A user experience-oriented drone edge network task offloading method

Abstract

The present invention discloses a user experience-oriented drone edge network task offloading method, provides a global algorithm for solving the shrinkage rate minimization problem in the context of binary offloading in a drone edge computing network, introduces partitioning to reduce the problem scale, and implements fixed-radius circle coverage based on the Welzl algorithm, thereby converting larger user devices into smaller partitions, optimizes the processing method when there are time-dependent variables in the target, scales the time-dependent variables to reduce the problem scale from the number of user devices M to the number of partitions G, and solves the non-convex resource allocation problem based on successive convex approximation and first-order Taylor expansion, optimizes the traveling salesman problem modeling method when there are time-dependent variables in the target, separates the order correlation in the time-dependent variables from the invariant factor through approximate rounding, thereby allowing the adjacency matrix of the node path to be established and modeled as a standard traveling salesman problem.

Description

Technical Field

[0001] The present invention relates to the field of drone technology, and in particular to a method for offloading drone edge network tasks oriented to user experience. Background Art

[0002] With the development of the Internet of Things and 5G technology, the number and demand for terminal devices are rapidly increasing. This generates massive amounts of data and traffic, placing immense pressure on cloud computing models. While edge computing networks using fixed base stations can significantly reduce this pressure, they still face challenges such as inflexible deployment and regional hotspots. Consequently, drone-based edge networks are being widely used in complex scenarios, such as establishing emergency networks in disaster areas and exploring complex terrain like mountainous areas and forests.

[0003] The massive presence of mobile devices also poses significant challenges to the allocation of network bandwidth and computing resources. Modeling the allocation problem directly for each device requires dealing with more complex coupling relationships and making more decisions, resulting in linear or even exponential increases in processing time.

[0004] Drone edge networks often involve trajectory planning for drones. Due to the limited coverage of drones, user devices may need to wait for task offloading services to become available, meaning that the drones reach their effective service range. This is a time-dependent variable, meaning the total time it takes for a device to execute tasks through the drone edge network is often strongly correlated with the order in which the drones are served. This complicates the optimization problem, making it more challenging to solve. Summary of the Invention

[0005] To address the challenges of the prior art, the present invention aims to provide a user-friendly task offloading method for drone edge networks, while achieving low time complexity and good convergence. Our goal is to minimize the sum of the shrinkage rates of all users in a drone edge computing network by addressing the task offloading decisions of user devices, the allocation of drone bandwidth and computing resources, and the drone's trajectory, within the context of binary task offloading. The shrinkage rate of a user device is defined as the ratio of the total time it takes to execute its task via the drone edge network to the total time it takes to compute its task locally. Binary offloading means that the tasks of a user device are indivisible and can only be executed as a whole locally or on an edge server. To reduce the problem size while leveraging the regional coverage characteristics of drones, a partitioning strategy is first used to divide all user devices in the area into multiple circular partitions, each of the same size as the drone's coverage area. The problem of minimizing the total shrinkage rate of binary offloading in the drone edge computing network is then modeled as a mixed-integer nonlinear programming problem based on the partition shrinkage rates. Reducing the problem size from users to partitions allows the use of higher-complexity optimization algorithms with better convergence, while keeping the increased time complexity within an acceptable range.

[0006] To solve the above problems, the present invention adopts the following technical solutions.

[0007] A method for offloading tasks from a drone edge network oriented to user experience, comprising the following steps:

[0008] Obtain the location of the current user device, input the location information of all user devices into the partitioning algorithm, and obtain the strategy for dividing all user devices in the current system into partitions using a fixed-radius circle coverage method, including the center point of the partition and the user devices included in each partition;

[0009] After obtaining the partitioning strategy, the total shrinkage minimization problem of binary offloading in the UAV edge computing network is modeled as a mixed integer nonlinear programming problem based on the hover-fly-hover mode. The block coordinate descent method is used to alternately iteratively optimize the resource allocation decision and trajectory planning decision for a total of iterations. The resource allocation decision includes the task offloading decision, the bandwidth of the UAV, and the computing resource allocation method. The trajectory planning decision refers to the trajectory of the UAV;

[0010] Given the UAV trajectory, minimizing the sum of shrinkage rates by adjusting resource allocation decisions is a difficult mixed integer nonlinear programming problem. This problem is solved by a resource allocation algorithm that applies the successive convex approximation technique. The successive convex approximation requires iterative approximation of the original optimal solution, with a total of R iterations. max Second-rate;

[0011] After a given resource allocation decision, the optimal trajectory is solved by the trajectory planning algorithm to minimize the sum of the shrinkage rates. It can be modeled as a Miller-Tucker-Zemlin model and the optimal trajectory is obtained by solving a small-scale TSP problem.

