Unmanned aerial vehicle path optimization method based on improved branch and bound algorithm

Abstract

The invention discloses an unmanned aerial vehicle path optimization method based on an improved branch and bound algorithm, and the method comprises the steps: dividing task points into different priority levels, and designing a dynamic weight mechanism to drive a high-priority task to respond preferentially; secondly, a global MTSP problem is converted into clustering of a plane point set and a local TSP problem, and collaborative solving is achieved by fusing K-means clustering and a branch and bound algorithm; for the computational complexity challenge in a large-scale task scene, an approximate optimization strategy based on space division is provided, and a multi-stage optimization architecture is adopted to balance the solution precision and the computational efficiency; compared with a traditional heuristic algorithm and a branch and bound algorithm, the method has the advantages that a better solution can be obtained in a small-scale TSP instance, and the calculation efficiency of the algorithm is greatly improved for a large-scale task scene; and the access time sequence of the high-priority task nodes is optimized and preposed through a dynamic weight mechanism, so that the response timeliness and the comprehensive QoS of the system 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 homogenize task requirements based on the assumption that the requirements of task points are equal, but fail 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 grows exponentially with the increase of the problem size. 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: 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; 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, the points on the plane are divided and the nodes are continuously updated to reduce the branches of the branch and bound method and complete the calculation.

[0005] The technical solution further defined in the present invention is: Furthermore, 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 expressed as 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.

[0006] As described above, in the UAV path optimization method based on the improved branch and bound algorithm, in step S1, the task point set V={V1,V2,...,V m} is decomposed into n mutually exclusive subsets , 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.

[0007] As described above, in a UAV path optimization method based on an improved branch and bound algorithm, in step S1, considering the mutual exclusion constraint of task point allocation, battery capacity constraint and task point timing coupling constraint, for any two UAV service areas U i and U j ,satisfy ; For subset U j , the path distance of its cruise planning is less than the longest flight distance of the UAV, that is, , where 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.

[0008] As described above, in the UAV path optimization method based on the improved branch and bound algorithm, in step S1, the service quality of the UAV cruise system is quantified and expressed as: Among them, the task priority score , 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 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 Used to measure the timeliness of the drone's response to the mission point, and its weight Reflects the nonlinear impact of the timeliness of the drone’s arrival at the mission point on the service quality; Drone quantity penalty , 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 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, and their weights are Used to measure the hard limits of drone endurance on mission sustainability.

[0009] As described above, in the UAV path optimization method based on the improved branch and bound algorithm, 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: fd=Var(d1,d2,...,d n ); 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.

[0010] As described above, in the UAV path optimization method based on the improved branch and bound algorithm, 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.

[0011] As described above, in a method for optimizing the path of a UAV based on an improved branch and bound algorithm, in step S3, the lower bound is calculated according to different access states of nodes in 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: .

[0012] As described above, in the UAV path optimization method based on the improved branch and bound algorithm, 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. mThen 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 ].

[0013] As described above, in the UAV path optimization method based on the improved branch and bound algorithm, 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 O 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 ; Secondly, select The first (km) nodes in the middle are used as the benchmark 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.

[0014] The beneficial effects of the present invention are: In the present invention, firstly, the task points are divided into different priority levels, and a dynamic weight mechanism is designed to drive high-priority tasks to respond first; secondly, the global MTSP problem is transformed into the clustering of plane point sets and the local TSP problem, and a collaborative solution is achieved by integrating K-means clustering and branch-and-bound algorithm; in view of 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 used 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 better solutions 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 the access timing of high-priority task nodes is optimized in advance through a dynamic weight mechanism, which improves the system response time by 66.8% and the system comprehensive QoS by 18.2%-114.7%. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a schematic diagram of the overall process of the present invention; Figure 2 This is a schematic diagram of a UAV cruise system in an embodiment of the present invention; Figure 3 Schematic diagram of the flow of the branch and bound algorithm in an embodiment of the present invention; 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; Figure 5 Graph showing the relationship between the shortest path length and the path length of a single UAV and the number of mission points under different thresholds in an embodiment of the present invention. DETAILED DESCRIPTION

[0016] This embodiment provides a method for optimizing the path of a UAV based on an improved branch and bound algorithm. Figure 1 As shown, the following steps are included: 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, 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.

