An aircraft cluster path planning method based on multi-target wave search algorithm
Patent Information
- Application Number
- CN202611103131.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-07-23
- Publication Date
- 2026-11-03
AI Technical Summary
Existing technologies fail to effectively consider the unique needs and constraints of each aircraft in aircraft swarm trajectory planning, resulting in the neglect of the differences between individual aircraft and the interactions between aircraft, making it difficult to achieve collaborative path planning in complex environments.
A multi-objective wave search algorithm is adopted, combined with Pareto optimal solution and collaborative planning technology. By establishing a three-dimensional map and cost function, the trajectory of each aircraft is optimized. The multi-objective wave search algorithm is used to collaboratively plan the trajectory of the aircraft cluster. Combined with the Pareto optimal update mechanism, the position and performance scores between aircraft are dynamically adjusted to optimize the trajectory layout.
It realizes collaborative path planning for aircraft clusters in complex scenarios with high dimensions and multiple constraints, ensuring the performance optimization of each aircraft and the fairness of the solution, improving the search efficiency and solution quality of the algorithm, and satisfying multiple constraints.
Smart Images
Figure CN123028592A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of collaborative trajectory planning technology for aircraft swarms, and relates to a method for trajectory planning of aircraft swarms based on a multi-target wave search algorithm. Background Technology
[0002] In complex mission environments, trajectory planning for aircraft swarms is a critical issue. Through collaborative work, aircraft swarms can significantly improve mission efficiency and effectiveness. Collaborative trajectory planning is a key technology for ensuring the effective operation of aircraft swarms. It requires finding multiple optimal flight paths for each aircraft from its starting point to its respective target point within a specific mission scenario. To meet the maneuverability requirements of the aircraft, the planning algorithm needs fast solution speed and stability. Swarm trajectory planning faces a complex decision-making environment, including path length, collision risk, mission efficiency, and swarm interaction. While traditional single total cost optimization methods simplify the problem model and make problem handling more intuitive and easier—by summing the costs of all aircraft to form a comprehensive optimization objective and focusing on minimizing the overall cost—this method often overlooks the differences and specific needs of individual aircraft, as well as the interactions between aircraft. Summary of the Invention
[0003] The technical problem solved by this invention is to overcome the shortcomings of the prior art and propose an aircraft swarm trajectory planning method based on a multi-objective wave search algorithm. This method optimizes the unique needs and constraints of each aircraft and, through Pareto optimal solution and collaborative planning technology, not only ensures the optimal performance of each aircraft but also ensures the fairness and balance of the solution. This effectively solves the collaborative path planning problem of aircraft swarms in complex scenarios with high dimensions and multiple constraints.
[0004] The solution of this invention is: a method for planning the trajectory of an aircraft swarm based on a multi-target wave search algorithm, comprising: Create a 3D map containing several threat sources and determine the flight path of each aircraft; Establish the cost function for aircraft swarm trajectory planning ; A multi-objective wave search algorithm is employed to collaboratively plan the trajectories of all aircraft, including: initializing the population; executing the multi-objective wave search algorithm to find the initial optimal solution; collaboratively updating the position of each aircraft in the population, and using a cost function. Update the performance score of each aircraft; evaluate the position and performance score of each aircraft based on the Pareto optimal update mechanism, and optimize the aircraft swarm trajectory layout.
[0005] Furthermore, the aforementioned collaborative updating of the position of each aircraft in the population includes: For all aircraft of the current generation, calculate the distance matrix between them; For each aircraft, the new position is calculated by selecting the nearest neighbors based on the distance matrix; Add random perturbations at the new locations to increase exploration and obtain the updated locations for each aircraft.
[0006] Furthermore, the aforementioned cost function for establishing aircraft swarm trajectory planning ,include: Path cost for each aircraft F 1 ( X i ); The cost of constructing obstacle threat per aircraft F 2 ( X i ); Total altitude threat cost for constructing the entire path for each aircraft F 2 ( X i ); Cost of constructing corner threat per aircraft F 4 ( X i ); The cost function for F 1 ( X i ), F 2 ( X i ), F 2 ( X i ), F 4 ( X i The weighted sum of ), where X i Indicates the entire flight path, subscript i Indicates the first i A flight path.
