A Multi-Operator Co-evolutionary Method for 3D Multi-Objective Path Planning of Unmanned Aerial Vehicles

Abstract

This invention relates to the field of UAV path planning technology, specifically to a multi-operator co-evolutionary UAV 3D multi-objective path planning method. The method minimizes path length and path threat as optimization objectives, while simultaneously satisfying obstacle collision avoidance and flight angle constraints. A 3D environment and flight constraint model is constructed, and a feasible initial population is generated using a fast expanding random tree. The population is dynamically divided into subpopulations through fast non-dominated sorting, and an external archive is maintained. In several stages of the improved artificial bee colony algorithm, multiple differentiated evolutionary operators are configured to achieve path segment recombination, path smoothing, goal-oriented optimization, categorical information-guided updates, and restarting of stalled individuals. This invention solves the problems of algorithms easily getting trapped in local optima, insufficient path safety, and difficulty in balancing multiple objectives in complex 3D environments. It improves the quality of the solution set, the uniformity of its distribution, and the search convergence efficiency, and can output a UAV 3D Pareto path set that balances distance and safety.

Description

Technical Field

[0001] This invention relates to the field of UAV path planning technology, specifically a multi-operator cooperative evolution method for UAV three-dimensional multi-objective path planning. Background Technology

[0002] In the process of unmanned aerial vehicle (UAV) mission execution, path planning is a key technology for achieving autonomous flight and reliable mission execution. Its core objective is to generate a feasible flight path from the starting point to the target point for the UAV in complex environments. Existing path planning methods typically use path length as the sole optimization objective. However, when performing UAV path planning in complex 3D scenarios, it is necessary to consider not only flight distance but also a variety of factors such as obstacle distribution, spatial threat areas, and flight safety. Therefore, existing single-objective path planning methods struggle to generate high-quality flight paths that balance path length and safety in complex 3D environments.

[0003] Furthermore, existing methods still have other shortcomings in complex 3D environments. Some algorithms are prone to getting trapped in local optima during the search process, leading to insufficient path quality and stability. In addition, existing methods typically employ a single population, fixed operators, or perform homogeneous searches on all individuals, failing to construct functionally complementary subpopulations based on individual quality, target bottlenecks, and search stages. They also lack differentiated configurations and sequential connection mechanisms for multiple path evolution operators, easily causing an imbalance between global exploration and local development, and insufficient utilization of information from high-quality solutions, thus affecting search efficiency and solution quality in complex 3D environments. Therefore, there is an urgent need for a UAV multi-objective path planning method that is applicable to complex 3D environments, balances path length and path safety, and possesses strong global search capabilities. Summary of the Invention

[0004] To address the technical problems existing in the background art described above, this invention proposes a multi-operator cooperative evolution method for UAV three-dimensional multi-objective path planning.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] S1. Establish a discrete 3D environment model and flight angle constraint model for the UAV, and set the starting point and target point;

[0007] S2. Initialize algorithm parameters, including population size. Maximum number of consecutive evolutionary failures for an individual Deadline for operation;

[0008] S3. An initial population is generated using a sampling-based initialization strategy, and an initial path that simultaneously satisfies obstacle avoidance constraints and flight angle constraints is generated using a fast expanding random tree algorithm.

[0009] S4. Perform fast non-dominated sorting and crowding distance calculation on the population, divide the population into elite subpopulations, intermediate subpopulations and inferior subpopulations, and update the external archive set.

[0010] S5, the stage of hiring bees, executes the nearest path segment crossover operator, the direction-guided mutation operator, the height profile shaping operator, and the curvature constraint smoothing operator in sequence for candidate individuals. Based on the subpopulation category, individual target bottleneck, and evolutionary state, the height-aware simplification operator and the distance-bounded safety operator are called in a differentiated manner, so that the same operator pool forms different cooperative paths in different subpopulations, so as to take into account global search, local development and multi-objective balance.

[0011] S6. During the observation phase, a leader-based information guidance strategy is implemented for non-dominated solutions, and a dual-source information guidance strategy is implemented for dominant solutions to improve the convergence ability of high-quality solutions and the development ability of dominant solutions.

[0012] S7, the scout bee phase, implements an individual restart strategy for individuals that have been stagnant for a long time without updating, in order to maintain population activity and avoid the algorithm getting trapped in local optima;

[0013] S8. Determine if the termination condition is met. If it is, output the non-dominated solution set; otherwise, return to step S4.

