Multi-unmanned aerial vehicle cooperative regional patrol path planning method based on hierarchical optimization

Abstract

The invention discloses a multi-unmanned aerial vehicle cooperative regional patrol path planning method based on hierarchical optimization, and the method comprises the steps: firstly, abstracting a task space containing a base station and a plurality of target points into a weighted undirected complete graph, and building a mathematical model with a target of minimizing the total completion time of a system and the standard deviation of task time; then solving is carried out through a hierarchical strategy; firstly, k-means clustering is adopted to carry out initial task allocation; solving a traveling salesman problem for each task cluster by using a simulated annealing algorithm, generating an initial path, and performing local optimization by using a 2-OPT algorithm; and finally, carrying out global collaborative optimization by adopting adaptive large-scale neighborhood search, dynamically adjusting task allocation and paths through a cross-unmanned aerial vehicle damage and repair operator, and carrying out iterative optimization according to a composite acceptance criterion and an adaptive mechanism to generate a near-optimal scheme. According to the method, through tight coupling of task allocation and path planning, the defect that a traditional method is prone to local optimization is effectively overcome, and joint optimization of completion time and load balancing is achieved.

Description

Technical Field

[0001] This invention belongs to the field of UAV cooperative control technology, and in particular relates to a multi-UAV cooperative area patrol path planning method based on hierarchical optimization. Background Technology

[0002] With the increasing demand for automated and intelligent inspections from modern industries, such as in large-scale photovoltaic power plants, power transmission networks, vast farmlands, and post-disaster area assessments, inspection tasks are exhibiting unprecedented requirements for scale, precision, and timeliness. Against this backdrop, traditional single-drone operation modes, due to physical bottlenecks such as endurance, payload limitations, and coverage efficiency, are no longer sufficient to meet the demands for efficient and comprehensive tasks. Therefore, collaborative swarm systems composed of multiple drones have become a key technological approach to solving such complex problems. Multi-drone collaborative inspection is modeled in operations research as a complex multi-objective combinatorial optimization problem, essentially a variant of the multi-traveling salesman problem. The core challenge lies in generating a complete collaborative strategy that includes task allocation and path sequences. This strategy must achieve an optimal balance between two mutually constraining key performance indicators: task completion time and task load fairness, to maximize overall operational efficiency and the system's sustainable operation capability.

[0003] Existing technologies primarily rely on heuristic algorithms for solving multi-UAV path planning problems. In implementing these paths, these methods generally employ a decoupling strategy: first, target point sets are allocated to each UAV according to some rule or preliminary optimization, forming a task allocation scheme; then, with the allocation results fixed, path planning is performed independently for each UAV's task subset to optimize its flight sequence. Regarding optimization objectives, most schemes focus on efficiency metrics, such as minimizing the total task completion time or total flight distance, to improve the overall speed and economy of the operation. While some improved methods attempt to incorporate load balancing considerations, they typically employ simple optimization techniques such as greedy strategies, making local adjustments after fixing the allocation scheme to improve fairness within a limited scope.

[0004] However, the aforementioned existing technologies have several deep-seated flaws. First, their commonly used "allocation before planning" decoupling strategy artificially severs the inherent strong coupling between task allocation and path planning. This leads to suboptimal decisions in the initial allocation phase severely restricting the optimization space of subsequent path planning, making it difficult to approach the global optimum. Second, the existing technologies suffer from a serious imbalance in their optimization objectives, unilaterally pursuing efficiency while neglecting or weakening load fairness. This approach, which sacrifices long-term system robustness and operational economy, cannot meet the demands of high reliability and low-cost continuous operation in practical applications. Finally, even when a few algorithms attempt to balance fairness, they often employ simple greedy strategies and other methods with insufficient ability to explore the solution space, easily getting trapped in local optima. They fail to find a high-quality balance between the conflicting objectives of efficiency and fairness, ultimately resulting in poor overall performance of the generated collaborative strategy. Summary of the Invention

[0005] Purpose of the invention: The purpose of this invention is to provide a multi-UAV collaborative regional patrol path planning method based on hierarchical optimization, which solves the defects of existing multi-UAV path planning methods such as decoupling of task allocation and path planning, single optimization objective, and easy getting trapped in local optima.

[0006] Technical solution: The multi-UAV collaborative area patrol path planning method of the present invention includes the following steps:

[0007] System Modeling: The task space, which includes a central base station and multiple target points to be inspected, is abstracted into a weighted undirected complete graph, where vertices represent spatial locations and edge weights represent flight costs; and the allocation variables and path decision variables between the UAV and the target points are defined, and a mathematical model is constructed with the joint optimization objective of minimizing the total system completion time and minimizing the standard deviation of the task time.