[0017] like Figure 2 As shown in the figure, the drone cruise system includes drones, drone base stations and mission points of different priorities. The drone cluster will perform task allocation and cruise all mission points in order of priority to ensure service quality and optimal path; the number of drone base stations is expressed as 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 cruise mission points in total; through reasonable task allocation, it is ensured that each mission point has only one drone serving; through reasonable arrangement of drone paths, it is ensured that the mission points are cruised in order of priority.

[0018] This embodiment can be regarded as a multi-depot multiple traveling salesman problem (MD-MTSP), where the task point set V = {V1, V2, ..., V m} is decomposed into n mutually exclusive subsets , 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 completing all the mission points.

[0019] 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.

[0020] Considering the mutual exclusion 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 ,satisfy ; For subset U j , the path distance of its cruise planning is less than the longest flight distance of the UAV, that is, , where 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.

[0021] In order to better evaluate the service quality of the system, the service quality of the drone cruise system is quantified and expressed as: Among them, the task priority score , 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 It is used to quantify the gain effect of the service order of task points with different priorities on service quality. The larger the value, the more sensitive the system service quality evaluation model is to priority stratification.

[0022] 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 Used to measure the timeliness of the drone's response to the mission point, and its weight Reflects the nonlinear impact of the timeliness of the drone's arrival at the mission point on QoS.

[0023] Drone quantity penalty , 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 Characterizes the cost increase caused by the expansion of drone swarm scale, and its negative weight design is intended to suppress resource redundancy; Energy Consumption Score , E act is the actual energy consumption, E min and Emax are the theoretical minimum energy consumption and the maximum allowable energy consumption, and their weights are Used to measure the hard limits of drone endurance on mission sustainability.

[0024] 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.

[0025] In this embodiment, the collaborative solution is achieved by integrating K-means clustering and branch and bound algorithm. The specific implementation steps of the K-means algorithm are as follows: 1) Given the number of clusters n and the data set to be processed 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; 2) For each group of initialized center points, record them as C={c1,c2,...,c n}; 3) For each sample x in the dataset i , calculate its Euclidean distance with each cluster center, and assign it to the cluster corresponding to the nearest cluster center; 4) Based on the current cluster assignment results, recalculate the center point of each cluster: , where |S j | represents the number of samples in the jth cluster; calculate the sum of squared errors of all clusters; 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. The maximum number of iterations t is reached. max ; iii. The sum of squared distances from all samples to the cluster center converges; 6) Finally, the data set M is divided into n non-overlapping subsets, and the corresponding cluster center sets are obtained.

[0026] In the practical application of K-means clustering algorithm, clustering results are often random and diverse. In order to screen out solutions 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: S2.1. Considering that the average distance between the node group and the corresponding UAV layout point should be kept relatively balanced, 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: fd=Var(d1,d2,...,d n ); Among them, d i It represents the Euclidean distance from the center point of the i-th cluster to the corresponding UAV 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.

[0027] S2.2. In order to measure the balance of the number of tasks in each cluster, the dispersion variable Dv is introduced as the second evaluation index. It 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: 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.

[0028] S3. Based on the improved branch and bound method, trajectory planning is performed, the upper bound is generated using a greedy strategy, the lower bound is calculated according to the different access states of the nodes during the search process, and dynamic pruning is performed according to the single-step and multi-step backtracking situations.

[0029] After the clustering is completed in step S2, the UAV cluster collaborative path planning problem is converted into a combinatorial optimization problem of multiple traveling salesman problems (TSP).

[0030] In order to better illustrate the improved branch and bound algorithm used in this embodiment, the traditional branch and bound algorithm is introduced below. Figure 3 As shown, the following steps are included: 1) Initialize the search node set and store the current node group; 2) Calculate the upper bound formed by the storage node; 3) Select the node to be expanded from the storage node set according to predefined rules; 4) Calculate the lower bound after expanding the new node; 5) If the lower bound is smaller than the upper bound, add the new node to the set, update the current path and repeat steps 3) and 4); 6) If the lower bound is greater than or equal to the upper bound, backtrack to the previous node and remove the new node; 7) If the stored node set is empty and the lower bound is greater than the upper bound, update the upper bound; 8) Terminate the algorithm when the search tree traversal is completed or the preset computation time limit is reached.