[0014] Preferably, in step S1, a discrete three-dimensional path representation method is used to model the UAV flight path, and a feasible path is represented as follows: ,in, This represents a path, where S represents the drone's starting point and T represents the target point. Each track point is represented by three-dimensional coordinates. express;

[0015] Flight angle constraints include horizontal turning angle constraints and vertical turning angle constraints. Let the projection vectors of adjacent path segments onto the horizontal plane be... The horizontal turning angle between two consecutive segments is Let the vertical component of the path segment be... The vertical turning angle between two consecutive segments is Then the constraint relationship is:

[0016] ,

[0017] ,

[0018] Among them, 45° is the maximum horizontal turning angle of adjacent flight segments, and 30° is the maximum vertical climb or descent turning angle of adjacent flight segments; all newly generated or reconstructed paths must simultaneously satisfy the above flight angle constraints and obstacle collision avoidance constraints.

[0019] Preferably, in step S1, the UAV path planning model simultaneously uses path length and path threat as optimization objectives. The path length objective is obtained by accumulating the three-dimensional Euclidean distances between adjacent waypoints in the path, and the calculation formula is as follows: ,in, Representing a path The length of the path threat target is calculated by determining the minimum distance between each path segment and the nearest obstacle. The calculation formula is: ,in, Indicates the threat level of the path. This represents the minimum distance between the path segment and the nearest obstacle. w is a display scaling constant set according to the magnitude of the 3D environment data. w is only used to unify the display scale of the two target values, does not participate in weighted optimization, and does not change the Pareto dominance relationship between individuals.

[0020] The multi-objective path planning problem for unmanned aerial vehicles (UAVs) involves determining the path length while satisfying obstacle avoidance and flight angle constraints. Path threats Perform Pareto minimization.

[0021] Preferably, in step S3, the sampling-based initialization strategy uses a fast expanding random tree algorithm to randomly sample and expand from the starting point to the target point. When generating a new node, it is determined whether the connection between nodes collides with an obstacle, and whether the newly added path segment satisfies the horizontal turning angle and vertical turning angle constraints. Only when both the collision avoidance constraint and the flight angle constraint are satisfied is the new node added to the path until a complete feasible path is generated.

[0022] Preferably, in step S4, the fast non-dominated sorting method compares the dominance relationships of individuals in the population based on path length and path threat objectives, and assigns individuals to different frontiers. The crowding distance calculation method calculates the crowding distance of individuals within the same frontier in the target space, prioritizing the retention of individuals with larger crowding distances to improve the evenness of population distribution. Furthermore, step S4 employs a dynamic subpopulation size adjustment mechanism, where the size of the elite subpopulation gradually increases as the algorithm runs, the size of the inferior subpopulation gradually decreases, and the size of the intermediate subpopulation is determined based on the total population size and the sizes of the other two subpopulations. This allows the algorithm to gradually transition from early diversified exploration to later refined optimization of bottleneck objectives. The formula for calculating the size of the elite subpopulation is: ,in, For population size, Let represent the initial and final proportions of the elite subpopulation, respectively, and t represent the current time. The maximum running time; the formula for calculating the size of the inferior subpopulation is: ,in, These represent the initial and final proportions of the inferior subpopulation, respectively; the size of the intermediate subpopulation is calculated as follows: ;

[0023] After completing the fast non-dominated sorting, individuals are first selected from the first frontier to construct an elite subpopulation. When the number of individuals in the first frontier exceeds the preset size of the elite subpopulation, individuals with larger crowding distances are selected to join the elite subpopulation through crowding distance sorting. When the number of individuals in the first frontier is insufficient, individuals are selected from subsequent frontiers in descending order of dominance level, with priority given to retaining individuals with larger crowding distances, until the preset size of the elite subpopulation is reached.

[0024] After the elite subpopulation is divided, an intermediate subpopulation is constructed based on the remaining individuals. The intermediate subpopulation is selected according to the non-dominance level and crowding distance, prioritizing the retention of individuals with higher dominance levels and larger crowding distances, until the preset size of the intermediate subpopulation is reached.

[0025] After the elite subpopulation and intermediate subpopulation are divided, the remaining unselected individuals constitute the inferior subpopulation.