[0008] Formal definition of the problem: The mathematical model is defined as a multi-objective optimization problem, and the constraints of the multi-objective optimization problem are set.

[0009] Initial task allocation: Using the k-means clustering algorithm, the target points are divided into multiple task clusters equal to the number of drones based on their geographic spatial location, and each task cluster is assigned to one drone.

[0010] Individual path construction: For each task cluster, with the cluster centroid as the reference point, the inspection task of each UAV is modeled as a traveling salesman problem, and the simulated annealing algorithm is used to solve the traveling salesman problem to generate an initial path to all assigned target points;

[0011] Local path optimization: For each initial path, the 2-OPT local search algorithm is used for optimization. By checking and eliminating intersecting edges in the path, each individual path reaches a local optimum.

[0012] Global collaborative optimization: The origin and destination of all optimized paths are unified to the real base station. An adaptive large-scale neighborhood search framework is adopted. By alternately executing cross-UAV destruction and repair operators, the task allocation and path structure are dynamically adjusted. Based on the multi-level composite acceptance criteria and operator adaptive weight adjustment mechanism, the total system completion time and task load fairness are iteratively optimized, and finally a near-optimal collaborative inspection scheme is generated.

[0013] This invention constructs an optimization model that balances minimizing total completion time and ensuring fairness in task load by using system modeling and formal definition of multi-objective problems. Initial task allocation based on k-means clustering achieves spatially balanced partitioning of target points, and the combination of simulated annealing and 2-OPT local search algorithms effectively improves the rationality and local optima of single-machine paths. Furthermore, an adaptive large-scale neighborhood search framework is introduced, which achieves deep collaborative optimization of task allocation and path planning through cross-path task redistribution and multi-level acceptance criteria. This significantly overcomes the shortcomings of traditional methods, such as decoupling between the two, single optimization objective, and susceptibility to local optima. Finally, a highly efficient and load-balanced UAV collaborative patrol scheme is generated at the global level.

[0014] Preferably, the construction process of the weighted undirected complete graph includes:

[0015] The entire inspection task space is abstracted as a weighted undirected complete graph. ,in Represents a vertex set, consisting of a central base station. and A set of target points to be inspected Composition, that is Each vertex Having two-dimensional Euclidean space coordinates edge set Defined as connecting all vertex pairs The set of edges, where the weight of each edge is defined by the Euclidean distance between the vertices, representing the flight cost of the drone between the two points, i.e.:

[0016]

[0017] in, , and They represent and The position coordinates of the two points, the drone is Composed of isomorphic drones, assembled as at a constant speed flight.

[0018] By abstracting the inspection space into a weighted undirected complete graph with the central base station and target point as vertices and Euclidean distance as edge weights, a unified and quantified flight cost model was constructed, providing a precise mathematical basis and global optimization premise for subsequent multi-UAV cooperative path planning.

[0019] Preferably, the process of constructing the mathematical model of the joint optimization objective includes:

[0020] Define variables Let $\mathbf{i}$ represent the association variable between the target point $i$ and the drone $k$. If target point $i$ is served by drone $k$, that is, target point $i$ is assigned to drone $k$, then $\mathbf{i}$ is the associated variable. ,otherwise ;

[0021] Define completion time Define a binary decision variable to represent the time taken by any drone to complete its mission. This indicates whether drone k flies directly from vertex i to vertex j, and the total flight distance of drone k. and task time They are respectively:

[0022]

[0023]

[0024] Then the system completion time for:

[0025]

[0026] The load balancing degree is quantified by the standard deviation of all drone mission times. First, the average mission time is calculated. :

[0027]

[0028] Define the fairness index F as:

[0029] .

[0030] By introducing task allocation and path decision variables, and taking the total system completion time and the standard deviation of task time as optimization objectives, the task allocation and path planning processes are effectively unified. While pursuing the maximization of overall efficiency, the load balance among multiple drones is also taken into account, laying a precise quantitative foundation for generating a collaborative inspection plan that balances efficiency and fairness.

[0031] Preferably, the formal definition of the problem includes:

[0032]

[0033] st (1)

[0034] (2)

[0035] (3)

[0036] (4)

[0037] (5)

[0038] in and These represent the target allocation and flight decision sets, respectively. and The two flight decisions of UAV k are: taking off from the base station (i=0) and returning to the base station (j=0). The constraints are: (1) Ensure that each inspection target point is visited by only one UAV; (2) Ensure that the actual flight path of the UAV strictly follows the assigned task; (3) Ensure that once the UAV flies into an intermediate target point, it must fly out from that point to form a continuous trajectory; (4) Stipulate that each UAV must start from the base station and eventually return to the base station to form a complete closed-loop task; (5) Define the values ​​of all decision variables.