[0031] In the traditional branch and bound process, the calculation of the upper and lower bounds is a key factor in determining the efficiency of the algorithm. The upper bound in this embodiment adopts a greedy algorithm strategy, which specifically includes the following 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.

[0032] The lower bound calculation in this embodiment is divided into the following three cases according to the access status of the node during the search process: 1) 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 rows respectively.

[0033] 2) 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 sum of the smallest two values ​​of other nodes outside the search node group in the distance matrix row; in this case, the calculation formula of lb can be expressed as the sum of the distances to adjacent nodes in the search node group, half of the minimum value of the nodes on both sides to other nodes (except the nodes in the search node group), and half of the sum of the smallest two values ​​in the distance matrix row to other nodes.

[0034] 3) If the search node set S contains all nodes, the lower bound lb is expressed as the complete path length: .

[0035] Node backtracking is also the key in the branch and bound process. In terms of node backtracking strategy, this embodiment adopts the following two processing mechanisms according to whether the current node is an end node: 1) When the lower bound is greater than the upper bound and the current node is not the terminal 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 ].

[0036] 2) When the lower bound is greater than the upper bound and the current node is the 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 ].

[0037] S4. Through the approximate optimization strategy based on space partitioning, combined with the greedy algorithm and the branch and bound method, the points on the plane are divided and the nodes are continuously updated to reduce the branches of the branch and bound method and complete the calculation.

[0038] In view of the exponential computational complexity challenge faced when solving large-scale TSP problems, this embodiment proposes an approximate optimization strategy based on space partitioning, which significantly improves computational efficiency at the cost of controllable precision. This strategy decomposes the global optimization problem into multiple local optimal sub-problems by constructing a hierarchical solution framework, which specifically includes the following 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 O 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 accurately solve the sub-region node set V i The optimal path ; Secondly, select The first (km) nodes in the middle are used as the benchmark 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.

[0039] 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 can be achieved. This hybrid strategy combines the advantages of the rapidity of the greedy algorithm and the accuracy of the branch and bound method, and is suitable for solving TSP problems with large node scales.

[0040] In this embodiment, a total of 35 mission points are set, six groups of mission scale gradients n∈{10,15,20,25,30,35} are set, and the UAV system is equipped with five base stations K={k1,...,k j ,...,k5}, each base station deploys a homogeneous drone; n d represents the critical threshold of node scale, which is 5, 10, and 15 in the experiment. d As the critical threshold of the node scale of path planning, its role is to dynamically adjust the balance between the accuracy and efficiency of the algorithm; when the number of nodes on the path to be planned is less than n d When the number of nodes in the path to be planned is greater than or equal to n, the optimal solution algorithm based on the branch and bound method is adopted; when the number of nodes in the path to be planned is greater than or equal to n d When , the improved branch and bound method is used to obtain the approximate solution.

[0041] like Figure 4 As shown, it indicates n d The running time of the algorithm proposed in this embodiment is 5, 10, and 15 respectively, with different numbers of task points. Through the systematic analysis of the task point scale and the algorithm switching threshold, the coupling influence mechanism of the two on the running time can be revealed. The growth rate of the operation time reflects the changing trend of the algorithm time complexity with the expansion of the task scale, and its calculation formula is: In general, in the small-scale (10-20 task points) task range, the running time growth rate is relatively slow, with an average of 0.24s / task point; when the task scale exceeds 25, the average growth rate increases sharply to 101.54s / 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 The impact on running time is small, and the optimal solution exact algorithm shows extremely high efficiency.

[0042] However, when the number of task points increases, the parameter n dThe setting has a great influence on the operation efficiency. d The larger the value, the longer the running time required. d When n is 5, even large-scale node requirements can be completed quickly; d When the parameter n is 15, the required running time increases sharply when dealing with the needs of large-scale nodes. For large-scale nodes, when the number of nodes is 30, the parameter n d For every increase of 5, the algorithm efficiency increases by 86.84% and 82.41% respectively; when the number of nodes is 35, the parameter n d For every increase of 5, the algorithm operation efficiency increases by 91.92% and 97.63% respectively.