[0026] An external archive set is used to store high-quality non-dominated solutions. When a new non-dominated solution is generated, it is checked whether a dominated individual exists in the external archive set. If it does, the dominated individual is deleted, and the new non-dominated solution is added to the external archive set, which has a size of [size missing]. .

[0027] Preferably, in step S5, all individuals in the elite subpopulation participate in evolution; some individuals in the intermediate subpopulation participate in evolution based on their fitness value and the number of successful evolutions; and some individuals in the inferior subpopulation participate in evolution based on the number of successful evolutions.

[0028] The fitness value is obtained by summing the normalized values ​​for path length and path threat targets, respectively. The calculation formula is as follows: ,in and Let represent the path length and path threat value of the i-th individual, respectively. and These represent the maximum and minimum path length values ​​in the corresponding subpopulations, respectively. and These represent the maximum and minimum path threat values ​​in the corresponding subpopulations, respectively.

[0029] Preferably, in step S5:

[0030] The input to the nearest path segment intersection operator is two parent path individuals, denoted as . and Where S represents the starting point and T represents the target point. Represent intermediate waypoints in the path, calculate the spatial distance between any pair of path segments in two parent paths, and determine the pair of path segments with the smallest distance. and If connected and as well as and If none of the line segments collide with obstacles, two candidate paths are generated by reconnecting the endpoints, and it is checked whether the candidate paths satisfy the flight angle constraint. Fast non-dominated sorting is performed on the parent path and the candidate paths, and the non-dominated solution is selected as the output; otherwise, the current path is kept unchanged.

[0031] The input to the direction-guided mutation operator is the path output by the nearest path segment intersection operator, with intermediate waypoints randomly selected. And construct its predecessor node. With successor nodes The straight line L between them; when When located below L, make Move upwards along the height direction without crossing L, when When located above L, make Move downwards along the height direction without crossing L to obtain candidate nodes. Only when and Only when both the obstacle collision avoidance constraints and the reconstructed path satisfy the flight angle constraints will the better path between the original path and the new path be selected as the output.

[0032] The height profile shaping operator is used to coordinately adjust the height distribution of local path segments, randomly selecting two intermediate waypoints. and ,in Keeping the horizontal coordinates of each waypoint between the two unchanged, in order to and The height is used as the boundary, and a linear reference height is established based on the cumulative path distance; for trackpoints Its height is updated according to the following formula: , ,in, for waypoints The original height, From to The cumulative path length, To adjust the intensity coefficient, obstacle collision detection and flight angle constraint detection are performed on the entire path after the update, and the better path is selected between the original path and the new path to suppress unnecessary altitude oscillations;

[0033] The curvature-constrained smoothing operator first calculates the horizontal and vertical turning angles at each intermediate track point, and then determines the track point N with the largest vertical turning angle. i and the track point with the largest horizontal turning angle For each of the aforementioned waypoints, auxiliary waypoints are inserted on its two adjacent path segments. The distance between the auxiliary waypoints and the aforementioned waypoints is one-third of the length of the corresponding path segment. The local path is reconstructed using the auxiliary waypoints. The reconstructed path is only accepted when the obstacle collision avoidance constraint and flight angle constraint are satisfied, so as to distribute the directional changes concentrated on a single node to multiple continuous path segments.

[0034] Preferably, in step S5, for the selected candidate individuals in the elite subpopulation, intermediate subpopulation, and inferior subpopulation, the nearest path segment crossover operator, direction-guided mutation operator, height profile shaping operator, and curvature constraint smoothing operator are executed sequentially. Subsequently, based on the subpopulation to which the individual belongs and its target performance, a target-oriented operator is applied. For individuals in the elite subpopulation, the bottleneck target is determined based on the normalized results of the path length target and the path threat target, and its calculation formula is as follows: ,in, For the bottleneck target of the i-th individual, when the normalized result corresponding to the path length target is large, only the high-awareness simplification operator is executed; when the normalized result corresponding to the path threat target is large, only the distance-bounded safety operator is executed, thus prioritizing the improvement of the weaker target and preserving the existing advantages of the other target as much as possible.

[0035] For individuals in the intermediate subpopulation, after completing the four basic evolutionary operators—the nearest path segment crossover operator, the direction-guided mutation operator, the height profile shaping operator, and the curvature-constrained smoothing operator—the height-aware simplification operator and the distance-bounded safety operator are executed sequentially to simultaneously explore the trade-off between path length and path threat. For individuals in the disadvantaged subpopulation, after completing the aforementioned four basic evolutionary operators, the height-aware simplification operator or the distance-bounded safety operator is randomly selected for operation to conduct extensive exploration from different target directions and introduce new diversity into the population.