[0039] The formal definition of this problem, by constructing a complete set of constraints, strictly ensures the completeness and non-conflictability of task allocation, the continuity and logical consistency of flight paths, and the closure of the mission paths of each UAV. This transforms the complex multi-UAV collaborative patrol problem into a rigorous and solvable mathematical optimization model, laying a solid theoretical foundation for subsequent algorithms to implement feasible planning schemes that meet the requirements of actual tasks.

[0040] Preferably, the initial task allocation process includes:

[0041] The input is the set of coordinates of all target points. Given the number of drones K, an optimal target point partitioning scheme is found through iterative optimization. The objective function is to minimize the sum of squares within the cluster.

[0042]

[0043] in, It is a task cluster The centroid is calculated using the following formula:

[0044]

[0045] Each centroid This serves as a temporary takeoff and landing base station for the corresponding UAV k in the next stage of path construction.

[0046] The initial task allocation process uses the k-means clustering algorithm to efficiently divide spatially adjacent target points into task clusters consistent with the number of drones. The cluster centroid is used as a temporary base station to generate an initial, internally compact task set for each drone, thus laying a good spatial structural foundation for achieving load balancing and subsequent efficient individual path planning.

[0047] Preferably, the process of constructing the individual path includes:

[0048] For a drone k, a path is a set of destination points it visits. A permutation or combination, represented as a sequence The total cost of the path is the flight distance. Defined as:

[0049]

[0050] In each iteration, the 2-OPT flip operation is used as the neighborhood operator, starting from the current solution. Generate a new solution Calculate the cost difference between the old and new solutions. The decision on whether to accept the new solution is based on the Metropolis criterion:

[0051]

[0052] Where T is the current system temperature;

[0053] Set initial temperature And cool it down according to an exponential cooling strategy: ,in ∈(0,1) is the cooling coefficient. This indicates the temperature of the previous iteration. This represents the temperature after cooling according to the cooling strategy at the current iteration. In the early stages of the algorithm when the temperature is high, it is more likely to accept poor solutions; in the later stages when the temperature is low, it tends to accept only good solutions in order to converge to a high-quality solution.

[0054] The individual path construction process solves the traveling salesman problem using the simulated annealing algorithm and generates new paths using the 2-OPT flip operation. Combined with the exponential cooling strategy and the Metropolis acceptance criterion, the algorithm has strong global exploration capabilities in the early stage to escape local optima, and strengthens local development in the later stage to achieve stable convergence. This allows the algorithm to efficiently generate near-optimal UAV inspection paths for each task cluster.

[0055] Preferably, the local path optimization process includes:

[0056] For a given path Iterate through all non-adjacent edge pairs, such as and Determine if reconnecting edges is possible. and To shorten the total path length, the conditions for performing this operation are:

[0057]

[0058] If the conditions are met, the swap is performed, and its topological effect is equivalent to swapping the original path... and Flip the subsequences between them; iterate this process repeatedly until there are no edge pairs in the path that satisfy the above conditions. At this point, the path reaches a 2-OPT local optimum.

[0059] This local path optimization process systematically detects and eliminates intersecting edges in the path using the 2-OPT algorithm, which can effectively shorten the total flight distance of a single path, thereby further improving the path quality at the individual path level and enabling it to reach a local optimum.

[0060] Preferably, the cross-UAV damage and repair operator includes:

[0061] Four cross-UAV neighborhood operators are defined for use from the current solution Generate neighborhood solutions :

[0062] Swap Operator: From two drones k and Randomly select a target point from each of the paths. and and exchange them;

[0063] Migration operator: Removes a target point from the path of drone k. and in drones Find the best insertion position in the path. , making The path increment is minimized, and the optimal insertion position is determined based on the following formula:

[0064]

[0065] in Indicates drone The number of target points included in the path. and This represents the two target points corresponding to the insertion position, that is... insert ;

[0066] Cross-swap operator: Select one edge in the paths of each of the two drones and swap all path segments after these two edges;

[0067] Balance operator: From the current path leading to the maximum completion time Select a target point and move it to the point with the shortest current path. In this way, fairness indicators can be directly optimized.

[0068] This global collaborative optimization process introduces four cross-UAV neighborhood operators—exchange, migration, cross-exchange, and balancing—to achieve dynamic redistribution of tasks and adjustment of path structure across different UAV paths. This not only effectively breaks the local optimum limitation of single-UAV path optimization but also collaboratively optimizes the total completion time and load balance at the system level, thereby significantly improving the overall performance and fairness of the multi-UAV collaborative patrol scheme.

