An Unmanned Aerial Vehicle Path Optimization Method Based on Improved Branch and Bound Algorithm

Abstract

The present invention discloses a method for optimizing the path of an unmanned aerial vehicle based on an improved branch and bound algorithm. First, the task points are divided into different priority levels, and a dynamic weight mechanism is designed to drive high-priority tasks to be preferentially responded to. Secondly, the global MTSP problem is transformed into the clustering of a planar point set and the local TSP problem, and collaborative solution is achieved by fusing the K-means clustering and the branch and bound algorithm. Aiming at the challenge of computational complexity in large-scale task scenarios, an approximate optimization strategy based on space partitioning is proposed, and a multi-level optimization architecture is adopted to balance the solution accuracy and the computational efficiency. Compared with the traditional heuristic algorithm and the branch and bound algorithm, the method of the present invention can obtain a better solution in small-scale TSP instances. For large-scale task scenarios, the computational efficiency of the algorithm is greatly improved. And through the dynamic weight mechanism, the access timing of high-priority task nodes is optimized and advanced, so that both the system response timeliness and the system comprehensive QoS are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned aerial vehicle path planning, and in particular to a method for optimizing the path of an unmanned aerial vehicle based on an improved branch and bound algorithm. Background Art

[0002] Drone systems have been widely used in the civilian field due to their compact structure, low-cost deployment, high maneuverability, payload adaptability and strong environmental adaptability. In the civilian field, relying on the "low-altitude economy" strategy, the application breadth of drone systems in logistics distribution, infrastructure inspection and emergency response continues to expand. Among them, the intelligent inspection system based on drone swarms has achieved an order of magnitude improvement in monitoring coverage and spatiotemporal resolution compared to traditional intelligent transportation systems through three-dimensional spatial operation capabilities, providing key technical support for the construction of new intelligent transportation systems.

[0003] There are three core limitations in the current field of multi-UAV path planning: (1) Existing studies generally assume that the demands of task points are equal, thus homogenizing the task demands. This fails to fully consider the priority differences and quality of service (QoS) requirements of task points in actual scenarios, resulting in high-value task response delays and suboptimal system utility problems. (2) Although the branch-and-bound method shows good performance in small-scale scenarios with a small number of nodes, its time complexity increases exponentially with the increase in the size of the problem. The improved methods of the branch-and-bound method in existing studies, such as the dynamic reduction matrix, only achieve linear acceleration, and the improvement in computational efficiency is still difficult to meet real-time requirements. (3) Most current studies usually consider single-dimensional indicators such as the shortest trajectory or shortest time, and lack multi-objective coordinated optimization such as load balancing and energy efficiency. This may cause some UAVs to be overloaded while other UAVs are underutilized, affecting the overall stability and sustainability of the system and significantly increasing the risk of system failure. Summary of the invention

[0004] In order to solve the above technical problems, the present invention provides a UAV path optimization method based on an improved branch and bound algorithm, comprising the following steps:

[0005] S1. Construct a drone cruise system; combine the task priority with the shortest path as the goal, construct the optimal path objective function of drone cruise, construct the constraint function according to the mutual exclusivity of task point allocation, battery capacity and task point timing coupling; construct a system service quality evaluation model;

[0006] S2, input the task point set and the location of the drone base station, perform task allocation based on the K-means algorithm, introduce variance and dispersion evaluation for clustering screening, and output n mutually exclusive subtask sets;

[0007] S3. Conduct trajectory planning based on the improved branch and bound method, generate the upper bound using the greedy strategy, calculate the lower bound according to the different access states of nodes during the search process, and perform dynamic pruning based on single-step and multi-step backtracking;

[0008] S4. Through the approximate optimization strategy based on space partitioning, combining the greedy algorithm and the branch and bound method, divide the points on the plane, continuously update the nodes to reduce the branches of the branch and bound method, and complete the calculation.

[0009] The further limited technical solution of the present invention is:

[0010] Further, in step S1, the UAV cruise system includes UAVs, UAV base stations, and task points with different priorities. The number of UAV base stations is represented as K = {k1, k2,..., k n}, there are n UAV base stations in total, and one homogeneous UAV is deployed at each base station; the task point set is represented as V = {V1, V2,..., V m}, there are m cruise task points in total; each task point is served by exactly one UAV, and the task points are cruised in order of priority.

[0011] For the UAV path optimization method based on the improved branch and bound algorithm as described above, in step S1, the task point set V = {V1, V2,..., V m} is decomposed into n mutually exclusive subsets The area served by the UAV base station k j is represented as U j , then it is necessary to plan the optimal path for the UAV to start from its affiliated base station, traverse all the task points in the area U j and then return; considering the different urgency levels of the cruise task points, the task node priority factor p i ∈{1, 2, 3} is introduced. Therefore, the objective function of the UAV cruise path planning problem is expressed as:

[0012]

[0013] Among them, represents the distance from UAV j to the first task point in the subset U j when cruising from the base station k j , represents the distance from the last task point in the subset U j back to the corresponding cruise UAV base station k j , is the distance from the task point v j to v i in the subset U i+1 .

