Unmanned aerial vehicle network routing method under spectrum denial based on low earth orbit satellite cooperation

By introducing low-orbit satellites and simulated annealing algorithms into the UAV network, the problem of UAV network communication quality degradation under spectrum interference is solved, efficient communication path planning and bandwidth allocation are achieved, and the communication of the UAV network is improved. Quality and suitability.

CN119316903AActive Publication Date: 2025-01-14NANJING UNIV OF AERONAUTICS & ASTRONAUTICS

Patent Information

Application Number
CN202411310401.7
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-09-19
Publication Date
2025-01-14
Estimated Expiration
2044-09-19

AI Technical Summary

Technical Problem

In the environment of spectrum interference, the quality of the communication link of the drone network declines, resulting in delays or interruptions in data transmission, affecting the navigation and mission execution of the drone. The existing technology has high hardware requirements and long solution time when dealing with strong interference. and the local optimal solution problem.

Method used

Low-orbit satellites are used as auxiliary communication nodes for UAV networks, and simulated annealing algorithms are used to plan communication paths and rationally allocate network bandwidth resources to achieve reliable routing under spectrum interference.

Benefits of technology

It effectively improves the communication quality of the UAV network, avoids the long solution time of the precise algorithm and the local optimal solution problem of the traditional path search algorithm, and can obtain an approximate solution in a short time, which is suitable for large-scale UAV networks.

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Abstract

The invention discloses an unmanned aerial vehicle network routing method under spectrum rejection based on low-orbit satellite collaboration, which aims at the problem of unmanned aerial vehicle communication under spectrum interference, introduces low-orbit satellites as auxiliary communication nodes of an unmanned aerial vehicle network, and formulates a routing scheme by using a network controller. Specifically, a network controller firstly formulates an initial routing scheme for all data streams based on global network information, including calculation of a transmission path and distribution of network bandwidth, and evaluates the performance of the routing scheme, and then continuously iteratively optimizes to explore a better solution on the basis of the initial routing scheme by using a simulated annealing framework. The method has the advantages that the problem that the solution time of an accurate algorithm is too long is avoided, the problem that a traditional path search algorithm is prone to falling into a local optimal solution is also avoided, and an approximate solution can be obtained within a short time.
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Description

Technical Field

[0001] The present invention relates to the field of UAV network routing under spectrum denial, and in particular to a UAV network routing method under spectrum denial based on low-orbit satellite collaboration. Background Art

[0002] Drones have been widely used in all walks of life due to their advantages such as high flexibility, rapid response and strong environmental adaptability. Drone network is a special wireless self-organizing network. Through communication and information exchange between multiple drones, they can play the advantages of the group, cooperate with each other and complete more functions. In the military field, drones can perform military tasks such as tactical reconnaissance, situational awareness, long-range strikes, and communication relays, and their position in the weapon and equipment system is becoming increasingly prominent. In recent years, the US military has successively issued a number of regulations in the field of electromagnetic spectrum, raising the construction of electromagnetic spectrum operations to the strategic level and promoting it to become the "sixth combat domain" on par with land, sea, air, space and network. Spectrum interference is an inevitable threat that drone networks will encounter in future battlefields. Interference signals will reduce the quality of drone communication links, resulting in data transmission delays or interruptions, or affect the navigation system of drones, causing them to lose their positioning capabilities and deviate from the scheduled route of the mission, reducing the battlefield effectiveness of drones and affecting intelligence acquisition and combat operations.

[0003] One of the main strategies for dealing with interference is cognitive radio technology. UAVs can avoid interference sources by dynamically sensing the radio environment and adjusting communication parameters according to environmental changes. The core of this technology is adaptive capability, which allows UAVs to ensure the stability of communication links in complex electromagnetic environments. Another strategy is trajectory planning technology, which optimizes the flight path of UAVs based on geographic information and real-time environmental data, avoids known or possible interference areas, and improves the success rate of missions. For UAV clusters, nodes that cannot communicate can be discarded, and the remaining nodes can be reorganized to form a formation, and the network can be quickly restored using the autonomy and coordination capabilities of UAVs. The above two strategies have certain limitations in practical applications: 1) Cognitive radio technology relies on efficient spectrum sensing algorithms and fast spectrum switching capabilities, and has high requirements for the hardware and computing power of UAVs. At the same time, due to limited spectrum resources, it may still be restricted in a strong interference environment, and it is difficult to find an uninterrupted frequency band for communication. 2) In the case of frequent changes in enemy interference, UAVs may not be able to adjust their positions in time, and the effect of trajectory planning will be limited. In addition, moving UAVs to restore network connectivity may conflict with the original mission and have a negative impact on the combat plan.