[0069] Preferably, the multi-level composite acceptance criteria include:

[0070] For the generated new solution A three-tiered criterion is used to determine whether to accept it as the new current solution:

[0071] Global optimality criterion: If the completion time of the new solution is... Better than the historical best solution ,Right now If so, then it is unconditionally accepted;

[0072] Balance improvement criterion: If the completion time of the new solution is similar to that of the historical best solution. However, its fairness indicators If it's better, then accept it;

[0073] Simulated annealing criterion: For other cases, accept the inferior solution with a certain probability in order to escape the local optimum. The acceptance probability is:

[0074]

[0075] in, This is the current temperature of ALNS. It is a composite cost function that incorporates changes in completion time, total path length, and fairness: ,in , and These represent the changes in completion time, total path length, and fairness, respectively. , and These represent the weighted weights for completion time, total path length, and fairness changes, respectively.

[0076] This multi-level composite acceptance criterion, by integrating three mechanisms—global optimum, balanced improvement, and simulated annealing—not only ensures the continuous optimization of the algorithm's overall efficiency and proactive improvement of load balancing, but also retains the ability to accept temporary poor solutions with a controllable probability during the search process. This effectively enhances the algorithm's comprehensive ability to escape local optimum traps and explore better global solutions.

[0077] Preferably, the operator adaptive weight adjustment mechanism includes:

[0078] At the end of an iteration segment, a score is given based on the operator's performance in that segment. and number of times used Update its weights:

[0079]

[0080] in ∈[0,1] is the response factor, and operators with higher scores will have a greater probability of being selected in subsequent iterations.

[0081] This adaptive weight adjustment mechanism dynamically tracks the historical performance of different neighborhood operators and adjusts their selection probabilities in a feedback manner, enabling the algorithm to autonomously tend to use more effective search strategies in the current problem-solving stage, thereby significantly improving the intelligence of the optimization process and the overall search efficiency.

[0082] Beneficial Effects: Compared with existing technologies, this invention has the following significant advantages: 1. By using hierarchical optimization and adaptive large-scale neighborhood search, task allocation and path planning are tightly coupled, effectively overcoming the shortcomings of traditional decoupling methods that are prone to getting trapped in local optima. This achieves joint optimization of total system completion time and load balancing, resulting in a collaborative inspection scheme with superior overall performance. 2. By using the task time standard deviation as the core optimization objective, the load balancing among multiple UAVs is significantly improved, avoiding excessive wear and tear on individual UAVs. This enhances the stability of the UAV group under high-intensity continuous operation and effectively extends the overall service life of the system. 3. Combining simulated annealing, 2-OPT local search, and adaptive operator selection mechanisms, this scheme possesses both powerful global exploration and refined local optimization capabilities. It can quickly respond to changes in complex task spaces, efficiently generate high-quality feasible paths, and has good engineering practicality. 4. This integrated collaborative optimization framework takes into account both operational efficiency (total completion time) and economy (load balancing), making it widely applicable and of significant practical value in wide-area collaborative operation scenarios requiring high efficiency and high reliability, such as power grid inspection, emergency rescue, agricultural surveying, and urban logistics. Attached Figure Description

[0083] Figure 1This is a schematic diagram of the method flow of the present invention;

[0084] Figures 2-6 Here is an example of the path planning results of the present invention and the comparison method ( Figure 2-5 In order: CWS, Random, MOPSO, GNA, and this invention).

[0085] Figures 7-8 This provides a quantitative comparison of the path planning results of the present invention and the comparative method. Detailed Implementation

[0086] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0087] This invention provides a multi-UAV collaborative area patrol path planning method based on hierarchical optimization, such as... Figure 1 As shown, it includes the following steps:

[0088] System Modeling: The task space, which includes a central base station and multiple target points to be inspected, is abstracted into a weighted undirected complete graph, where vertices represent spatial locations and edge weights represent flight costs; and the allocation variables and path decision variables between the UAV and the target points are defined, and a mathematical model is constructed with the joint optimization objective of minimizing the total system completion time and minimizing the standard deviation of the task time.

[0089] Formal definition of the problem: The mathematical model is defined as a multi-objective optimization problem, and the constraints of the multi-objective optimization problem are set.

[0090] Initial task allocation: Using the k-means clustering algorithm, the target points are divided into multiple task clusters equal to the number of drones based on their geographic spatial location, and each task cluster is assigned to one drone.