[0043] like Figure 5 As shown, it indicates n d The relationship between the total shortest cruise path length and the path length of UAV 1 when it cruises alone and the number of mission points when the number of mission points is 5, 10, and 15 respectively; in the scenario of multi-UAV collaboration, since the mission points are assigned to each UAV, each UAV is assigned fewer mission nodes, so the total shortest cruise path length of the system is d The value of shows strong robustness.

[0044] from Figure 5 It can be seen that for different task point scales, n d The total length of the shortest cruise path of the system for schemes 10 and 15 is consistent; in order to more clearly show the parameter n d Regarding the impact of path length, this embodiment also conducts a single UAV path sensitivity analysis to observe the path length when only UAV No. 1 is sent for cruising, such as Figure 5 This is shown by the last three broken lines (purple, green, and light blue) in the legend in the upper left corner.

[0045] Depend on Figure 5 It can be seen that in the small-scale (10-15 points) task stage, n d = 5, the path length increases by only 7.55%, n d =10 and n d =15 solutions have the same path length, indicating that the optimal solution exact algorithm converges well in the solution space in 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 length remains highly consistent; however, when n d =5, due to the early switching to the approximate solution estimation algorithm, the solution space is not fully explored, and it falls into the local optimal solution. The path length growth rate is significantly improved to 11.067km / node; in the large-scale (n≥25) task stage, the sensitivity of the threshold parameter is significantly enhanced; when the number of task points is expanded to 30 nodes, nd =10 The path length of the solution is shorter than n d =15 plan increases by 13.59%, while n d =5 scheme compared to n d =10 scenario further increases by 37.13%.

[0046] Comprehensive analysis of the simulation data, parameter n d The optimal choice of the value plays a key role in the trade-off between algorithm efficiency and solution accuracy; when n d =10, the algorithm runs in a shorter time than n in large-scale task scenarios. d =5 solution is shortened by 82.41%, and the path length is shorter than n d =15 plan only increased by 13.59%.

[0047] In order to deeply explore the comprehensive impact of the priority mechanism on the collaborative path planning of multiple UAVs, this embodiment designs a systematic comparative experiment and constructs a multi-dimensional evaluation framework. The experiment sets the task point scale gradient n∈{10, 15, 20, 25, 30, 35}, and examines the three core performance indicators of the UAV system's shortest cruising path length, algorithm running time, and service quality with and without priority constraints, respectively, to characterize the path planning efficiency, computational complexity, and quantitative task response timeliness and resource allocation rationality.

[0048] The simulation results reveal the trade-off characteristics of system performance: the priority mechanism introduces a 36.6%-60.3% path length cost in exchange for an 18.2%-114.7% improvement in QoS and a 66.8% reduction in computational time.

[0049] The method of this embodiment first divides the task points into different priority levels, and designs a dynamic weight mechanism to drive high-priority tasks to respond first; secondly, the global MTSP problem is transformed into a clustering of plane point sets and a local TSP problem, and a collaborative solution is achieved by integrating 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 used 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 better solutions 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 the access timing of high-priority task nodes is optimized and advanced through a dynamic weight mechanism, which improves the system response time by 66.8% and the system comprehensive QoS by 18.2%-114.7%.

[0050] In addition to the above embodiments, the present invention may also have other implementation modes. Any technical solution formed by equivalent replacement or equivalent transformation falls 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 performed 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, the points on the plane are divided and the nodes are continuously updated to reduce the branches of the branch and bound method and complete the calculation.

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 , 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 mutual exclusion constraint of task point allocation, battery capacity constraint and task point timing coupling constraint, for any two UAV service areas U i and U j ,satisfy ; For subset U j , the path distance of its cruise planning is less than the longest flight distance of the UAV, that is, , where 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 , 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 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 Used to measure the timeliness of the drone's response to the mission point, and its weight Reflects the nonlinear impact of the timeliness of the drone’s arrival at the mission point on the service quality; Drone quantity penalty , 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 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, and their weights are 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.

7. 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 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.

8. 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 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: 。 9. The method for optimizing the path of a UAV based on an improved branch and bound algorithm according to claim 8, characterized in that: 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 ].

10. 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 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 O as the origin of the polar coordinate system and establish the angle division criteria; Secondly, the plane area covered by path P0 is divided 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 ; Secondly, select The first (km) nodes in the middle are used as the benchmark 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.

Images