[0004] The rapid development of low-orbit satellites has brought new development opportunities for drones. Low-orbit satellites have the advantages of low link loss and short transmission delay, and they perform outstandingly in terms of anti-interference ability and communication stability, and can assist drone networks in communicating under spectrum interference. Therefore, the present invention introduces low-orbit satellites as auxiliary communication nodes for drone networks, designs a drone network routing method under spectrum denial based on low-orbit satellite collaboration, and uses a simulated annealing algorithm to plan communication paths and reasonably allocate network bandwidth resources, effectively improving the communication quality of the system. In particular, for large-scale drone networks, this method not only avoids the problem of long solution time for precise algorithms, but also avoids the problem that traditional path search algorithms are prone to falling into local optimal solutions. It can obtain an approximate solution in a short time, which has practical significance and good application scenarios. Summary of the invention

[0005] Purpose of the invention: In view of the above-mentioned deficiencies in the prior art, the present invention uses low-orbit satellites as auxiliary communication nodes of the UAV network, provides a UAV network routing method under spectrum denial based on low-orbit satellite collaboration, realizes reliable routing between UAVs under spectrum interference, and improves communication quality.

[0006] Technical solution: A UAV network routing method under spectrum denial based on low-orbit satellite collaboration, characterized in that it includes a network controller, a low-orbit satellite, and a UAV network. The UAV network consists of multiple master UAVs and slave UAVs. Each master UAV is equipped with a satellite communication module, which can communicate with the low-orbit satellite in two directions. All UAVs can communicate with neighboring UAVs without interference. The network controller can control all UAVs and, after being interfered with by the spectrum, decide the routing of the entire network based on the global network information and formulate a transmission plan for all data streams in the network. Specifically, the following steps are included:

[0007] (1) The network controller obtains global network information: The network controller interacts with the UAV to obtain information such as the UAV’s location, interference conditions, and data streams to be transmitted in the network;

[0008] (2) Formulate an initial routing plan: Based on the global network information, the network controller first calculates the transmission path for all data flows, then allocates network bandwidth to obtain the initial routing plan for the data flow;

[0009] (3) Evaluate the performance of the initial routing solution: The network controller evaluates the latency performance and network bandwidth performance of all data flows respectively, calculates the routing performance of the data flows in combination with the weight adjustment parameters, and then evaluates the comprehensive routing performance of the initial routing solution;

[0010] (4) Optimizing routing scheme: Based on the simulated annealing framework, the network controller iteratively optimizes the path selection and network bandwidth allocation of the initial routing scheme until the termination condition is met to obtain the final routing scheme.

[0011] Furthermore, the detailed steps of formulating the initial routing plan in step (2) are:

[0012] (2.1) For all data flows, the Dijkstra algorithm is used to calculate the shortest delay path from its starting point to its end point as the transmission path.

[0013] (2.2) Since several data flows may pass through the same node, and different data flows have different requirements for network bandwidth, the network controller needs to allocate network bandwidth for the data flows. For any two nodes u and v, define C(u, v) as the upper limit of the network bandwidth between u and v. When there is only one data flow forwarded from node u to node v, if C(u, v) is greater than the demand of the data flow, the network bandwidth allocated to the data flow is equal to its demand, otherwise C(u, v) is allocated to the data flow. When there are multiple data flows forwarded from node u to node v, if C(u, v) is greater than the sum of the network bandwidth requirements of these data flows, the network bandwidth allocated to each data flow is equal to the network bandwidth requirement of the data flow; otherwise, C(u, v) is allocated to these data flows in proportion to the network bandwidth requirements of these data flows. After calculating the network bandwidth allocation plan for all nodes, the actual available network bandwidth of the data flow is equal to the minimum value of the network bandwidth allocated to it by all nodes on its path.

[0014] Furthermore, the detailed steps of evaluating the performance of the initial routing solution in step (3) are as follows:

[0015] (3.1) For any data flow F in the network i , its delay performance S(h i ) is evaluated and expressed as:

[0016]

[0017] where h i Represents data flow F i The end-to-end delay, D i Represents F i exp represents the exponential function with the natural constant e as the base.