[0091] Individual path construction: For each task cluster obtained in step S3, with the cluster centroid as the reference point, the inspection task of each UAV is modeled as a traveling salesman problem, and the simulated annealing algorithm is used to solve the traveling salesman problem to generate an initial path to all assigned target points;

[0092] Local path optimization: For each initial path generated in step S4, the 2-OPT local search algorithm is used for optimization. By checking and eliminating the intersecting edges in the path, each individual path reaches a local optimum.

[0093] Global collaborative optimization: The origin and destination of all optimized paths are unified to the real base station. An adaptive large-scale neighborhood search framework is adopted. By alternately executing cross-UAV destruction and repair operators, the task allocation and path structure are dynamically adjusted. Based on the multi-level composite acceptance criteria and operator adaptive weight adjustment mechanism, the total system completion time and task load fairness are iteratively optimized, and finally a near-optimal collaborative inspection scheme is generated.

[0094] Furthermore, the construction process of the weighted undirected complete graph includes:

[0095] The entire inspection task space is abstracted as a weighted undirected complete graph. ,in Represents a vertex set, consisting of a central base station. and A set of target points to be inspected Composition, that is Each vertex Having two-dimensional Euclidean space coordinates edge set Defined as connecting all vertex pairs The set of edges, where the weight of each edge is defined by the Euclidean distance between the vertices, representing the flight cost of the drone between the two points, i.e.:

[0096]

[0097] in, , and They represent and The position coordinates of the two points, the drone is Composed of isomorphic drones, assembled as at a constant speed flight.

[0098] Furthermore, the process of constructing the mathematical model for the joint optimization objective includes:

[0099] Define variables Let $\mathbf{i}$ represent the association variable between the target point $i$ and the drone $k$. If target point $i$ is served by drone $k$, that is, target point $i$ is assigned to drone $k$, then $\mathbf{i}$ is the associated variable. ,otherwise ;

[0100] Define completion time Define a binary decision variable to represent the time taken by any drone to complete its mission. This indicates whether drone k flies directly from vertex i to vertex j, and the total flight distance of drone k. and task time They are respectively:

[0101]

[0102]

[0103] Then the system completion time for:

[0104]

[0105] The load balancing degree is quantified by the standard deviation of all drone mission times. First, the average mission time is calculated. :

[0106]

[0107] Define the fairness index F as:

[0108] .

[0109] Furthermore, the formal definition of the problem includes:

[0110]

[0111] st (1)

[0112] (2)

[0113] (3)

[0114] (4)

[0115] (5)

[0116] in and These represent the target allocation and flight decision sets, respectively. and The two flight decisions of UAV k are: taking off from the base station (i=0) and returning to the base station (j=0). The constraints are: (1) Ensure that each inspection target point is visited by only one UAV; (2) Ensure that the actual flight path of the UAV strictly follows the assigned task; (3) Ensure that once the UAV flies into an intermediate target point, it must fly out from that point to form a continuous trajectory; (4) Stipulate that each UAV must start from the base station and eventually return to the base station to form a complete closed-loop task; (5) Define the values ​​of all decision variables.

[0117] Furthermore, the initial task allocation process includes:

[0118] The input is the set of coordinates of all target points. Given the number of drones K, an optimal target point partitioning scheme is found through iterative optimization. The objective function is to minimize the sum of squares within the cluster.

[0119]

[0120] in, It is a task cluster The centroid is calculated using the following formula:

[0121]

[0122] Each centroid This serves as a temporary takeoff and landing base station for the corresponding UAV k in the next stage of path construction.

[0123] Furthermore, the process of constructing the individual path includes:

[0124] For a drone k, a path is a set of destination points it visits. A permutation or combination, represented as a sequence The total cost of the path is the flight distance. Defined as:

[0125]

[0126] In each iteration, the 2-OPT flip operation is used as the neighborhood operator, starting from the current solution. Generate a new solution Calculate the cost difference between the old and new solutions. The decision on whether to accept the new solution is based on the Metropolis criterion:

[0127]

[0128] Where T is the current system temperature;

[0129] Set initial temperature And cool it down according to an exponential cooling strategy: ,in ∈(0,1) is the cooling coefficient. This indicates the temperature of the previous iteration. This represents the temperature after cooling according to the cooling strategy at the current iteration. In the early stages of the algorithm when the temperature is high, it is more likely to accept poor solutions; in the later stages when the temperature is low, it tends to accept only good solutions in order to converge to a high-quality solution.