[0014] As described above, a method for optimizing the path of an unmanned aerial vehicle (UAV) based on an improved branch-and-bound algorithm. In step S1, considering the mutual exclusion constraint of task point allocation, the battery capacity constraint, and the task point timing coupling constraint, for any two UAV service areas U i and U j , it satisfies For the subset U j , the path distance of its cruise plan is less than the maximum flight distance of the UAV, that is where L max is the maximum flight distance of each UAV; for any two task nodes v i and v j , if p i < p j , then

[0015] As described above, a method for optimizing the path of an unmanned aerial vehicle (UAV) based on an improved branch-and-bound algorithm. In step S1, the service quality of the UAV cruise system is quantified, expressed as:

[0016]

[0017] where the task priority score is used to characterize the response ability of the UAV cruise system to tasks with different priorities. The smaller the value of the priority factor p i , the higher the priority level of the task point; its weight ω p is used to quantify the gain effect of the service order of task points with different priorities on the service quality. The larger its value, the stronger the sensitivity of the system service quality evaluation model to priority stratification;

[0018] The arrival time score is shown as follows:

[0019]

[0020] where the actual time for the UAV to reach the task point v i is t i , the latest arrival time is The expected arrival time is The arrival time score S ti is used to measure the response timeliness of the UAV to the task point, and its weight ω t reflects the non-linear impact of the timeliness of the UAV reaching the task point on the service quality;

[0021] The UAV quantity penalty term is used to evaluate the number of UAVs dispatched by the system. s is the number of UAVs dispatched, and n is the total number of available UAVs. Its weight ω u characterizes the cost increase brought by the expansion of the UAV cluster scale;

[0022] Energy consumption score E act is the actual energy consumption, E min and E max are the theoretical minimum energy consumption and the maximum allowable energy consumption respectively, and their weights ω e are used to measure the hard limit of the drone's endurance ability on the mission sustainability.

[0023] A method for optimizing the path of a drone based on an improved branch and bound algorithm as described above, step S2 specifically includes the following sub-steps:

[0024] S2.1. Introduce the screening variance fd as the first evaluation index, which is defined as the variance of the distances from the center points of n clusters to the corresponding drone layout points after K-means clustering. Its mathematical expression is:

[0025] fd = Var(d1, d2,..., d n )

[0026] where d i represents the Euclidean distance from the center point of the i-th cluster to the corresponding drone layout point; by adjusting the threshold of fd, the scale of the screening results is controlled. The larger fd is, the more feasible clustering schemes are obtained;

[0027] S2.2. Introduce the dispersion variable Dv as the second evaluation index, which is defined as the difference between the number of nodes in the largest cluster and the smallest cluster after K-means clustering. Its mathematical expression is:

[0028] Dv = max(C1, C2,..., C n ) - min(C1, C2,..., C n )

[0029] where C i represents the number of stages of the i-th cluster; adjust the threshold of Dv according to actual needs. The larger the allowable Dv value is, the more feasible clustering schemes are obtained.

[0030] A method for optimizing the path of a drone based on an improved branch and bound algorithm as described above, in step S3, generating the upper bound using the greedy strategy specifically includes the following sub-steps:

[0031] S3.1. Starting from the starting node, select the unvisited node closest to the current node as the next visited node;

[0032] S3.2. Repeat the above step until all nodes are visited;

[0033] S3.3. Return to the starting node to form a complete loop;

[0034] S3.4. Calculate the total distance of this loop as the upper bound.

[0035] For a UAV path optimization method based on an improved branch and bound algorithm as described above, in step S3, calculate the lower bound according to the different access states of nodes during the search process;

[0036] If the search node set S only contains the starting node, consider the case where the entry and exit of each node are exactly the shortest distances. The calculation formula for the lower bound lb is:

[0037]

[0038] where D is the distance matrix, and min1 and min2 represent the minimum value and the second minimum value in the matrix row respectively;

[0039] If the search node set S contains the starting node and some intermediate nodes, the calculation formula for the lower bound lb is:

[0040]

[0041] where S represents the number of visited nodes, and \ represents the set difference operation;

[0042] If the search node set S contains all nodes, the lower bound lb represents the complete path length:

[0043]

[0044] For a UAV path optimization method based on an improved branch and bound algorithm as described above, in step S3, judge whether the current node is an end node,

[0045] When the lower bound is greater than the upper bound and the current node is not an end node, perform single-step backtracking; first remove the recently added node v k , then select the next candidate node v k+1 , and finally update the search path [S[1], S[2],..., S[k - 1], v k+1 ;

[0046] When the lower bound is greater than the upper bound and the current node is an end node, perform multi-step backtracking; first continuously remove the end nodes until a non-end node v is encountered m , then select the next candidate node v of v m , and finally update the search path to [S[1], S[2], …, S[m - 1], v m+1 . m+1