[0012] The partitioning algorithm involves finding a circle with a minimum radius that contains all points within the region on or within it. This algorithm is then iterated to solve the fixed-radius circle coverage problem. The region boundary is continuously reduced until the point closest to the boundary lies just above the reduced boundary. Each time the region is reduced, each point on the boundary is processed sequentially, while the points within the region are sorted in order relative to the current boundary point. The closest points are continuously added to the set. The Welzl method is then called to attempt to construct a circle with a radius no greater than r, where r is the coverage range of the drone. If such a circle cannot be constructed, the resulting point set is considered a partition. The next boundary point is then processed. Once all boundary points have been processed, the region is further reduced and the above process is repeated until all points have been added to the point set of a partition. This results in a complete partitioning result, consisting of the center points of G partitions and the user devices contained in each partition.

[0013] Given a UAV trajectory Ω = {ω1, ω2, ..., ω G}, the resource allocation problem can be formulated as the following mixed integer nonlinear programming problem:

[0014]

[0015] The resource allocation algorithm involves the offloading decision a, the UAV's bandwidth B, and the CPU frequency f. The offloading decision is a binary variable, while the bandwidth and CPU frequency are constrained continuous variables. Given the UAV trajectory, the integer constraints in the optimization objective are eliminated by introducing slack variables instead of integer variables:

[0016]

[0017] Secondly, we scale the waiting time and eliminate the offloading decision in the product by scaling, thus obtaining a non-convex upper bound on the waiting time. This approximates the waiting time based on the user dimension to the waiting time based on the partition dimension, simplifying the expression. The approximate formula is:

[0018]

[0019] The simplified function is:

[0020]

[0021] Finally, we have the non-convex objective function Perform a first-order Taylor expansion and transform it into a convex function at a specified point, thereby applying convex optimization techniques to solve the resource allocation problem. Successive convex approximation techniques are then used to gradually adjust the position of the initial point, gradually approaching the optimal solution to the original problem.

[0022] After obtaining the resource allocation results, we need to adjust the drone trajectory to minimize the sum of the shrinkage rates. Since the waiting time has been reduced from the user dimension to the partition dimension, this problem can be modeled as a traveling salesman problem based on the partition shrinkage rate. However, since the trajectory will affect the waiting time in the optimization objective, that is, the order of the path from partition i to j in the final trajectory will affect the length of the path, we cannot establish the corresponding adjacency matrix in advance.

[0023] In order to simplify the path cost, we first remove the part of the optimization objective that is not affected by the trajectory, and then we have:

[0024]

[0025] Considering the approximate rounding of the waiting time based on the partition dimension and ignoring the weight coefficients of different distributions, an adjacency matrix based on the partition shrinkage rate can be established. According to the following formula, the path cost of any two partitions i and j is expressed as the hovering time of partition i and the flight time from partition i to j, both of which are known quantities. In addition, an additional order vector u is required as a decision variable to attach different weights to the path. If the path<i,j> If it is the first path in the final trajectory, it should be multiplied by the weight G, where G is the total number of partitions.

[0026]

[0027] Through approximate derivation, we separate the timing factors in the waiting time from the optimization objective. This allows the adjacency matrix to be expressed as the product of the path cost and the order vector, and the order vector can be solved as a decision variable. In addition, since the order vector represents the order of the edges in the path, this is consistent with the order vector function used to solve the subring constraint in the Miller-Tucker-Zemlin (MTZ) model of the traveling salesman problem. Therefore, when G is small, we can directly model the trajectory planning problem as the following integer programming problem based on this model:

[0028]

[0029] The decision variable W is the edge selection matrix of G*G, which represents the edge<i,j> Whether it is selected as one of the final paths. The constant matrix C is the adjacency matrix of G*G, which represents the edge<i,j> Shrinkage cost:

[0030]

[0031] The component u[i] in the G-dimensional vector u is the sequence number of the i-th edge in the final path. The optimal solution of the trajectory can be obtained through the solver, where the edge selection matrix W and the sequence vector u can jointly determine the final trajectory. When G is large, the traveling salesman problem can be solved through heuristic methods such as genetic algorithms or ant colony algorithms.