[0018] (3.2) For any data flow F in the network i , its network bandwidth performance S(f i ) is evaluated and expressed as:

[0019]

[0020] Among them, R i Represents data flow F iThe network bandwidth required.

[0021] (3.3) Since different data flows have different requirements for latency and network bandwidth, for any data flow F in the network i , its routing performance S(f i ) is equal to the delay performance S(h i ) and network bandwidth performance S(f i ), expressed as:

[0022] S i =λ i S(h i )+(1-λ i )S(f i )

[0023] Among them, λ i Represents data flow F i The weight adjustment parameter.

[0024] (3.4) Based on the routing performance of each data flow, the comprehensive routing performance S of the initial routing scheme is evaluated, where S is the sum of the routing performance of all data flows.

[0025] Furthermore, the detailed steps of route optimization in step (4) are:

[0026] (4.1) Set the initial temperature, end temperature, cooling coefficient, and maximum number of cycles of simulated annealing, and set the current temperature equal to the initial temperature;

[0027] (4.2) Based on the current routing plan, generate a new routing plan by following the steps below:

[0028] (4.2.1) Randomly select a data stream F m , whose transmission path is p m , the starting point and the end point are s m and t m . Construct an intermediate node set, including all nodes that meet the following conditions: the node and s m is connected; the node and t m is connected; the node is not in p m superior.

[0029] (4.2.2) Randomly select a node n in the intermediate node set and use Dijkstra's algorithm to calculate the m The shortest delay path p to node n n1 and nodes n to t m The shortest delay path p n2 , p n1 and p n2 Merge to get a new path

[0030] (4.2.3) According to the network bandwidth allocation plan in step (2.2), reallocate the network bandwidth for all data flows to obtain a new routing plan.

[0031] (4.3) According to the performance evaluation method of step (3), the performance of the new routing solution is evaluated, and the Metropolis acceptance criterion is used to determine whether to accept the new routing solution. If the comprehensive routing performance of the new routing solution is greater than the comprehensive routing performance of the current routing solution, the new routing solution is accepted; otherwise, the new routing solution is rejected with probability p. accept Accept the new route:

[0032]

[0033] Among them, exp represents the exponential function with the natural constant e as the base, S new represents the comprehensive routing performance of the new routing solution, S temp represents the comprehensive routing performance of the current routing scheme, and T represents the current temperature of the simulated annealing system.

[0034] (4.4) If the number of cycles at the current temperature reaches the maximum number of cycles, multiply the current temperature by the temperature reduction coefficient to update the value of the current temperature and jump to step (4.5), otherwise return to step (4.2);

[0035] (4.5) If the current temperature is less than the termination temperature, end the loop and output the current routing plan as the optimal routing plan, otherwise return to step (4.2).

[0036] Beneficial effects: The spectrum denial UAV network routing method designed by the present invention based on low-orbit satellite collaboration uses low-orbit satellites as auxiliary communication nodes of the UAV network, and effectively improves the communication quality of the system by planning communication paths and reasonably allocating network bandwidth resources. In particular, for large-scale UAV networks, this method not only avoids the problem of long solution time of the precise algorithm, but also avoids the problem that the traditional path search algorithm is prone to fall into the local optimal solution, and can obtain an approximate solution in a short time. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a flow chart of the present invention.

[0038] Figure 2 The figure is a comparison chart of the comprehensive routing performance simulation results of each algorithm in a low-load scenario.

[0039] Figure 3 The figure is a comparison chart of the average delay performance simulation results of each algorithm in a low-load scenario.

[0040] Figure 4The following is a comparison chart of the average network bandwidth performance simulation results of each algorithm in a low-load scenario.

[0041] Figure 5 The figure is a comparison chart of the comprehensive routing performance simulation results of each algorithm under high-load scenarios.

[0042] Figure 6 The figure below is a comparison chart of the average delay performance simulation results of each algorithm under high load scenarios.