[0047] As described above, a method for optimizing the path of an unmanned aerial vehicle based on an improved branch and bound algorithm. In step S4, the approximate optimization strategy based on space partitioning decomposes the global optimization problem into multiple locally optimal sub-problems by constructing a hierarchical solution framework, which specifically includes the following sub-steps:

[0048] S4.1. Use a greedy algorithm to generate an initial feasible solution, form a closed path P0, and calculate its total distance as the benchmark upper bound;

[0049] S4.2. Perform spatial region partitioning on the points in the plane: First, take the starting point 0 as the origin of the polar coordinate system and establish an angle partitioning criterion; Second, divide the plane area covered by the path P0 into k sector sub-regions {R1, R2,..., R k}; Finally, select a node set V i = {v1, v2,..., v i} within each sub-region R m ;

[0050] S4.3. Hierarchical optimization iteration: First, use the improved branch and bound method in step S3 to solve the optimal path P i of the node set V i * in the current layer; Second, select the first (k - m) nodes in P i * as the benchmark node set B = {b1, b2,..., v k-m} for the next layer of optimization; Finally, allocate the remaining nodes to the neighborhoods of each benchmark node according to the principle of spatial proximity to form a new candidate node set V j = {v1, v2,..., v t};

[0051] S4.4. Dynamic update mechanism: First, perform local branch and bound optimization on each candidate node set V j ; Then, merge the local optimal solutions to form a global approximate solution P';

[0052] S4.5. Stop until all nodes are added.

[0053] The beneficial effects of the present invention are:

[0054] In the present invention, first, task points are divided into different priority levels, and a dynamic weight mechanism is designed to drive high-priority tasks to respond first; second, the global MTSP problem is transformed into the clustering of a planar point set and a local TSP problem, and collaborative solution is achieved by fusing the K-means clustering and branch-and-bound algorithms; in response to the computational complexity challenge in large-scale task scenarios, an approximate optimization strategy based on space partitioning is proposed, and a multi-level optimization architecture is adopted to balance solution accuracy and computational efficiency; compared with traditional heuristic algorithms and branch-and-bound algorithms, the method of the present invention can obtain a better solution in small-scale TSP instances. For large-scale task scenarios, the algorithm achieves an 82.41%-97.63% improvement in computational efficiency with a path length loss of 13.59%-37.13%; and through the dynamic weight mechanism, the access timing of high-priority task nodes is optimized and advanced, resulting in a 66.8% improvement in the system response time and an 18.2%-114.7% improvement in the overall system QoS. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 is a schematic diagram of the overall process of the present invention;

[0056] Figure 2 is a schematic diagram of the UAV cruise system in an embodiment of the present invention;

[0057] Figure 3 is a schematic diagram of the process of the branch-and-bound algorithm in an embodiment of the present invention;

[0058] Figure 4 is a graph showing the relationship between the running time and the number of task points under different thresholds in an embodiment of the present invention;

[0059] Figure 5 is a graph showing the relationship between the shortest path length and the path length of a single UAV and the number of task points under different thresholds in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0060] A UAV path optimization method based on an improved branch-and-bound algorithm provided in this embodiment, as Figure 1 shown, includes the following steps:

[0061] S1. Construct a UAV cruise system; combine task priorities and take the shortest path as the goal to construct an optimal path objective function for UAV cruising, and construct constraint functions according to the mutual exclusivity of task point allocation, battery capacity, and task point timing coupling; construct a system service quality evaluation model.

[0062] As Figure 2As shown in the figure, the UAV cruise system includes UAVs, UAV base stations, and task points with different priorities. The UAV cluster will perform task allocation and cruise all task points in the order of priority to ensure service quality and the optimal path. The number of UAV base stations is expressed as K = {k1, k2,..., k n}, and there are n UAV base stations in total. One homogeneous UAV is deployed at each base station. The set of task points is expressed as V = {V1, V2,..., V m}, and there are m cruise task points in total. Through reasonable task allocation, it is ensured that each task point is served by exactly one UAV. By reasonably arranging the paths of the UAVs, it is ensured that the task points are cruised in the order of priority.

[0063] This embodiment can be regarded as a Multi-Depot Multiple Traveling Salesman Problem (MD-MTSP). The set of task points V = {V1, V2,..., V m} is decomposed into n mutually exclusive subsets The area served by the UAV base station k j is expressed as U j . Then, it is necessary to plan the optimal path for the UAV to start from its affiliated base station, traverse all the task points in the area U j and then return.

[0064] Considering the different degrees of urgency of the cruise task points, the task node priority factor p i ∈{1, 2, 3} is introduced. Therefore, the objective function of the path planning problem for UAV cruise is expressed as:

[0065]

[0066] Among them, represents the distance from UAV j cruising from base station k j to the first task point in the subset U j , represents the distance from the last task point in the subset U j back to the corresponding cruise UAV base station k j , is the distance from task point v j to v i in the subset U i+1 .