[0130] Furthermore, the local path optimization process includes:

[0131] For a given path Iterate through all non-adjacent edge pairs, such as and Determine if reconnecting edges is possible. and To shorten the total path length, the conditions for performing this operation are:

[0132]

[0133] If the conditions are met, the swap is performed, and its topological effect is equivalent to swapping the original path... and Flip the subsequences between them; iterate this process repeatedly until there are no edge pairs in the path that satisfy the above conditions. At this point, the path reaches a 2-OPT local optimum.

[0134] Furthermore, the cross-UAV damage and repair operator includes:

[0135] Four cross-UAV neighborhood operators are defined for use from the current solution Generate neighborhood solutions :

[0136] Swap Operator: From two drones k and Randomly select a target point from each of the paths. and and exchange them;

[0137] Migration operator: Removes a target point from the path of drone k. and in drones Find the best insertion position in the path. , making The path increment is minimized, and the optimal insertion position is determined based on the following formula:

[0138]

[0139] in Indicates drone The number of target points included in the path. and This represents the two target points corresponding to the insertion position, that is... insert ;

[0140] Cross-swap operator: Select one edge in the paths of each of the two drones and swap all path segments after these two edges;

[0141] Balance operator: From the current path leading to the maximum completion time Select a target point and move it to the point with the shortest current path. In this way, fairness indicators can be directly optimized.

[0142] Furthermore, the multi-level composite acceptance criteria include:

[0143] For the generated new solution A three-tiered criterion is used to determine whether to accept it as the new current solution:

[0144] Global optimality criterion: If the completion time of the new solution is... Better than the historical best solution ,Right now If so, then it is unconditionally accepted;

[0145] Balance improvement criterion: If the completion time of the new solution is similar to that of the historical best solution. However, its fairness indicators If it's better, then accept it;

[0146] Simulated annealing criterion: For other cases, accept the inferior solution with a certain probability in order to escape the local optimum. The acceptance probability is:

[0147]

[0148] in, This is the current temperature of ALNS. It is a composite cost function that incorporates changes in completion time, total path length, and fairness: ,in , and These represent the changes in completion time, total path length, and fairness, respectively. , and These represent the weighted weights for completion time, total path length, and fairness changes, respectively.

[0149] Furthermore, the operator adaptive weight adjustment mechanism includes:

[0150] At the end of an iteration segment, a score is given based on the operator's performance in that segment. and number of times used Update its weights:

[0151]

[0152] in ∈[0,1] is the response factor, and operators with higher scores will have a greater probability of being selected in subsequent iterations.

[0153] Through the aforementioned hierarchical and progressive optimization steps, this invention can start with coarse-grained task division, gradually refine individual paths, and finally find a multi-UAV collaborative inspection scheme that performs well in terms of completion time and task fairness at the global level through adaptive, multi-objective collaborative optimization.

[0154] The following specific experiment verifies the described embodiment. All simulation experiments were conducted in the MATLAB R2024b environment. The experimental scenario is set in a... Within a 1-meter spatial area, there are 100 target detection points and 3 homogeneous UAVs (speed 20 m / s, altitude 120 m). The geographic coordinates of the target detection points are obtained from user location data in the EUA dataset. We set the maximum number of iterations of ALNS to 200, the system temperature T = 100, and the cooling coefficient... =0.995.

[0155] To evaluate performance, four benchmark algorithms were compared: Greedy Neighborhood Algorithm (GNA), Multi-Objective Particle Swarm Optimization (MOPSO), Clarke-Wright Savings (CWS), and a stochastic path strategy. Ablation experiments were conducted to test scenarios involving module removal: SA (No_SA), 2-OPT (No_2-OPT), ALNS (No_ALNS), and k-means (No_k-means).

[0156] Examples of path planning results are shown below. Examples of path planning using different methods are also attached. Figure 2 -Appendix Figure 6 As shown, all five algorithms successfully completed target allocation and closed-loop path planning for three UAVs, but significant differences in quality were observed. The Random algorithm exhibited severe path intersections and repetitions, resulting in the worst planning efficiency. The GNA algorithm, due to its greedy strategy, led to path intersections and long-distance jumps. The MOPSO and CWS algorithms improved path quality by optimizing path smoothness and did not show significant intersection issues. The algorithm presented in this invention (HO-MUCI) generated the most compact and efficient path, achieving a balance in task allocation among UAVs through global cooperation, while also possessing excellent individual path quality.