[0032] Beneficial effects of the present invention

[0033] Compared with the prior art, the advantages of the present invention are:

[0034] First, this method is primarily used to minimize the shrinkage ratio of indivisible tasks in drone edge computing networks. Since shrinkage ratio takes into account user waiting time, it provides a more comprehensive measure of the efficiency improvement provided by the system to user devices, compared to computation time, thereby improving the overall user experience. Since waiting time is a time-dependent variable, this method employs a series of techniques to process this parameter, thereby simplifying the optimization problem.

[0035] Secondly, compared to similar existing technologies, this method reduces the problem size through partitioning, thereby reducing algorithmic complexity, allowing good suboptimal solutions to optimization problems within an acceptable time delay. Furthermore, compared to reinforcement learning or heuristic methods, this method offers higher precision, resulting in more accurate and stable convergence. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 It is the algorithm flow chart of the present invention.

[0037] Figure 2 It is a partition diagram of the present invention. DETAILED DESCRIPTION

[0038] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention; it is obvious that the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0039] Consider establishing a drone edge computing network in an area of ​​a specified size. Assume there are M user devices, each with a task to be computed, and these tasks are inseparable. Furthermore, drones can assist users in performing these tasks. Decisions must be made based on variables such as user offload, drone flight trajectory, transmission power allocation, and CPU frequency allocation to minimize the total system contraction rate.

[0040] Assume a m= {0, 1} indicates whether user m performs offloading, where 0 indicates local computing and 1 indicates edge computing. The shrinkage rate consists of two parts. The first part is the total time T required for the user to perform the computing task locally. m ,The second part is based on the time required for the drone edge computing network to perform computing tasks Shrinkage Φ m The meaning is the optimization ratio of the time brought to users by the drone edge computing network relative to their own computing, that is:

[0041]

[0042] in Represents partition ω g The time that user m waits for the drone to arrive at the effective service range can be expressed as:

[0043]

[0044] represents the time it takes for user m to offload the task to the drone, represents the time that user m waits for the drone to perform its mission. Then the system optimization goal is

[0045] At the same time, the present invention considers striking a balance between the time complexity of the algorithm and the accuracy of the solution, and reduces the time complexity of the algorithm while ensuring the quality of the solution.

[0046] First, the partitioning strategy aims to maximize the regional coverage characteristics of drones. We consider partitioning based solely on the location distribution of user devices, thus separating the partitioning strategy from the original optimization problem. Second, when a user uses the U-MEC system to offload tasks, they may need to wait for the drone to arrive at their partition. The time it takes for the drone to arrive at partition g is denoted as the waiting time for that partition. This value depends on the drone's trajectory and the time it hovers over each partition. The hovering time in each partition, in turn, depends on the resource allocation strategy.

[0047] Based on the above analysis, we designed an alternating iterative optimization algorithm. Figure 1 The main process of the global algorithm is described. The overall algorithm consists of three sub-algorithms: partitioning algorithm, resource allocation algorithm, and trajectory planning algorithm. We describe the algorithm process as follows:

[0048] Obtain the location of the current user device, input the location information of all user devices into the partitioning algorithm, and obtain the strategy for dividing all user devices in the current system into partitions through the fixed radius circle coverage method, including the center point of the partition and the user devices included in each partition.

[0049] After obtaining the partitioning strategy, the problem of minimizing the total contraction rate of binary offloading in the UAV edge computing network was modeled as a mixed integer nonlinear programming problem based on the hover-fly-hover model. The block coordinate descent method was used to alternately iteratively optimize the resource allocation decision and trajectory planning decision for a total of . The resource allocation decision includes the task offloading decision, the UAV's bandwidth, and the allocation of computing resources. The trajectory planning decision refers to the UAV's trajectory.

[0050] Given the trajectory of the UAV, minimizing the sum of the shrinkage rates by adjusting the resource allocation decision is a difficult mixed integer nonlinear programming problem. This problem is solved by a resource allocation algorithm that applies the successive convex approximation technique. Successive convex approximation requires iterative approximation of the original optimal solution, with a total of S iterations. max Second-rate.