[0067] Considering the mutually exclusive constraints of task point allocation, battery capacity constraints, and task point timing coupling constraints, for any two UAV service areas U i and U j , it satisfies For the subset U j, the path distance of its cruise plan is less than the maximum flight distance of the UAV, that is Among them, L max is the maximum flight distance of each UAV; for any two task nodes v i and v j , if p i <p j , then

[0068] In order to better evaluate the service quality of the system, the service quality of the UAV cruise system is quantified, expressed as:

[0069]

[0070] Among them, the task priority score is used to characterize the response ability of the UAV cruise system to tasks with different priorities. The smaller the value of the priority factor p i , the higher the priority level of the task point; its weight ω p is used to quantify the gain effect of the service order of task points with different priorities on the service quality. The larger its value, the stronger the sensitivity of the system service quality evaluation model to priority stratification.

[0071] The arrival time score is shown in the following formula:

[0072]

[0073] Among them, the actual time for the UAV to reach the task point v i is t i , the latest arrival time is The expected arrival time is The arrival time score S ti is used to measure the response timeliness of the UAV to the task point, and its weight ω t reflects the non-linear impact of the timeliness of the UAV reaching the task point on Qos.

[0074] The UAV quantity penalty term is used to evaluate the number of UAVs dispatched by the system. s is the number of UAVs dispatched, and n is the total number of available UAVs. Its weight ω u characterizes the cost increase brought about by the expansion of the UAV cluster scale. Its negative weight design aims to suppress resource redundancy;

[0075] The energy consumption score E act is the actual energy consumption, E min and E max are the theoretical minimum energy consumption and the maximum allowable energy consumption respectively. Its weight ω e is used to measure the hard limit of the UAV endurance ability on the task sustainability.

[0076] S2. Input the set of task points and the positions of UAV base stations, perform task allocation based on the K-means algorithm, introduce variance and dispersion evaluation for clustering screening, and output n mutually exclusive sub-task sets.

[0077] In this embodiment, a collaborative solution is implemented by integrating the K-means clustering and branch-and-bound algorithms. The specific implementation steps of the K-means algorithm are as follows:

[0078] 1) Given the number of clusters n, and given the dataset M = {x1, x2,..., x m}, where x i ∈R d represents a sample point in the d-dimensional feature space. Given the maximum number of iterations t max , initialize the count t = 0;

[0079] 2) Initialize the center points for each group, denoted as C = {c1, c2,..., c n};

[0080] 3) For each sample x i in the dataset, calculate its Euclidean distance from each cluster center and assign it to the cluster corresponding to the nearest cluster center;

[0081] 4) Based on the current cluster assignment result, recalculate the center point of each cluster: where S j represents the number of samples in the j-th cluster; calculate the sum of squared errors of all clusters;

[0082] 5) Repeat steps 3) and 4) until one of the following termination conditions is met: i. The change in the cluster center is less than the preset threshold; ii. Reach the maximum number of iterations t max ; iii. The sum of the squared distances from all samples to the cluster center converges;

[0083] 6) Finally, divide the dataset M into n non-overlapping subsets and obtain the corresponding set of cluster centers.

[0084] In the practical application of the K-means clustering algorithm, the clustering results often have randomness and diversity; to screen out a scheme with good clustering effect and high computational efficiency, two key evaluation indicators for clustering screening are proposed; step S2 specifically includes the following sub-steps:

[0085] S2.1. Considering that the average distance between the node group and the corresponding UAV layout points should be relatively balanced, the screening variance fd is introduced as the first evaluation index, which is defined as the variance of the distances from the central points of n clusters to the corresponding UAV layout points after K-means clustering. Its mathematical expression is:

[0086] fd = Var(d1, d2,..., d n )

[0087] where d i represents the Euclidean distance from the central point of the i-th cluster to the corresponding UAV layout point; by adjusting the threshold of fd, the scale of the screening result is controlled. The larger fd is, the more feasible clustering schemes can be obtained.

[0088] S2.2. To measure the balance of the number of tasks in each clustering cluster, the dispersion variable Dv is introduced as the second evaluation index, which is defined as the difference between the number of nodes in the largest cluster and the smallest cluster after K-means clustering. Its mathematical expression is:

[0089] Dv = max(C1, C2,..., C n ) - min(C1, C2,..., C n )

[0090] where C i represents the number of stages of the i-th cluster; the threshold of Dv is adjusted according to actual needs. The larger the allowed Dv value is, the more feasible clustering schemes can be obtained.

[0091] S3. Based on the improved branch and bound method for path planning, a greedy strategy is used to generate the upper bound, the lower bound is calculated according to the different access states of nodes in the search process, and dynamic pruning is performed according to the single-step and multi-step backtracking situations.

[0092] After the clustering grouping in step S2 is completed, the UAV swarm cooperative path planning problem is transformed into a combinatorial optimization problem of multiple Traveling Salesman Problems (TSP).