[0157] The path planning results are quantified as shown in the attached figure. Figure 7 and attached Figure 8As shown, the algorithm of this invention (HO-MUCI) outperforms other methods in both completion time and fairness metrics. Its optimal completion time is 159.5 seconds, representing improvements of 11.0% and 21.8% compared to CWS (179.3 seconds) and GNA (204.1 seconds), respectively. Regarding fairness, the algorithm of this invention (HO-MUCI) exhibits a more significant advantage, with a fairness metric of only 3.97, which is 82.8% better than the best comparison algorithm CWS (23.15). These results validate the effectiveness of its hierarchical optimization and ALNS global collaboration mechanism in shortening task duration and balancing load.

[0158] The ablation experiments in Appendix 1 confirm the necessity of each core component of this invention. Removing any module leads to performance degradation: eliminating ALNS results in a 452% decrease in fairness (from 3.97 to 21.92) and an 8.8% increase in completion time, highlighting its central role in collaborative optimization. Removing 2-OPT increases path length by 15.1% and completion time by 13.5%, confirming the fundamental role of single-path quality. Removing SA initialization and k-means clustering, respectively, increases completion time by 2.9% and 2.0%. Overall, all components of the algorithm of this invention (HO-MUCI) contribute significantly to performance improvement.

[0159] Table 1. Ablation experimental results of the algorithm of this invention (HO-MUCI)

[0160] index HO-MUCI No_k-means No_SA No_2-OPT No_ALNS Completion Time 159.5±11.6 162.7±10.7 164.2±10.9 181.1±15.1 173.5±15.1 Path length 8258.7±620.7 8486.1±510.4 8620.1±623.6 9504.5±814.5 7907.7±298.9 Fairness 3.97±4.23 3.38±5.29 2.55±2.11 5.03±5.16 21.92±10.21

Claims

1. A multi-UAV collaborative regional patrol path planning method based on hierarchical optimization, characterized in that, Includes the following steps: System Modeling: The task space, which includes a central base station and multiple target points to be inspected, is abstracted into a weighted undirected complete graph, where vertices represent spatial locations and edge weights represent flight costs; and the allocation variables and path decision variables between the UAV and the target points are defined, and a mathematical model is constructed with the joint optimization objective of minimizing the total system completion time and minimizing the standard deviation of the task time. Formal definition of the problem: The mathematical model is defined as a multi-objective optimization problem, and the constraints of the multi-objective optimization problem are set. Initial task allocation: Using the k-means clustering algorithm, the target points are divided into multiple task clusters equal to the number of drones based on their geographic spatial location, and each task cluster is assigned to one drone. Individual path construction: For each task cluster, with the cluster centroid as the reference point, the inspection task of each UAV is modeled as a traveling salesman problem, and the simulated annealing algorithm is used to solve the traveling salesman problem to generate an initial path to all assigned target points; Local path optimization: For each initial path, the 2-OPT local search algorithm is used for optimization. By checking and eliminating intersecting edges in the path, each individual path reaches a local optimum. Global collaborative optimization: The origin and destination of all optimized paths are unified to the real base station. An adaptive large-scale neighborhood search framework is adopted. By alternately executing cross-UAV destruction and repair operators, the task allocation and path structure are dynamically adjusted. Based on the multi-level composite acceptance criteria and operator adaptive weight adjustment mechanism, the total system completion time and task load fairness are iteratively optimized, and finally a near-optimal collaborative inspection scheme is generated.

2. The multi-UAV collaborative area patrol path planning method according to claim 1, characterized in that, The construction process of the weighted undirected complete graph includes: The entire inspection task space is abstracted as a weighted undirected complete graph. ,in Represents a vertex set, consisting of a central base station. and A set of target points to be inspected Composition, that is Each vertex Having two-dimensional Euclidean space coordinates edge set Defined as connecting all vertex pairs The set of edges, where the weight of each edge is defined by the Euclidean distance between the vertices, representing the flight cost of the drone between the two points, i.e.: in, , and They represent and The position coordinates of the two points, the drone is Composed of isomorphic drones, assembled as at a constant speed flight.

3. The multi-UAV collaborative area patrol path planning method according to claim 1, characterized in that, The process of constructing the mathematical model for the joint optimization objective includes: Define variables Let $\mathbf{i}$ represent the association variable between the target point $i$ and the drone $k$. If target point $i$ is served by drone $k$, that is, target point $i$ is assigned to drone $k$, then $\mathbf{i}$ is the associated variable. ,otherwise ; Define completion time Define a binary decision variable to represent the time taken by any drone to complete its mission. This indicates whether drone k flies directly from vertex i to vertex j, and the total flight distance of drone k. and task time They are respectively: Then the system completion time for: The load balancing degree is quantified by the standard deviation of all drone mission times. First, the average mission time is calculated. : Define the fairness index F as: 。 4. The multi-UAV collaborative area patrol path planning method according to claim 1, characterized in that, The formal definition of the problem includes: s.t. (1) (2) (3) (4) (5) in and These represent the target allocation and flight decision sets, respectively. and The two flight decisions of UAV k are: taking off from the base station (i=0) and returning to the base station (j=0). The constraints are: (1) Ensure that each inspection target point is visited by only one UAV; (2) Ensure that the actual flight path of the UAV strictly follows the assigned task; (3) Ensure that once the UAV flies into an intermediate target point, it must fly out from that point to form a continuous trajectory; (4) Stipulate that each UAV must start from the base station and eventually return to the base station to form a complete closed-loop task; (5) Define the values ​​of all decision variables.