[0051] Given a resource allocation decision, a trajectory planning algorithm is used to find the optimal trajectory to minimize the sum of the contraction rates. This is an integer programming problem that can be modeled as a Miller-Tucker-Zemlin model and obtained by solving a small-scale TSP problem.

[0052] The ideas of these three sub-algorithms are introduced in detail below:

[0053] 1.Partition algorithm

[0054] To reduce the massive problem size caused by the large number of user devices and leverage the regional coverage of drones, we abstracted the user devices into a smaller number of partitions. Due to the limited coverage of drones, we partitioned the user devices using fixed-radius circle coverage, where the radius is the drone's coverage area. We implemented an incremental algorithm based on the Welzl algorithm to solve the fixed-radius circle coverage problem.

[0055] The Welzl algorithm is an incremental algorithm for solving the minimum circle cover problem. Its purpose is to find a circle with the minimum radius that contains all points in the area on or within the circle. We will iteratively call this algorithm to solve the fixed radius circle cover problem. Figure 2As shown, we continuously shrink the boundary of the area so that the point closest to the boundary is just above the shrunken boundary. Each time the area is shrunk, each point on the boundary is processed sequentially. The points in the area are sorted in the order of the current boundary point, and the closest points are continuously added to the set. The Welzl method is called to try to construct a circle with a radius not exceeding r, where r is the coverage range of the drone. When such a circle cannot be constructed, the resulting point set is a partition. At this time, continue to process the next boundary point. When all boundary points have been processed, continue to shrink the area and repeat the above process until all points are added to the point set of a partition. The complete partition result can be obtained, including the center points of G partitions and the user devices contained in each partition.

[0056] 2.Resource allocation algorithm

[0057] Given a UAV trajectory Ω = {ω1, ω2, ..., ω G}, the resource allocation problem can be formulated as the following mixed integer nonlinear programming problem:

[0058]

[0059] The resource allocation algorithm involves the offloading decision a, the drone's bandwidth B, and the CPU frequency f. The offloading decision is a binary variable, while the bandwidth and CPU frequency are constrained continuous variables. Given the drone's trajectory, a direct solution is difficult because the waiting time involves the product of the offloading decision and a concave pointwise maximum function.

[0060] First, we remove the integer constraints from the optimization objective by introducing slack variables instead of integer variables:

[0061]

[0062] Secondly, we scale the waiting time and eliminate the offloading decision in the product by scaling, thus obtaining a non-convex upper bound on the waiting time. This approximates the waiting time based on the user dimension to the waiting time based on the partition dimension, simplifying the expression. The approximate formula is:

[0063]

[0064] The simplified function for:

[0065]

[0066] Finally, we have the non-convex objective function Perform a first-order Taylor expansion and transform it into a convex function at a specified point, thereby applying convex optimization techniques to solve the resource allocation problem. Successive convex approximation techniques are then used to gradually adjust the position of the initial point, gradually approaching the optimal solution to the original problem.

[0067] Finally, it is necessary to discretize the continuous variables into integer variables based on a certain strategy. The present invention proposes a heuristic strategy: first, the mean of all continuous unloading variables is calculated as the proportion of users who choose to unload, denoted as p. Secondly, the continuous unloading variables are sorted in descending order to obtain a sorted user list. Finally, the first p users in the sorted user list are taken as the users who choose to unload, thereby obtaining the binary unloading decision of all users. By bringing the integer variables into the original optimization problem, the resource allocation problem becomes a convex optimization problem. The optimal bandwidth and computing resource allocation strategy can be obtained through convex optimization technology. In addition, the discretization strategy here can also use a threshold judgment method or a method with other heuristic rules.

[0068] 3.Trajectory planning algorithm

[0069] After obtaining the resource allocation results, the drone trajectory needs to be adjusted to minimize the sum of the shrinkage rates. Since the waiting time has been reduced from the user dimension to the partition dimension, this problem can be modeled as a traveling salesman problem based on the partition shrinkage rate. However, since the trajectory affects the waiting time in the optimization objective—that is, the order of the path from partition i to j in the final trajectory affects the path length—the corresponding adjacency matrix cannot be established in advance.

[0070] In order to simplify the path cost, we first remove the part of the optimization objective that is not affected by the trajectory. Then we have:

[0071]

[0072] Considering the approximate rounding of the waiting time based on the partition dimension and ignoring the weight coefficients of different distributions, an adjacency matrix based on the partition shrinkage rate can be established. According to the following formula, the path cost of any two partitions i and j is expressed as the hovering time of partition i and the flight time from partition i to j, both of which are known quantities. In addition, an additional order vector u is required as a decision variable to attach different weights to the path. If the path<i,j> If it is the first path in the final trajectory, it should be multiplied by the weight G, where G is the total number of partitions.