[0093] To better illustrate the improved branch and bound algorithm adopted in this embodiment, the traditional branch and bound algorithm will be introduced below, as Figure 3 shown, including the following steps:

[0094] 1) Initialize the search node set and store the current node group;

[0095] 2) Calculate the upper bound formed by the stored nodes;

[0096] 3) Select the node to be expanded from the stored node set according to the predefined rule;

[0097] 4) Calculate the lower bound after expanding the new node;

[0098] 5) If the lower bound is less than the upper bound, add the new node to the set, update the current path, and repeat steps 3) and 4);

[0099] 6) If the lower bound is greater than or equal to the upper bound, backtrack to the previous node and remove the new node;

[0100] 7) If the stored node set is empty and the lower bound is greater than the upper bound, update the upper bound;

[0101] 8) Terminate the algorithm when the search tree traversal is completed or the pre - set calculation time limit is reached.

[0102] In the traditional branch - and - bound process, the calculation of the upper and lower bounds is the key factor determining the algorithm efficiency; the upper bound in this embodiment adopts the greedy algorithm strategy, which specifically includes the following sub - steps:

[0103] S3.1. Starting from the starting node, select the unvisited node closest to the current node as the next visited node;

[0104] S3.2. Repeat the above step until all nodes are visited;

[0105] S3.3. Return to the starting node to form a complete loop;

[0106] S3.4. Calculate the total distance of this loop as the upper bound.

[0107] The lower - bound calculation in this embodiment is divided into the following three cases according to the access status of nodes during the search process:

[0108] 1) If the search node set S only contains the starting node, consider the case where the in - and - out of each node is exactly the shortest distance. The calculation formula for the lower bound lb is:

[0109]

[0110] where D is the distance matrix, and min1 and min2 represent the minimum and the second - minimum values in the matrix row respectively.

[0111] 2) If the search node set S contains the starting node and some intermediate nodes, the calculation formula for the lower bound lb is:

[0112]

[0113] Among them, S represents the number of visited nodes, and \ represents the set difference operation; in this case, the calculation formula of lb can be expressed as the sum of the distances between adjacent nodes in the search node group, half of the minimum value of the distances from the two side nodes to other nodes (excluding the nodes in the search node group), and half of the sum of the two smallest values in the row of the distance matrix of other nodes.

[0114] 3) If the search node set S contains all nodes, the lower bound lb is expressed as the complete path length:

[0115]

[0116] Node backtracking is also crucial in the branch and bound process. In this embodiment, regarding whether the current node is an end node in the node backtracking strategy, the following two processing mechanisms are adopted:

[0117] 1) When the lower bound is greater than the upper bound and the current node is not an end node, perform single-step backtracking; first remove the most recently added node v k , then select the next candidate node v k+1 , and finally update the search path [S[1], S[2],..., S[k - 1], v k+1 .

[0118] 2) When the lower bound is greater than the upper bound and the current node is an end node, perform multi-step backtracking; first continuously remove the end nodes until a non-end node v is encountered m , then select the next candidate node v of v m , and finally update the search path to [S[1], S[2], …, S[m - 1], v m+1 . m+1 .

[0119] S4. By means of an approximate optimization strategy based on space partitioning, combining the greedy algorithm and the branch and bound method, through partitioning the points on the plane and continuously updating the nodes to reduce the branches of the branch and bound method, the calculation is completed.

[0120] For the challenge of exponential computational complexity faced when solving large-scale TSP problems, this embodiment proposes an approximate optimization strategy based on space partitioning, trading off a controllable accuracy loss for a significant improvement in computational efficiency; this strategy decomposes the global optimization problem into multiple local optimal sub-problems by constructing a hierarchical solution framework, specifically including the following steps:

[0121] S4.1. Use the greedy algorithm to generate an initial feasible solution, form a closed path P0, and calculate its total distance as the benchmark upper bound;

[0122] S4.2. Spatial region division of points on the plane: First, taking the starting point 0 as the origin of the polar coordinate system, establish an angle division criterion; second, divide the plane region covered by the path P0 into k sector sub-regions {R1, R2, …, R k}; finally, select a node set V i = {v1, v2, ..., v i} in each sub-region R m ;

[0123] S4.3. Hierarchical optimization iteration: First, use the improved branch and bound method in step S3 to accurately solve the optimal path P i of the node set V i * in the current layer; second, select the first (k - m) nodes in P i * as the benchmark node set B = {b1, b2, ..., v k-m} for the next layer of optimization; finally, allocate the remaining nodes to the neighborhoods of each benchmark node according to the principle of spatial proximity to form a new candidate node set V j = {v1, v2, …, v t};

[0124] S4.4. Dynamic update mechanism: First, perform local branch and bound optimization on each candidate node set V j ; then, merge the local optimal solutions to form a global approximate solution P′;

[0125] S4.5. Terminate until all nodes are added.

[0126] By dividing the points on the plane and continuously updating the root node to reduce the branches of the branch and bound method, fast calculation is achieved. This hybrid strategy combines the rapidity of the greedy algorithm and the accuracy advantage of the branch and bound method, and is applicable to solving the TSP problem with a large node scale.