[0007] Furthermore, the path cost per aircraft... F 1 ( X i ):
[0008] in The flight path point of the aircraft at the 1st i The first of the flight paths j The three-dimensional spatial position of the aircraft at each path point, and the entire flight path. Indicated as containingn A three-dimensional array of path points; Indicates from the path point To the waypoint The track segment vector, which is the first... i The first aircraft j Segment path, It is the first j Length of the flight path ，n This represents the total number of waypoints for the aircraft. The obstacle threat cost per aircraft F 2 ( X i ):
[0009] in, It is a piecewise function that calculates the threat cost based on the distance between the flight path segment and the obstacle:
[0010] K Represents the total number of obstacles. k Representing the k There are one obstacle; the threat area in the 3D condition is modeled as a cylinder with center coordinates of... , radius is For the first Obstacle Center to track segment The distance; The total altitude threat cost for each aircraft along its entire path. F 3 ( X i ):
[0011] in, For the current path point Relevant cost functions:
[0012] in, Indicates a high penalty coefficient; Indicates the minimum flight altitude of the aircraft; Indicates the maximum altitude at which the aircraft can fly; For the aircraft at the waypoint The height of the location from the reference terrain surface.
[0013] Furthermore, the cornering threat cost per aircraft... F 4 ( X i ):
[0014]
[0015]
[0016]
[0017] Where a1 is the penalty coefficient for the horizontal turning angle, and a2 is the penalty coefficient for the change in the vertical pitch angle. Representing the i The first aircraft j Horizontal turning angle of the flight path Representing the i The first aircraft j Vertical pitch angle of the flight path It is the projection vector of the trajectory vector onto the horizontal plane. It is a unit vector in the vertical direction. and These correspond to path points respectively. and Elevation coordinates.
[0018] Furthermore, the step of selecting the nearest neighbors based on the distance matrix to calculate the new location includes: For aircraft and each neighboring aircraft Calculate the distance-based weight decay factor:
[0019] in, Indicates the first The aircraft and the first The Euclidean distance between the aircraft; Calculate performance-based weights: in, It is the first The performance score of the aircraft; Calculate the total weight: ; Computational aircraft New location:
[0020] in, This indicates that the results selected based on the distance matrix are related to the first... The set of several nearest neighboring aircraft of an aircraft. Indicates aircraft Current location Indicates aircraft The current location.
[0021] Furthermore, the process of executing the multi-target wave search algorithm to find the initial optimal solution includes: S1. First, define the problem parameters and initialize the random perturbation vector; S2, First aspect: The initial optimal position and score are obtained through the initialization module; with the iteration number T as the loop condition, if T is not reached, the position is iteratively updated, the fitness is evaluated, and the updated optimal score and position are obtained. The condition triggers electromagnetic emission, evaluates and updates the position; otherwise, S3 is executed. Second aspect: with the iteration number T as the loop condition, if T is not reached, the optimal score and position are optimized and updated through the gradient method; otherwise, S3 is executed. S3. After each iteration, the optimal score, position, and recorded curve are output.
[0022] Furthermore, the position and performance scores of each aircraft are evaluated based on the Pareto optimal update mechanism, including: Pareto front initialization; After each iteration, the updated position and performance score of each aircraft are evaluated, and the Pareto front is updated. Iterate through all solutions, examine each solution, and extract the Pareto front; The extracted Pareto front is stored for subsequent analysis and as the final output.
[0023] Furthermore, the updated Pareto front includes: For the solution of the new evaluation, check whether there is any solution in the current Pareto front that can dominate it; If any such solution exists, the newly evaluated solution is not added to the Pareto optimal solution set; If the newly evaluated solution is not dominated by any solution in the Pareto front, then check whether it dominates any solution in the Pareto front. If the newly evaluated solution dominates any solution, then the dominated solution is removed from the Pareto optimal solution set and the newly evaluated solution is added. If the newly evaluated solution neither dominates nor is dominated by solutions in the Pareto front, it is directly added to the Pareto optimal solution set.
[0024] Furthermore, the extraction of the Pareto front includes: traversing all newly evaluated solutions, and for each other solution, using a non-dominated check formula to verify whether the newly evaluated solution is dominated; the undominated solutions constitute a new set of Pareto optimal solutions to ensure that the solutions of the Pareto front are mutually non-dominated in each iteration.
[0025] The advantages of this invention compared to the prior art are: This invention employs a multi-objective wave search algorithm to solve the cooperative trajectory planning problem of aircraft swarms in a 3D scene. Based on a Pareto optimal solution set and a cooperative optimization update mechanism, it adapts to the needs of multi-objective optimization. By dynamically adjusting the positions and performance scores among the aircraft, the overall trajectory layout is optimized, improving the algorithm's search efficiency and solution quality, while simultaneously satisfying multiple constraints such as flight altitude, obstacle avoidance, and turning angle. Attached Figure Description
[0026] Figure 1 This is a flowchart of the overall process of the method of the present invention.