[0043] Figure 7 The following is a comparison chart of the average network bandwidth performance simulation results of each algorithm under high-load scenarios. DETAILED DESCRIPTION

[0044] The present invention is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0045] A method for UAV network routing under spectrum denial based on low-orbit satellite collaboration includes a network controller, a low-orbit satellite, and a UAV network. The UAV network consists of multiple master UAVs and slave UAVs that can move freely. Each master UAV is equipped with a satellite communication module that can communicate with the low-orbit satellite in both directions. All UAVs can communicate with neighboring UAVs without interference, and the network controller can control all UAVs. There are multiple data streams in the network. After being interfered with by the spectrum, the transmission of the data stream is affected. The network controller can decide the routing of the entire network based on the global network information, and plan the transmission path selection and network bandwidth allocation of the data stream. Figure 1 As shown in the figure, the specific implementation steps of routing decision are as follows:

[0046] 1. The network controller interacts with the drone to obtain global network information, including the drone’s location, interference conditions, and data streams to be transmitted in the network.

[0047] 2. Based on the global network information, the network controller develops an initial routing plan for all data flows, including calculating the transmission path and allocating network bandwidth.

[0048] 2.1 For all data flows, use the Dijkstra algorithm to calculate the shortest delay path from its starting point to the end point as the transmission path.

[0049] 2.2 Since several data flows may pass through the same node, and different data flows have different requirements for network bandwidth, the network controller needs to allocate network bandwidth for the data flows. For any two nodes u and v, define C(u,v) as the upper limit of the network bandwidth between u and v. When there is only one data flow forwarded from node u to node v, if C(u,v) is greater than the demand of the data flow, the network bandwidth allocated to the data flow is equal to its demand, otherwise C(u,v) is allocated to the data flow. When there are multiple data flows forwarded from node u to node v, if C(u,v) is greater than the sum of the network bandwidth requirements of these data flows, the network bandwidth allocated to each data flow is equal to the network bandwidth requirement of the data flow; otherwise, C(u,v) is allocated to these data flows in proportion to the network bandwidth requirements of these data flows. After calculating the network bandwidth allocation plan for all nodes, the actual available network bandwidth of the data flow is equal to the minimum value of the network bandwidth allocated to it by all nodes on its path.

[0050] 3. The network controller evaluates the performance of the initial routing solution.

[0051] 3.1 For any data flow F in the network i , its delay performance S(h i ) is evaluated and expressed as:

[0052]

[0053] where h i Represents data flow F i The end-to-end delay, D i Represents F i exp represents the exponential function with the natural constant e as the base.

[0054] 3.2 For any data flow F in the network i , its network bandwidth performance S(f i ) is evaluated and expressed as:

[0055]

[0056] Among them, R i Represents data flow F i The network bandwidth required.

[0057] 3.3 Since different data flows have different requirements for latency and network bandwidth, for any data flow F in the network i , its routing performance S(f i ) is equal to the delay performance S(h i ) and network bandwidth performance S(f i ), expressed as:

[0058] S i =λ i S(h i )+(1-λ i )S(f i )

[0059] Among them, λ i Represents data flow F i The weight adjustment parameter.

[0060] 3.4 Based on the routing performance of each data flow, the comprehensive routing performance S of the initial routing solution is evaluated, where S is the sum of the routing performance of all data flows.

[0061] 4. The network controller uses the simulated annealing framework to iteratively optimize the initial routing plan and generate the final routing plan.

[0062] 4.1 Set the initial temperature, end temperature, cooling coefficient, and maximum number of cycles of simulated annealing, and set the current temperature equal to the initial temperature.

[0063] 4.2 Based on the current routing plan, generate a new routing plan by following the steps below:

[0064] 4.2.1 Randomly select a data stream F m , whose transmission path is p m , the starting point and the end point are s m and t m . Construct an intermediate node set, including all nodes that meet the following conditions: the node and s m is connected; the node and t m is connected; the node is not in p m superior.

[0065] 4.2.2 Randomly select a node n in the intermediate node set and use Dijkstra algorithm to calculate the m The shortest delay path p to node n n1 and nodes n to t m The shortest delay path p n2 , p n1 and p n2 Merge to get a new path

[0066] 4.2.3 According to the network bandwidth allocation plan in step 2.2, reallocate the network bandwidth for all data flows to obtain a new routing plan.