[0127] In this embodiment, a total of 35 task points are set, and six groups of task scale gradients n ∈ {10, 15, 20, 25, 30, 35} are set. The unmanned aerial vehicle system configures base stations at 5 different locations K = {k1, ..., k j , ..., k5}, and one homogeneous unmanned aerial vehicle is deployed at each base station; n d represents the node scale critical threshold, and the values are 5, 10, and 15 respectively in the experiment. n d is used as the node scale critical threshold for path planning, and its function is to dynamically regulate the balance between the accuracy and efficiency of the algorithm; when the number of nodes of the path to be planned is less than n d , an optimal solution algorithm based on the branch and bound method is adopted; when the number of nodes of the path to be planned is greater than or equal to n dWhen it comes to this, an improved branch and bound method is adopted to solve its approximate solution.

[0128] As Figure 4 shown, it represents the running time of the algorithm proposed in this embodiment under different numbers of task points when n d is 5, 10, and 15 respectively; through the systematic analysis of the task point scale and the algorithm switching threshold, the coupled influence mechanism of the two on the running time can be revealed; the growth rate of the operation time reflects the change trend of the algorithm time complexity with the expansion of the task scale, and its calculation formula is:

[0129]

[0130] Generally speaking, in the small-scale (10 - 20 task points) task interval, the growth rate of the running time is relatively gentle, with an average value of 0.24 s / task point; when the task scale breaks through 25, the average growth rate suddenly increases to 101.54 s / task point, and the running time of the algorithm increases exponentially with the increase in the number of nodes; therefore, when the number of nodes is small, the parameter n d has little influence on the running time, and the optimal solution exact algorithm shows extremely high efficiency.

[0131] However, when the number of task points increases, the setting of the parameter n d has a greater impact on the running efficiency. The larger n d is, the longer the required running time; when n d is 5, even large-scale node requirements can be completed quickly; while when n d is 15, when dealing with large-scale node requirements, the required running time increases sharply; for large-scale nodes, when the number of nodes is 30, for every increase of 5 in the parameter n d , the algorithm running efficiency increases by 86.84% and 82.41% respectively; when the number of nodes is 35, for every increase of 5 in the parameter n d , the algorithm running efficiency increases by 91.92% and 97.63% respectively.

[0132] As Figure 5 shown, it represents the relationship between the total shortest cruise path length and the path length of the No. 1 UAV cruising alone and the number of task points when n d is 5, 10, and 15 respectively; in the scenario of multi-UAV cooperation, since the task points are assigned to each UAV and the number of task nodes assigned to each UAV is small, the total shortest cruise path length of the system shows strong robustness to the value of n d .

[0133] From Figure 5 it can be seen that for different task point scales, the total shortest cruise path lengths of the systems with n d being 10 and 15 are the same; to more clearly show the parameter nd Regarding the impact on the path length, in this embodiment, a single UAV path sensitivity analysis was also conducted to observe the path length when only UAV No. 1 was sent for cruising, as Figure 5 shown by the last three broken lines (purple, green, light blue) in the upper left legend in

[0134] From Figure 5 it can be seen that in the small-scale (10 - 15 points) task stage, when n d = 5, the path length only increases by 7.55%. When n d = 10 and n d = 15, the path lengths of the schemes are the same, indicating that the optimal solution exact algorithm has good convergence in the solution space of this interval. In the medium-scale (15 - 25 points) task stage, when the threshold parameter n d = 10 and n d = 15, the system path lengths are highly consistent. However, when the n d = 5 scheme is adopted, due to the premature switch to the approximate solution estimation algorithm, the exploration of the solution space is insufficient, and it falls into a local optimal solution, and the growth rate of the path length significantly increases to 11.067 km / node. In the large-scale (n ≥ 25) task stage, the sensitivity of the threshold parameter is significantly enhanced. When the number of task points expands to 30 nodes, the path length of the n d = 10 scheme is 13.59% longer than that of the n d = 15 scheme, and the n d = 5 scheme is further increased by 37.13% compared with the n d = 10 scheme.

[0135] Based on the systematic analysis of the simulation data, the optimal selection of the parameter n d value plays a key trade-off role between algorithm efficiency and solution accuracy. When n d = 10, in the large-scale task scenario, the running time of the algorithm is 82.41% shorter than that of the n d = 5 scheme, and the path length is only 13.59% longer than that of the n d = 15 scheme.

[0136] To deeply explore the comprehensive impact of the priority mechanism on the multi-UAV cooperative path planning, in this embodiment, a systematic comparative experiment was designed to construct a multi-dimensional evaluation framework. The experimental settings include a task point scale gradient n ∈ {10, 15, 20, 25, 30, 35}, and three core performance indicators, namely the shortest cruising path length, algorithm running time, and service quality of the UAV system under the conditions of with and without priority constraints, are respectively investigated to characterize the path planning efficiency, computational complexity, and to quantify the timeliness of task response and the rationality of resource allocation.