[0027] Figure 2 This is a flowchart of the wave search method used in this invention.
[0028] Figure 3 This is a diagram showing the trajectory planning result in a three-dimensional scene according to an embodiment of the present invention.
[0029] Figure 4 This invention provides a comparison of the average cost convergence curves for general scenarios under different planning algorithms provided in the embodiments of the present invention. Detailed Implementation
[0030] The present invention will be further described below with reference to the accompanying drawings and embodiments.
[0031] A method for planning the trajectory of an aircraft swarm based on a multi-target wave search algorithm includes the following steps: S1. Create a 3D map containing several threat sources; S2. Establish the cluster trajectory planning cost function; S3. Employ a multi-target wave search algorithm to collaboratively plan the trajectories of all aircraft.
[0032] (1) The specific implementation process of step S1 is as follows: Determine the starting point and target point of each aircraft, and divide the line connecting the starting point and target point of each aircraft into n+1 equal parts, that is, the track of each aircraft contains n track points.
[0033] (2) Step S2 includes: S21. Construct the path cost for each aircraft:
[0034] in The flight path point of the aircraft at the 1st i The first of the flight paths j The three-dimensional spatial position of the aircraft at each path point, and the entire flight path. Indicated as containing n A three-dimensional array of path points. Indicates from the path point To the waypoint The track segment vector, which is the first... i The first aircraft j Segment path, It is the first j The length of the flight path, n This represents the total number of waypoints for the aircraft.
[0035] S22, Cost of constructing obstacle threat per aircraft: Cost function related to aircraft obstacle avoidance threats for:
[0036] in, It is a piecewise function that calculates the threat cost based on the distance between the flight path segment and the obstacle:
[0037] K Represents the total number of obstacles. k Representing the k There are one obstacle; the threat area in the 3D condition is modeled as a cylinder with center coordinates of... , radius is For the first Obstacle Center to track segment The distance.
[0038] S23, Total altitude threat cost for constructing the entire path for each aircraft: Total altitude threat cost for each aircraft along its entire path:
[0039] in, For the current path point Relevant cost functions:
[0040] Indicates a high penalty coefficient; Indicates the minimum flight altitude of the aircraft; Indicates the maximum altitude at which the aircraft can fly; For the aircraft at the waypoint The height of the location from the reference terrain surface.
[0041] S24. Construction of Corner Threat Costs for Each Aircraft:
[0042]
[0043]
[0044]
[0045] Where a1 is the penalty coefficient for the horizontal turning angle, and a2 is the penalty coefficient for the change in the vertical pitch angle. Representing the i The first aircraft j Horizontal turning angle of the flight path Representing the i The first aircraft j Vertical pitch angle of the flight path It is the projection vector of the trajectory vector onto the horizontal plane. It is a unit vector in the vertical direction. and These correspond to path points respectively. and Elevation coordinates.
[0046] like Figure 1 The specific implementation process of step S3 is shown below: S31, Initial Population and WSA (Wave Search Algorithm): S311, During the initialization process: Define problem parameters: The value represents the population size, i.e., the number of individuals participating in the optimization. The value T represents the number of iterations, i.e., the maximum number of iterations the algorithm can run. and These represent the lower and upper limits of the random perturbation, respectively, used to define the feasible region for each individual. This represents the dimension of each solution, i.e., the degrees of freedom of each individual. It is the weighted sum of the four cost functions established in S2. Population initialization: Generate a population consisting of... An initial population consisting of individuals Each individual represents a point in the solution space.
[0047] S312. Steps for executing the WSA algorithm: Calculate fitness: Calculate the fitness value for each individual in the initial population W. Population division: The population was divided into three subpopulations. 1, 2 and 3. These represent the populations that emit, reflect, and receive electromagnetic waves, respectively. Finding the current optimal solution: Sort the fitness values of the entire population and find the current optimal solution. _ and _ .
[0048] Iterative Process: In each iteration, specific operations are performed on each subpopulation, including but not limited to emitting, reflecting, and receiving electromagnetic waves. The position of each subpopulation is updated, and its fitness is re-evaluated. If a better solution is found, the global optimal solution is updated. Termination Condition: The maximum number of iterations is reached. The algorithm terminates when other stopping criteria are met.