[0073]

[0074] Through approximate derivation, we separate the timing factors in waiting time from the optimization objective, allowing the adjacency matrix to be expressed as the product of path cost and order vector. The order vector can be solved as a decision variable. Furthermore, since the order vector represents the order of edges in the path, this function is consistent with the order vector used to solve subring constraints in the Miller-Tucker-Zemlin (MTZ) model of the traveling salesman problem. Therefore, when G is small (1 <= G <= 10, as determined by simulation results), we can directly model the trajectory planning problem as the following integer programming problem based on this model:

[0075]

[0076] The decision variable W is the edge selection matrix of G*G, and W[i][j]∈{0,1} represents the edge<i,j> Whether it is selected as one of the final paths. The constant matrix C is the adjacency matrix of G*G, and C[i][j] represents the edge<i,j> Shrinkage cost:

[0077]

[0078] The component u[i] in the G-dimensional vector u is the index of the i-th edge in the final path. The solver can be used to obtain the optimal solution for the trajectory. The edge selection matrix W and the sequence vector u together determine the final trajectory. When G is large (G>10), heuristic methods such as genetic algorithms or ant colony algorithms can be used to solve the traveling salesman problem.

[0079] 4. Summary

[0080] First, the system environment is initialized to a fixed-size area and a specified number of user devices are randomly generated. Next, the coordinate information of all user devices is input into the partition algorithm to obtain the partition strategy, that is, the coordinates of the centers of G circles and the set of user devices they contain.

[0081] Next, given an initial trajectory, the resource allocation algorithm is invoked to obtain suboptimal binary offloading decisions, drone bandwidth allocation strategies, and computing resource allocation strategies. Based on this solution, the trajectory planning algorithm is invoked to obtain the optimal trajectory under the current resource allocation scheme. This process is repeated iteratively until the algorithm converges to the desired range.

[0082] Finally, putting all the obtained decision variables together is the suboptimal solution given by the algorithm proposed in this invention for the binary task offloading problem oriented to user experience in the drone edge computing network.

[0083] The above description is merely a preferred embodiment of the present invention; however, the scope of protection of the present invention is not limited thereto. Any person skilled in the art who, within the technical scope disclosed by the present invention, makes equivalent substitutions or modifications based on the technical solutions and improved concepts of the present invention shall be covered by the scope of protection of the present invention.

Claims

1. A method for offloading tasks from a drone edge network oriented to user experience, characterized in that: The following steps are involved: Obtain the location of the current user device, input the location information of all user devices into the partitioning algorithm, and obtain the strategy for dividing all user devices in the current system into partitions using a fixed-radius circle coverage method, including the center point of the partition and the user devices included in each partition; After obtaining the partitioning strategy, the total shrinkage minimization problem of binary offloading in the UAV edge computing network is modeled as a mixed integer nonlinear programming problem based on the hover-fly-hover mode. The block coordinate descent method is used to alternately iteratively optimize the resource allocation decision and trajectory planning decision. The resource allocation decision includes the task offloading decision, the bandwidth and computing resource allocation method of the UAV, and the trajectory planning decision refers to the trajectory of the UAV. Given the UAV trajectory, minimizing the sum of shrinkage rates by adjusting resource allocation decisions is a difficult mixed integer nonlinear programming problem. This problem is solved by a resource allocation algorithm that applies the successive convex approximation technique. The successive convex approximation requires iterative approximation of the original optimal solution, with a total of R iterations. max Second-rate; After a given resource allocation decision, the optimal trajectory is solved by the trajectory planning algorithm to minimize the sum of the shrinkage rates. It can be modeled as a Miller-Tucker-Zemlin model and the optimal trajectory is obtained by solving a small-scale TSP problem.