[0137] The trade-off characteristics of the system performance are revealed by the simulation results: the priority mechanism exchanges a path length cost of 36.6% - 60.3% for a QoS improvement of 18.2% - 114.7% and reduces the computational time consumption by 66.8%.

[0138] The method of this embodiment first divides the task points into different priority levels and designs a dynamic weight mechanism to drive the high-priority tasks to respond first; secondly, it transforms the global MTSP problem into the clustering of plane point sets and local TSP problems, and realizes collaborative solution by integrating the K-means clustering and branch-and-bound algorithms; aiming at the computational complexity challenge in large-scale task scenarios, an approximate optimization strategy based on space division is proposed, and a multi-level optimization architecture is adopted to balance the solution accuracy and computational efficiency; compared with the traditional heuristic algorithm and branch-and-bound algorithm, the method of the present invention can obtain a better solution in small-scale TSP instances. For large-scale task scenarios, the algorithm achieves an 82.41% - 97.63% improvement in computational efficiency with a path length loss of 13.59% - 37.13%; and through the dynamic weight mechanism, the access timing of high-priority task nodes is optimized and advanced, so that the system response time is improved by 66.8%, and the system comprehensive QoS is improved by 18.2% - 114.7%.

[0139] In addition to the above embodiments, the present invention may have other embodiments. All technical solutions formed by equivalent replacement or equivalent transformation fall within the protection scope required by the present invention.

Claims

1. A UAV path optimization method based on an improved branch and bound algorithm, characterized in that: The following steps are involved: S1. Construct a UAV cruise system; combine the task priority with the shortest path as the goal, construct the optimal path objective function of the UAV cruise, and construct the constraint function according to the mutual exclusivity of task point allocation, battery capacity and task point timing coupling; Construct a system service quality evaluation model; S2, input the task point set and the location of the drone base station, perform task allocation based on the K-means algorithm, introduce variance and dispersion evaluation for clustering screening, and output n mutually exclusive subtask sets; S3, based on the improved branch and bound method, the trajectory planning is carried out, the upper bound is generated by the greedy strategy, the lower bound is calculated according to the different access states of the nodes in the search process, and dynamic pruning is carried out according to the single-step and multi-step backtracking conditions; S4, through the approximate optimization strategy based on space partitioning, combined with the greedy algorithm and the branch and bound method, by dividing the points on the plane, constantly updating the nodes to reduce the branches of the branch and bound method, the calculation is completed; In step S3, generating the upper bound using the greedy strategy specifically includes the following sub-steps: S3.1, starting from the starting node, select the unvisited node closest to the current node as the next visited node; S3.2, repeat the previous step until all nodes are visited; S3.3, return to the starting node to form a complete loop; S3.4, calculate the total distance of the loop as the upper bound; In step S3, the lower bounds are calculated according to different access states of the nodes during the search process; If the search node set S only contains the starting node, then considering the case where the entry and exit of each node are exactly the shortest distances, the calculation formula of the lower bound lb is: Where D is the distance matrix, min1 and min2 represent the minimum and second minimum values ​​in the matrix row respectively; If the search node set S includes the starting node and some intermediate nodes, the calculation formula of the lower bound lb is: Among them, |S| represents the number of visited nodes, \ represents the set difference operation; represents the sum of the distances between adjacent nodes in the search node group, min(D[S[1],:]\S) represents the minimum value from the first node in the search node group to other nodes outside the search node group, and min(D[S[|S|],:]\S) represents the minimum value from the last node in the search node group to other nodes outside the search node group. Represents the minimum sum of two values ​​of other nodes outside the search node group in the distance matrix row; If the search node set S contains all nodes, the lower bound lb is expressed as the complete path length: In step S3, it is determined whether the current node is an end node. When the lower bound is greater than the upper bound and the current node is not the terminal node, perform a single-step backtracking; first remove the most recently added node v k , then select the next candidate node v k+1 , and finally update the search path [S[1], S[2], ..., S[k-1], v k+1 ]; When the lower bound is greater than the upper bound and the current node is a terminal node, perform multi-step backtracking; first remove the terminal nodes continuously until a non-terminal node v is encountered. m Then select v m The next candidate node v m+1 , and finally update the search path to [S[1], S[2], …, S[m-1], v m+1 ]; In step S4, the approximate optimization strategy based on space partitioning decomposes the global optimization problem into multiple local optimal sub-problems by constructing a hierarchical solution framework, which specifically includes the following sub-steps: S4.

1. Use the greedy algorithm to generate the initial feasible solution, form a closed path P0, and calculate its total distance as the benchmark upper bound; S4.

2. Divide the points on the plane into spatial regions: First, take the starting point 0 as the origin of the polar coordinate system and establish the angle division criterion; second, divide the plane area covered by the path P0 into k sector-shaped sub-areas {R1, R2, ..., R k }; Finally, in each sub-region R i Internal selected node set V i = {v1, v2, ..., v m }; S4.3, hierarchical optimization iteration: First, at the current level, the improved branch and bound method in step S3 is used to solve the sub-region node set V i The optimal path P i * ; Secondly, select P i * The first (km) nodes in the middle are used as the reference node set B = {b1, b2, ..., v k-m }; Finally, the remaining nodes are assigned to the neighborhood of each benchmark node according to the principle of spatial proximity to form a new candidate node set V j = {v1, v2, ..., v t }; S4.4, Dynamic Update Mechanism: First, for each candidate node set V j Perform local branch and bound optimization; then, merge the local optimal solutions to form a global approximate solution P′; S4.5, until all nodes join the termination.