[0049] like Figure 2 As shown, the problem parameters are first defined and initialized; the initial optimal solution is obtained through the Initialization module; with the iteration number T as the loop condition, the position and optimal solution are optimized collaboratively through the Position_Update module, the Electromagnetic_Emission module triggered by the condition, and the Gradient_Method module, and the optimal score curve is recorded synchronously; after the iteration is completed, the optimal score, position and recorded curve are output.
[0050] The initialization process is as follows: generate uniformly random numbers, shuffle the numbers to obtain the initial positions, and use the positions located at... and The population W is initialized with positions between them, and the fitness of all positions in W is evaluated. The initial optimal positions and scores are identified. The Position_Update process is as follows: generate a new position within the range of [Wmin, Wmax], apply boundary conditions, evaluate the fitness of the new position, update the position based on the fitness comparison, and update the best score and best position if there is improvement; The Electromagnetic_Emission process is as follows: calculate theta for modulation, emit electromagnetic waves to modify the position, apply boundary conditions, and evaluate and update the best position if the fitness is improved. The Gradient_Method process is as follows: calculate the gradient approximation for all positions, update the positions using the gradient descent method, adjust the learning rate according to the new fitness, update the positions, and check if there is a new optimal score.
[0051] S313, Update Population: The initial optimal solution found using the WSA algorithm and This is used to update the population. This initial population will be used for subsequent search and optimization processes.
[0052] S32, Collaborative Update: S321. Calculate the distance matrix: For all aircraft of the current generation, calculate the distance matrix between them. Elements of the distance matrix. Indicates the first The aircraft and the first The Euclidean distance between the aircraft. By applying the Euclidean distance formula, for the ... frame and the first The position coordinates of the aircraft in various dimensions and Calculate each element of the distance matrix:
[0053] S322, Update the aircraft's position: Each aircraft selects the nearest [aircraft] based on the distance matrix. The new location is calculated for each neighbor. For each aircraft... and each of its neighbors Calculate the distance-based weight decay factor and performance-based weights ,in It is the first The performance score of the aircraft. Total weight. Used to calculate aircraft The new weighted position:
[0054] in This indicates that the values selected based on the distance matrix are the ones that are most similar to the first value. The set of several nearest neighboring aircraft of an aircraft; Indicates aircraft Current location Indicates aircraft The current location.
[0055] Normalized weights ensure the accuracy of the weighted positions and add a small random perturbation at the new positions: To increase the exploratory nature of the activity; among them, r From A random number that is uniformly distributed within an interval.
[0056] Updated location: And the recalculated target.
[0057] function value New performance assessments were provided for each aircraft.
[0058] S323, Overview of steps: During initialization, the position and performance scores of all aircraft in the current generation are first obtained. Then, based on the previously calculated distance matrix, the nearest neighbors are selected for each aircraft, and a weighted new position is calculated using the position and performance scores of these neighbors. The new position considers normalized weights and applies random perturbations. After updating the position and performance scores, this process is repeated for each aircraft until all aircraft have been updated. This collaborative update method ensures that the position and performance scores of the aircraft gradually approach the optimal solution, optimizing the efficiency and effectiveness of the algorithm.
[0059] S33, Pareto optimal update: In the aircraft swarm optimization problem, the set of Pareto optimal solutions provides a series of non-dominated solutions that are not dominated by other solutions on any target in the multidimensional target space.
[0060] S331, Pareto front initialization: An empty set `paretoFront` is initialized to store Pareto optimal solutions. At the beginning of each iteration, the performance score of each aircraft in the current population and their performance relative to the objective function are evaluated to determine whether they are eligible to join the Pareto front.
[0061] S332, Pareto update mechanism: After each iteration, the updated position and performance score of each aircraft are evaluated, and the Pareto front is updated according to the following steps: The first step is non-dominant checks.
[0062] For the newly evaluated solution currentSolution, check whether there exists any solution existingSolution in the current Pareto front that can dominate it: For two solutions a and b, the dominance relation Dominate(a, b) is defined as follows:
[0063] in Objectives Represents the set of all optimization objectives; , Let a and b represent the performance values of solutions a and b on the i-th optimization objective, respectively; if such an existing solution exists, the current solution is not added to paretoFront.
[0064] The second step is domination removal.
[0065] If the currentSolution is not dominated by any solution in the Pareto front, then check if it dominates any solution in the Pareto front. If the currentSolution dominates an existingSolution, remove the dominated solution from the ParetoFront and add the currentSolution.