2. The method for offloading tasks from a drone edge network based on user experience according to claim 1, characterized in that: The partitioning algorithm includes finding a circle with a minimum radius and including all points in the area on or within the circle. The algorithm is iteratively called to solve the fixed radius circle coverage problem, that is, the area boundary is continuously reduced so that the point closest to the boundary is just above the reduced boundary. Each time the area is reduced, each point on the boundary is processed sequentially, and the points in the area are sorted according to the order of the current boundary point. The closest points are continuously added to the set, and the Welzl method is called to try to construct a circle with a radius not exceeding r, where r is the coverage range of the drone. When such a circle cannot be constructed, the resulting point set is a partition, and the next boundary point is processed. When all boundary points are processed, the area is continued to be reduced and the above process is repeated until all points are added to the point set of a partition. A complete partitioning result can be obtained, including the center points of G partitions and the user devices contained in each partition.

3. The method for offloading tasks from a drone edge network based on user experience according to claim 1, characterized in that: Given a UAV trajectory Ω=(ω1,ω2,…,ω G }, the resource allocation problem can be formulated as the following mixed integer nonlinear programming problem: The resource allocation algorithm involves the offloading decision a, the UAV's bandwidth B, and the CPU frequency f. The offloading decision is a binary variable, while the bandwidth and CPU frequency are constrained continuous variables. Given the UAV trajectory, the integer constraints in the optimization objective are eliminated by introducing slack variables instead of integer variables: Secondly, we scale the waiting time to eliminate the offloading decision in the product, and obtain a non-convex upper bound on the waiting time. This approximates the waiting time based on the user dimension to the waiting time based on the partition dimension, simplifying the expression. The approximate formula is: The simplified function is: Finally, for the non-convex objective function Perform a first-order Taylor expansion and transform it into a convex function at the specified point, so as to apply the convex optimization technology to solve the resource allocation problem, and use the successive convex approximation technology to gradually adjust the position of the initial point, so as to gradually approach the optimal solution of the original problem; Assume a m = {0, 1} indicates whether user m performs offloading, where 0 indicates local computing and 1 indicates edge computing. The shrinkage rate consists of two parts. The first part is the total time T required for the user to perform the computing task locally. m ,The second part is based on the time required for the drone edge computing network to perform computing tasks Shrinkage Φ m The meaning of is the optimization ratio of the time brought by the drone edge computing network to the user relative to the self-computing, where Represents partition ω g The time that user m waits for the drone to arrive at the effective service range, represents the time it takes for user m to offload the task to the drone, represents the time that user m waits for the drone to perform its mission, then the system optimization goal is 4. The method for offloading tasks from a drone edge network based on user experience according to claim 1, characterized in that: After obtaining the resource allocation results, it is necessary to adjust the drone trajectory to minimize the sum of the shrinkage rates. Since the waiting time has been reduced from the user dimension to the partition dimension, this problem can be modeled as a traveling salesman problem based on the partition shrinkage rate. However, since the trajectory will affect the waiting time in the optimization objective, that is, the order of the path from partition i to j in the final trajectory will affect the length of the path, it is impossible to establish the corresponding adjacency matrix in advance. In order to simplify the path cost, we first remove the part of the optimization objective that is not affected by the trajectory, and then we have: Considering the approximate rounding of the waiting time based on the partition dimension and ignoring the weight coefficients of different distributions, the adjacency matrix based on the partition shrinkage rate can be established. According to the following formula, the path cost of any two partitions i and j is expressed as the hovering time of partition i and the flight time from partition i to j. Both values ​​are known quantities. In addition, an additional sequence vector u is required as a decision variable to add different weights to the path. If the path<i,j> If it is the first path in the final trajectory, it should be multiplied by the weight G, where G is the total number of partitions. Through approximate derivation, the timing factors in the waiting time are separated from the optimization objective. This allows the adjacency matrix to be expressed as the product of the path cost and the order vector, and the order vector can be solved as a decision variable. In addition, since the order vector represents the order of edges in the path, this is consistent with the order vector function used to solve subring constraints in the Miller-Tucker-Zemlin (MTZ) model of the traveling salesman problem. Therefore, when 1<=G<=10, the trajectory planning problem can be directly modeled as the following integer programming problem based on this model: The decision variable W is the edge selection matrix of G*G, which represents the edge<i,j> Whether it is selected as one of the final paths, the constant matrix C is the adjacency matrix of G*G, indicating the edge<i,j> Shrinkage cost: The component u[i] in the G-dimensional vector u is the sequence number of the i-th edge in the final path. The optimal solution of the trajectory can be obtained through the solver, where the edge selection matrix W and the sequence vector u can jointly determine the final trajectory. When G>10, the traveling salesman problem is solved by a heuristic method.

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