2. The method for optimizing the path of a UAV based on an improved branch and bound algorithm according to claim 1, characterized in that: In step S1, the drone cruise system includes drones, drone base stations, and mission points of different priorities. The number of drone base stations is represented by K = {k1, k2, ..., k n }, there are n drone base stations, each of which deploys a homogeneous drone; the mission point set is represented by V = {V1, V2, …, V m }, there are m patrol mission points in total; each mission point is served by one and only one drone, and the mission points are patrolled in order of priority.

3. The method for optimizing the path of a UAV based on an improved branch and bound algorithm according to claim 2, characterized in that: In step S1, the task point set V = {V1, V2, ..., V m } is decomposed into n mutually exclusive subsets u = {U1, U2, ..., U n }, UAV base station k j The service area is represented by U j , then it is necessary to plan the drone to depart from its base station and traverse the area U j The optimal path to return after all the mission points in the cruise is considered; considering the different urgency of the cruise mission points, the mission node priority factor p is introduced i ∈{1, 2, 3}, therefore, the objective function of the path planning problem of UAV cruising is expressed as: in, Indicates that drone j is from base station k j Cruise to subset U j The distance to the first task point in Represents the subset U j The last task point in the corresponding cruise drone base station k is returned j The distance For the subset U j Mid-mission point v i to v i+1 distance.

4. The method for optimizing the path of a UAV based on an improved branch and bound algorithm according to claim 3, characterized in that: In step S1, considering the task point allocation mutual exclusion constraint, battery capacity constraint and task point timing coupling constraint, for any two UAV service areas U i and U j ,satisfy For the subset U j , the path distance of its cruise planning is less than the longest flight distance of the UAV, that is, Among them, L max is the maximum flight distance of each drone; for any two mission nodes v i and v j , if p i <p j ,but p i and p j Represents the task node v i and v j The priority parameter, the smaller the value, the higher the priority; t i and t j Respectively represent the arrival task node v i and v j time, S(p i <p j ) is a conditional statement, indicating that if p i <p j , then the task node v i Must be in the global path sequence before the task node v j Visited earlier.

5. The method for optimizing the path of a UAV based on an improved branch and bound algorithm according to claim 4, characterized in that: In step S1, the service quality of the drone cruise system is quantified and expressed as: Among them, the task priority score It is used to characterize the responsiveness of the UAV cruise system to tasks of different priorities. The priority factor p i The smaller the value, the higher the priority of the task point; its weight ω p It is used to quantify the gain effect of the service order of different priority task points on service quality. The larger the value, the more sensitive the system service quality evaluation model is to priority stratification. The arrival time score is as follows: Among them, the drone arrives at the mission point v i The actual time is t i The latest arrival time is Expected arrival time is Arrival time score S ti It is used to measure the timeliness of the UAV’s response to the mission point, and its weight ω t Reflects the nonlinear impact of the timeliness of the drone’s arrival at the mission point on the service quality; Drone quantity penalty It is used to evaluate the number of drones dispatched by the system, s is the number of dispatched drones, n is the total number of available drones, and its weight ω u Characterize the increase in costs caused by the expansion of drone swarm size; Energy Consumption Score E act is the actual energy consumption, E min and E max are the theoretical minimum energy consumption and the maximum allowable energy consumption, respectively, and their weights ω e Used to measure the hard limits of drone endurance on mission sustainability.

6. The method for optimizing the path of a UAV based on an improved branch and bound algorithm according to claim 1, characterized in that: The step S2 specifically includes the following sub-steps: S2.

1. The screening variance fd is introduced as the first evaluation index, which is defined as the variance of the distance from the center point of n clusters to the corresponding UAV layout point after K-means clustering. Its mathematical expression is: <h2 style=";text-align:left;direction:ltr">fd = Var(d1, d2,..., d)<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> ); Among them, d i Represents the Euclidean distance from the center point of the i-th cluster to the corresponding drone layout point; by adjusting the threshold of fd, the scale of the screening results is controlled. The larger the fd, the more feasible clustering solutions are obtained; S2.2, introduce the dispersion variable Dv as the second evaluation index, which is defined as the difference between the number of nodes contained in the largest cluster and the smallest cluster after K-means clustering. Its mathematical expression is: Dv=max(|C1|,|C2|,...,|C n |)-min(|C1|,|C2|,...,|C n |); Among them, |C i | represents the number of stages of the i-th cluster; the threshold of Dv is adjusted according to actual needs. The larger the allowed Dv value is, the more feasible clustering solutions are obtained.

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