[0066] The third step is to add non-inferior ingredients.
[0067] If the currentSolution is neither dominated by nor dominated by a solution in the Pareto front, then add it directly to the ParetoFront.
[0068] S333, Extraction and updating of the Pareto front: At the end of each generation, the Pareto front is extracted from all solutions. This process involves iterating through all solutions and checking each one to confirm whether it is dominated by any other solution: The first step is to iterate through all solutions, currentSolution, and for each other solution, otherSolution, use the non-domination check formula to verify whether currentSolution is dominated.
[0069] The second step is to construct a new Pareto Front from the undominated solutions. This ensures that the solutions at the Pareto front in each generation are mutually non-dominated.
[0070] S334. Storage and output of solutions: All validated Pareto front solutions are stored in a structure array `paretoFront`, where each element contains the aircraft's position and corresponding performance score. This information can be used for subsequent analysis and provided as final output to users or other system components to support the decision-making process.
[0071] Figure 3 This is a diagram showing the trajectory planning result in a three-dimensional scene according to an embodiment of the present invention.
[0072] The flight paths of UAV1 to UAV5 from the starting point to the destination are shown, with the background including columnar obstacles and terrain undulations, which intuitively presents the path distribution of the cluster in a complex environment.
[0073] Figure 4 This invention provides a comparison of the average cost convergence curves for general scenarios under different planning algorithms provided in the embodiments of the present invention.
[0074] The multi-target wave search algorithm has significant advantages. It has the fastest convergence speed, reaching the lowest optimal score in about 30 iterations. Ultimately, it has the best performance. After the iteration, the optimal score is lower than the other two algorithms. Moreover, the score is stable after convergence without significant fluctuations, demonstrating more efficient and powerful optimization capabilities and more reliable optimization effects.
[0075] The wave search algorithm-based multi-objective optimization method can optimize for the unique needs and constraints of each aircraft. Through Pareto optimal solutions and collaborative planning techniques, it not only ensures the optimal performance of each aircraft but also guarantees the fairness and balance of the solution. This method allows the system to maintain high flexibility and adaptability in complex environments, showing particular advantage when facing variable mission requirements. Furthermore, the collaborative planning in multi-objective optimization further ensures that the actions of the aircraft are not only optimal for themselves but also effectively avoid mutual interference, thereby improving the overall efficiency and safety of the system.
[0076] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.
Claims
1. A method for planning the trajectory of an aircraft swarm based on a multi-target wave search algorithm, characterized in that, include: Create a 3D map containing several threat sources and determine the flight path of each aircraft; Establish the cost function for aircraft swarm trajectory planning ; A multi-objective wave search algorithm is employed to collaboratively plan the trajectories of all aircraft, including: initializing the population; executing the multi-objective wave search algorithm to find the initial optimal solution; collaboratively updating the position of each aircraft in the population, and using a cost function. Update the performance score of each aircraft; evaluate the position and performance score of each aircraft based on the Pareto optimal update mechanism, and optimize the aircraft swarm trajectory layout.
2. The method for planning aircraft swarm trajectories based on a multi-target wave search algorithm according to claim 1, characterized in that, The aforementioned collaborative update of the position of each aircraft in the population includes: For all aircraft of the current generation, calculate the distance matrix between them; For each aircraft, the new position is calculated by selecting the nearest neighbors based on the distance matrix; Add random perturbations at the new locations to increase exploration and obtain the updated locations for each aircraft.
3. The method for planning aircraft swarm trajectories based on a multi-target wave search algorithm according to claim 1, characterized in that, The aforementioned cost function for establishing aircraft swarm trajectory planning ,include: Path cost for each aircraft F 1 ( X i ); The cost of constructing obstacle threat per aircraft F 2 ( X i ); Total altitude threat cost for constructing the entire path for each aircraft F 3 ( X i ); Cost of constructing corner threat per aircraft F 4 ( X i ); The cost function for F 1 ( X i ), F 2 ( X i ), F 3 ( X i ), F 4 ( X i The weighted sum of ), where X i Indicates the entire flight path, subscript i Indicates the first i A flight path.
