resource allocation method for optimizing beam hopping delay and rate of low-orbit satellites, characterized in that: The steps include: S1. Divide the coverage of the satellite into several beam positions according to the radius of the beam. According to the service type of the user in the beam position, evaluate the delay sensitivity of each user and calculate the total weighted delay of the beam position. The specific method is: S11, dividing the coverage area of ​​the satellite into a number of beam positions according to the radius of the beam; S12: Determine the delay sensitivity according to the service type of each user in the wave position and set the delay sensitivity weight ; Delay Sensitive Weight The definition is: For delay-sensitive services, the delay-sensitive weight Set to a value greater than 1. For non-delay-sensitive services, the delay-sensitive weight Set to a value less than 1; the higher the delay sensitivity, The larger the value; S13, calculate the Total weighted delay within the wave position , and its calculation formula is: ; in, Indicates that it is located at Wavelength users business needs, Indicates that it is located at Wavelength users The average delay in the past, The set of all users in a wave position is ; S2. Taking the total weighted delay and balance of each cluster as the goal, all the wave positions are clustered; the specific method is: S21. Obtain the target value of the total weighted delay of each cluster ; S22, select a cluster, traverse each wave position, find the unassigned wave position, calculate the total weighted delay sum of the cluster after adding it to the current cluster and the target value The difference between them is selected, and the wave position with the smallest difference is added to the cluster; S23, loop step S22 until the total weighted delay of the cluster is greater than the target value When , the wave position allocation of the cluster is ended; S24, for the remaining clusters, repeat steps S22 to S23 to obtain the final clustering result; S3. According to the clustering results, a second-order difference objective function is established as a beam-hopping time slot allocation model, and the beam-hopping time slot allocated to each beam is calculated by using a zebra optimization algorithm; S4. Designing a beam hopping pattern based on the time slot allocation result and taking the maximum single dwell time of the beam as the goal; After obtaining the number of time slots allocated to each beam, all beams are arranged in order from largest to smallest according to demand, and time slots are allocated to the beam with the largest demand first. After all hopping beams in the current time slot are allocated, the next time slot is allocated until all time slots are allocated.

2. The resource allocation method for optimizing beam hopping delay and rate of low-orbit satellite according to claim 1, characterized in that: In step S21, the target value of the total weighted delay of each cluster is obtained. The method is: Set The total weighted delay within the wave position is ; According to the total weighted delay of each wave position , calculate the target value of the total weighted delay of each cluster , and its calculation formula is: ; in is the number of clusters, For the The total weighted delay within the wave position, is the set of all wave positions.

3. The resource allocation method for optimizing beam hopping delay and rate of low-orbit satellite according to claim 1, characterized in that: In step S3, according to the clustering result, a second-order difference objective function is established as a beam-hopping time slot allocation model, and the beam-hopping time slot allocated to each beam is calculated by the zebra optimization algorithm; the specific method is: S31. According to the clustering result, a second-order difference objective function is established as a beam hopping time slot allocation model; S32. Calculate the beam hopping time slots allocated to each beam through the zebra optimization algorithm.

4. The resource allocation method for optimizing the delay and rate of low-orbit satellite beam hopping according to claim 3, characterized in that: The second-order difference objective function established in step S31 is expressed as: ; ; in, Indicates Cluster The capacity required for each beam; Indicates that it is provided to Cluster The beam capacity of the beams; Indicates that the Cluster The number of time slots per beam; represents the beam hopping period length; Indicates the number of clusters; Indicates The number of beams in a cluster.

5. The resource allocation method for optimizing the delay and rate of low-orbit satellite beam hopping according to claim 4, characterized in that: In step S32, the beam hopping time slots allocated to each beam are calculated by using the zebra optimization algorithm. The specific method is as follows: First, randomly initialize the population in the optimization space: ; in Indicates Among individuals in a population The number of time slots allocated to each wave position, Indicates The minimum number of time slots allocated to each wave position, Indicates The maximum number of time slots that can be allocated to a wave position, is a random number between 0 and 1; Then the zebra foraging strategy and defense strategy are simulated in two stages to update the time slot allocation results of the individuals in the population.

6. The resource allocation method for optimizing beam hopping delay and rate of low-orbit satellite according to claim 5, characterized in that: The zebra foraging strategy and defense strategy are simulated in two stages to update the time slot allocation results of the population individuals. The specific method is as follows: In the first stage, the zebra foraging strategy is simulated. The best member of the population is considered the pioneer zebra and leads other population members to its position in the search space. The position update of the zebra in the foraging stage is mathematically modeled by the following formula: ; in represents the population change control parameter, which is a random value from the set {1, 2}. represents the state of the pioneer zebra, which is obtained by calculating the second-order difference objective function value for all individuals in the population, and the individual with the smallest objective function value is The number of time slots allocated to each wave position is , Indicates Among individuals in a population The number of time slots allocated after the wave position is updated, is a random number between 0 and 1; If the population individuals Updated time slot allocation results The value calculated by the second-order difference objective function Less than the previous calculated value , then the individuals of the population Updated to ; Otherwise, the individuals in the population unchanged, that is: ; In the second stage, the defense strategy of zebras against predator attacks is simulated to update the positions of population members in the search space; the defense strategy of zebras varies depending on the predator, and they can either flee or attack, assuming that the two situations occur with the same probability; When the zebra adopts the escape strategy, the strategy is modeled by the C1 mode in the following formula; when the zebra adopts the attack strategy, the strategy is modeled by the C2 mode in the following formula; ; in Indicates the current iteration number, represents the maximum number of iterations, is expressed as a constant of 0.01, is a random number between 0 and 1, is a random value from the set {1, 2}, represents the switching probability of the two strategies, The state of the attacked zebra is obtained by randomly selecting an individual from the population. The number of time slots allocated to each wave position is ; If the population individuals Updated time slot allocation results The value calculated by the second-order difference objective function Less than the previous calculated value , then the individuals of the population Updated to ; Otherwise, the individuals in the population unchanged, that is: 。

Citation Information

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