5. The multi-UAV collaborative area patrol path planning method according to claim 1, characterized in that, The initial task allocation process includes: The input is the set of coordinates of all target points. Given the number of drones K, an optimal target point partitioning scheme is found through iterative optimization. The objective function is to minimize the sum of squares within the cluster. in, It is a task cluster The centroid is calculated using the following formula: Each centroid This serves as a temporary takeoff and landing base station for the corresponding UAV k in the next stage of path construction.

6. The multi-UAV collaborative area patrol path planning method according to claim 1, characterized in that, The process of constructing the individual path includes: For a drone k, a path is a set of destination points it visits. A permutation or combination, represented as a sequence The total cost of the path is the flight distance. Defined as: In each iteration, the 2-OPT flip operation is used as the neighborhood operator, starting from the current solution. Generate a new solution Calculate the cost difference between the old and new solutions. The decision on whether to accept the new solution is based on the Metropolis criterion: Where T is the current system temperature; Set initial temperature And cool it down according to an exponential cooling strategy: ,in ∈(0,1) represents the cooling coefficient. This indicates the temperature of the previous iteration. This represents the temperature after cooling according to the cooling strategy at the current iteration. In the early stages of the algorithm when the temperature is high, it is more likely to accept poor solutions; in the later stages when the temperature is low, it tends to accept only good solutions in order to converge to a high-quality solution.

7. The multi-UAV collaborative area patrol path planning method according to claim 1, characterized in that, The local path optimization process includes: For a given path Iterate through all non-adjacent edge pairs, such as and Determine if reconnecting edges is possible. and To shorten the total path length, the conditions for performing this operation are: If the conditions are met, the swap is performed, and its topological effect is equivalent to swapping the original path... and Flip the subsequences between them; iterate this process repeatedly until there are no edge pairs in the path that satisfy the above conditions. At this point, the path reaches a 2-OPT local optimum.

8. The multi-UAV collaborative area patrol path planning method according to claim 1, characterized in that, The cross-UAV damage and repair operators include: Four cross-UAV neighborhood operators are defined for use from the current solution Generate neighborhood solutions : Swap Operator: From two drones k and Randomly select a target point from each of the paths. and and exchange them; Migration operator: Removes a target point from the path of drone k. and in drones Find the best insertion position in the path. , making The path increment is minimized, and the optimal insertion position is determined based on the following formula: in Indicates drone The number of target points included in the path. and This represents the two target points corresponding to the insertion position, that is... insert ; Cross-swap operator: Select one edge in the paths of each of the two drones and swap all path segments after these two edges; Balance operator: From the current path leading to the maximum completion time Select a target point and move it to the point with the shortest current path. In this way, fairness indicators can be directly optimized.

9. The multi-UAV collaborative area patrol path planning method according to claim 1, characterized in that, The multi-level composite acceptance criteria include: For the generated new solution A three-tiered criterion is used to determine whether to accept it as the new current solution: Global optimality criterion: If the completion time of the new solution is... Better than the historical best solution ,Right now If so, then it is unconditionally accepted; Balance improvement criterion: If the completion time of the new solution is similar to that of the historical best solution. However, its fairness indicators If it's better, then accept it; Simulated annealing criterion: For other cases, accept the inferior solution with a certain probability in order to escape the local optimum. The acceptance probability is: in, This is the current temperature of ALNS. It is a composite cost function that incorporates changes in completion time, total path length, and fairness: ,in , and These represent the changes in completion time, total path length, and fairness, respectively. , and These represent the weighted weights for completion time, total path length, and fairness changes, respectively.

10. The multi-UAV collaborative area patrol path planning method according to claim 1, characterized in that, The operator adaptive weight adjustment mechanism includes: At the end of an iteration segment, a score is given based on the operator's performance in that segment. and number of times used Update its weights: in ∈[0,1] is the response factor, and operators with higher scores will have a greater probability of being selected in subsequent iterations.

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