4. The method for planning aircraft swarm trajectories based on a multi-target wave search algorithm according to claim 3, characterized in that, The path cost per aircraft F 1 ( X i ): in The flight path point of the aircraft is at the 1st i The first of the flight paths j The three-dimensional spatial position of the aircraft at each path point, and the entire flight path. For inclusion n A three-dimensional array of path points; Indicates from the path point To the waypoint The track segment vector, It is the length of the track segment vector. ，n This represents the total number of waypoints for the aircraft. The obstacle threat cost per aircraft F 2 ( X i ): in, It is a piecewise function that calculates threat cost based on the distance between a flight path segment and an obstacle: K Represents the total number of obstacles. k Representing the k There are one obstacle; the threat area in the 3D condition is modeled as a cylinder with center coordinates of... , radius is For the first Obstacle Center to track segment The distance; The total altitude threat cost for each aircraft along its entire path. F 3 ( X i ): in, For the current path point Relevant cost functions: in, Indicates a high penalty coefficient; Indicates the minimum flight altitude of the aircraft; Indicates the maximum altitude at which the aircraft can fly; For the aircraft at the waypoint The height of the location from the reference terrain surface.
5. The method for planning aircraft swarm trajectories based on a multi-target wave search algorithm according to claim 4, characterized in that, The cornering threat cost per aircraft F 4 ( X i ): Where a1 is the penalty coefficient for the horizontal turning angle, and a2 is the penalty coefficient for the change in the vertical pitch angle. Representing the i The first aircraft j Horizontal turning angle of the flight path Representing the i The first aircraft j Vertical pitch angle of the flight path It is the projection vector of the trajectory vector onto the horizontal plane. It is a unit vector in the vertical direction. and These correspond to path points respectively. and Elevation coordinates.
6. The method for planning aircraft swarm trajectories based on a multi-target wave search algorithm according to claim 2, characterized in that, The method of selecting the nearest neighbors based on the distance matrix to calculate the new location includes: For aircraft and each neighboring aircraft Calculate the distance-based weight decay factor: in, Indicates the first The aircraft and the first The Euclidean distance between the aircraft; Calculate performance-based weights: in, It is the first The performance score of the aircraft; Calculate the total weight: ; Computational aircraft New location: in, This indicates that the results selected based on the distance matrix are related to the first... The set of several nearest neighboring aircraft of an aircraft. Indicates aircraft Current location Indicates aircraft The current location.
7. The method for planning aircraft swarm trajectories based on a multi-target wave search algorithm according to claim 1, characterized in that, The aforementioned multi-target wave search algorithm for finding the initial optimal solution includes: S1. First, define the problem parameters and initialize the random perturbation vector; S2, First aspect: The initial optimal position and score are obtained through the initialization module; with the iteration number T as the loop condition, if T is not reached, the position is iteratively updated, the fitness is evaluated, and the updated optimal score and position are obtained. The condition triggers electromagnetic emission, evaluates and updates the position; otherwise, S3 is executed. Second aspect: with the iteration number T as the loop condition, if T is not reached, the optimal score and position are optimized and updated through the gradient method; otherwise, S3 is executed. S3. After the iteration is completed, output the optimal score, position, and record the curve.
8. The method for planning aircraft swarm trajectories based on a multi-target wave search algorithm according to claim 1, characterized in that, The position and performance scores of each aircraft are evaluated based on the Pareto optimal update mechanism, including: Pareto front initialization; After each iteration, the updated position and performance score of each aircraft are evaluated, and the Pareto front is updated. Iterate through all solutions, examine each solution, and extract the Pareto front; The extracted Pareto front is stored for subsequent analysis and as the final output.
9. The method for planning aircraft swarm trajectories based on a multi-target wave search algorithm according to claim 8, characterized in that, The updated Pareto front includes: For the solution of the new evaluation, check whether there is any solution in the current Pareto front that can dominate it; If any such solution exists, the newly evaluated solution is not added to the Pareto optimal solution set; If the newly evaluated solution is not dominated by any solution in the Pareto front, then check whether it dominates any solution in the Pareto front. If the newly evaluated solution dominates any solution, then the dominated solution is removed from the Pareto optimal solution set and the newly evaluated solution is added. If the newly evaluated solution neither dominates nor is dominated by solutions in the Pareto front, it is directly added to the Pareto optimal solution set.
10. The method for planning aircraft swarm trajectories based on a multi-target wave search algorithm according to claim 9, characterized in that, The extraction of the Pareto front includes: traversing all newly evaluated solutions, and for each other solution, using the non-dominated check formula to verify whether the newly evaluated solution is dominated; the undominated solutions constitute a new set of Pareto optimal solutions to ensure that the solutions of the Pareto front are mutually non-dominated in each iteration.