[0067] 4.3 According to the performance evaluation method in step 3, the performance of the new routing solution is evaluated, and the Metropolis acceptance criterion is used to determine whether to accept the new routing solution. If the comprehensive routing performance of the new routing solution is greater than the comprehensive routing performance of the current routing solution, the new routing solution is accepted. Otherwise, the new routing solution is rejected with probability p. accept Accept the new route:

[0068]

[0069] Among them, exp represents the exponential function with the natural constant e as the base, S new represents the comprehensive routing performance of the new routing solution, S temp represents the comprehensive routing performance of the current routing scheme, and T represents the current temperature of the simulated annealing system.

[0070] 4.4 If the number of cycles at the current temperature reaches the maximum number of cycles, multiply the current temperature by the temperature reduction coefficient to update the value of the current temperature and jump to step 4.5, otherwise return to step 4.2.

[0071] 4.5 If the current temperature is less than the termination temperature, end the loop and output the current routing plan as the optimal routing plan, otherwise return to step 4.2.

[0072] The effect of the present invention can be further illustrated by the following simulation experiment.

[0073] The present invention uses PyCharm 2022.1 software for simulation, and some simulation parameters are shown in Table 1. The simulation area size is 800m×800m, centered on the location of the ground interference source. A specified number of drones are generated in the area, and the number of drones is 30, 40, 50, 60, and 70 respectively, and the coordinate positions of the drones are randomly generated, and then a specified number of data streams are generated, and the number of data streams is 50% and 100% of the number of drones. It is defined that "the number of data streams is equal to 50% of the number of drones" is a low-load scenario, and "the number of data streams is equal to 100% of the number of drones" is a high-load scenario, thereby forming 10 test scenarios with different numbers of drones and data streams.

[0074] Table 1

[0075] Simulation parameters Settings Drone altitude 100m Channel gain per unit distance -60dB UAV transmission power 6W Interference source transmission power 20W Ambient noise power -169dBm / Hz Channel bandwidth 5MHz The upper limit of transmission rate between drones and low-orbit satellites 50Mbps

[0076] The present invention uses average delay performance, average network bandwidth performance and comprehensive routing performance as performance indicators, wherein the average delay performance is the average value of the delay performance of all data flows, and the average network bandwidth performance is the average value of the network bandwidth performance of all data flows.

[0077] Experiments 1 and 2 tested the routing performance of drone networks of different sizes in low-load scenarios and high-load scenarios respectively. The experimental results are as follows: Figures 2 to 7 As shown. The present invention selects the precise algorithm Gurobi as one of the comparison schemes. Its advantage is that it can calculate the exact solution, but the calculation time increases exponentially with the expansion of the network scale. It has no practical application value and can only be used as a reference. The calculation time of the algorithm SA-ROP proposed in the present invention is often within a few seconds. The experimental results show that the present invention can quickly obtain an approximate solution under any circumstances, especially in terms of improving network bandwidth performance, and is very suitable for large-scale drone networks.

[0078] The above are only specific examples of the embodiments of the present invention. The protection scope of the present invention is not limited to the above embodiments. All technical solutions that meet the concept of the present invention belong to the protection scope of the present invention. It should be pointed out that for engineers and technicians in this field, several improvements and optimizations without departing from the principle of the present invention should be regarded as the protection scope of the present invention.

Claims

1. A UAV network routing method under spectrum denial based on low-orbit satellite collaboration, characterized by: The invention comprises a network controller, a low-orbit satellite, and a drone network. The drone network is composed of multiple master drones and slave drones. Each master drone is equipped with a satellite communication module, which can communicate with the low-orbit satellite in two directions. All drones can communicate with neighboring drones without interference. The network controller can control all drones and decide the route of the entire network based on the global network information after being interfered with by the spectrum, and formulate a transmission plan for all data streams in the network. Specifically, the following steps are included: (1) The network controller obtains global network information: The network controller interacts with the UAV to obtain information such as the UAV’s location, interference conditions, and data streams to be transmitted in the network; (2) Formulate an initial routing plan: Based on the global network information, the network controller first calculates the transmission path for all data flows, then allocates network bandwidth to obtain the initial routing plan for the data flow; (3) Evaluate the performance of the initial routing solution: The network controller evaluates the latency performance and network bandwidth performance of all data flows respectively, calculates the routing performance of the data flows in combination with the weight adjustment parameters, and then evaluates the comprehensive routing performance of the initial routing solution; (4) Optimizing routing scheme: Based on the simulated annealing framework, the network controller iteratively optimizes the path selection and network bandwidth allocation of the initial routing scheme until the termination condition is met to obtain the final routing scheme.

2. The spectrum denial UAV network routing method based on low-orbit satellite collaboration according to claim 1 is characterized in that: In step (2), the detailed steps of formulating the initial routing plan are: (2.1) For all data flows, use the Dijkstra algorithm to calculate the shortest delay path from its starting point to the end point as the transmission path; (2.2) Since several data flows may pass through the same node and different data flows have different demands for network bandwidth, the network controller needs to allocate network bandwidth to the data flows. For any two nodes u and v, C(u, v) is defined as the upper limit of the network bandwidth between u and v. When there is only one data flow forwarded from node u to node v, if C(u, v) is greater than the demand of the data flow, the network bandwidth allocated to the data flow is equal to its demand; otherwise, C(u, v) is allocated to the data flow. When there are multiple data flows forwarded from node u to node v, if C(u, v) is greater than the sum of the network bandwidth demands of these data flows, the network bandwidth allocated to each data flow is equal to the network bandwidth demand of the data flow; otherwise, C(u, v) is allocated to these data flows in equal proportion according to the network bandwidth demands of these data flows. After calculating the network bandwidth allocation plan for all nodes, the actual available network bandwidth of the data flow is equal to the minimum value of the network bandwidth allocated to it by all nodes on its path.

3. The spectrum denial UAV network routing method based on low-orbit satellite collaboration according to claim 1 is characterized in that: In step (3), the detailed steps of evaluating the performance of the initial routing solution are: (3.1) For any data flow F in the network i , its delay performance S(h i ) is evaluated and expressed as: where h i Represents data flow F i The end-to-end delay, D i Represents F i The expected delay of , exp represents the exponential function with the natural constant e as the base; (3.2) For any data flow F in the network i , its network bandwidth performance S(f i ) is evaluated and expressed as: Among them, R i Represents data flow F i The network bandwidth required; (3.3) Since different data flows have different requirements for latency and network bandwidth, for any data flow F in the network i Its routing performance S(f i ) is equal to the delay performance S(h i ) and network bandwidth performance S(f i ), expressed as: S i =λ i S(h i )+(1-λ i )S(f i ) Among them, λ i Represents data flow F i The weight adjustment parameter of (3.4) Based on the routing performance of each data flow, the comprehensive routing performance S of the initial routing scheme is evaluated, where S is the sum of the routing performance of all data flows.

4. The spectrum denial UAV network routing method based on low-orbit satellite collaboration according to claim 1 is characterized in that: In step (4), the detailed steps of route optimization are: (4.1) Set the initial temperature, end temperature, cooling coefficient, and maximum number of cycles of simulated annealing, and set the current temperature equal to the initial temperature; (4.2) Based on the current routing plan, generate a new routing plan by following the steps below: (4.2.1) Randomly select a data stream F m , whose transmission path is p m , the starting point and the end point are s m and t m , construct an intermediate node set, including all nodes that meet the following conditions: the node and s m is connected; the node and t m is connected; the node is not in p m superior; (4.2.2) Randomly select a node n in the intermediate node set and use Dijkstra's algorithm to calculate the m The shortest delay path p to node n n1 and nodes n to t m The shortest delay path p n2 , p n1 and p n2 Merge to get a new path (4.2.3) According to the network bandwidth allocation plan in step (2.2), reallocate the network bandwidth for all data flows to obtain a new routing plan; (4.3) According to the performance evaluation method of step (3), the performance of the new routing solution is evaluated, and the Metropolis acceptance criterion is used to determine whether to accept the new routing solution. If the comprehensive routing performance of the new routing solution is greater than the comprehensive routing performance of the current routing solution, the new routing solution is accepted; otherwise, the new routing solution is rejected with probability p. accept Accept the new route: Among them, exp represents the exponential function with the natural constant e as the base, S new represents the comprehensive routing performance of the new routing solution, S temp represents the comprehensive routing performance of the current routing scheme, and T represents the current temperature of the simulated annealing system; (4.4) If the number of cycles at the current temperature reaches the maximum number of cycles, multiply the current temperature by the temperature reduction coefficient to update the value of the current temperature and jump to step (4.5), otherwise return to step (4.2); (4.5) If the current temperature is less than the termination temperature, end the loop and output the current routing plan as the optimal routing plan, otherwise return to step (4.2).

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