[0036] The height-aware simplified operator is an operator oriented towards path length targets. First, the original path is projected onto a vertical plane aligned with the direction of the line connecting the starting point S to the target point T, and the intersection point of the projected path and the starting and ending point lines is determined. If an intersection exists, the path is divided into two parts based on whether the projected path is above or below the straight line. The proportion of each part projected onto the starting and ending straight lines is calculated, and the part with the smaller proportion is selected as a redundant path segment and deleted. The predecessor node of the deleted path segment is used as the reference point. As the starting point for connection, in its adjacent intersection point A new waypoint is generated at the midpoint between them. If the projected path is completely located on one side of the origin-end line, a redundant intermediate track point is randomly deleted and its predecessor node and successor node are directly connected. The path is accepted only if the reconstructed path satisfies both obstacle avoidance constraints and flight angle constraints.

[0037] The distance-bounded safety operator is an operator oriented towards path-threatening targets. It first identifies the intermediate waypoint with the minimum clearance distance to the obstacle. And calculate its distance d to the nearest obstacle, while constructing and Local connection line L between, when When located below L, make Move randomly upwards along the height direction, with a displacement not exceeding d and the new node must not cross L; when When positioned above L, it is still moved upwards, but the maximum displacement is limited to 0.5d. This upward movement is only permitted if the reconstructed path satisfies obstacle avoidance and flight angle constraints. replace This is to increase the clearance distance from obstacles while suppressing excessive height fluctuations.

[0038] Preferably, in step S6, a leader-based information guidance strategy is used to update the non-dominated solutions. A leader individual is selected using a roulette wheel method based on the crowding distance of individuals in the non-dominated solution set, denoted as... Individuals with larger crowding distances are located in sparser areas of the target space, making them more likely to be selected as leaders. This leads the population to search for less-explored areas, which is beneficial for non-dominant individuals currently awaiting updates. The update formula is adopted: New individuals are generated, among which, Let 'a' be a random number ranging from [-1, 1], and 'a' be an adjustment parameter ranging from [0, 1]. This applies to the newly generated individuals after the update. Simultaneously perform obstacle avoidance detection and flight angle constraint detection; when both types of constraints are satisfied, select between the old and new individuals based on the dominance relationship;

[0039] The dual-source information guidance strategy is used to update the dominated solution. It selects the optimal individual for the path length target and the optimal individual for the path threat target from the current non-dominated solution set as reference individuals. The optimal individual for the path length target is denoted as... The optimal individual for the path threat target is denoted as For the dominant individual currently awaiting update The update formula is adopted: Generate new candidate individuals, among which To guide the weighting coefficients, all are random numbers in the range of [0,1]. Then, obstacle avoidance detection and flight angle constraint detection are performed simultaneously on the newly generated individuals after the update. When both types of constraints are satisfied, a selection is made between the old and new individuals based on the dominance relationship.

[0040] Preferably, the individual restart strategy in step S7 is used to handle long-term stagnant individuals in the population, when the number of consecutive evolutionary failures of an individual exceeds a preset threshold. When an individual is identified as a stagnant individual, it indicates that it is unlikely to continue to make effective improvements under the current evolutionary direction. In order to improve the population activity and avoid the algorithm from getting trapped in local optima, different restart and update methods are adopted for non-dominated solutions and dominated solutions respectively.

[0041] For long-term stagnant non-dominated individuals, a high-quality solution is randomly selected from the external archive to replace it, so that the restarted individual inherits the effective path information from the historical high-quality solutions;

[0042] For a dominant individual that has been stagnant for a long period, two high-quality solutions are first randomly selected from the external archive set, denoted as follows: and Subsequently and Execute the nearest path segment crossover operator to generate new candidate individuals. When a newly generated individual satisfies both obstacle avoidance constraints and flight angle constraints, the corresponding stationary dominant individual is replaced with the new individual.

[0043] Compared with existing technologies, the advantages and positive effects of this invention are as follows: The multi-operator co-evolutionary UAV 3D multi-objective path planning method provided by this invention addresses the problems of path planning in complex 3D environments, such as easy getting trapped in local optima, insufficient path safety, and weak multi-objective balancing ability. Simultaneously, it uses path length and path threat as optimization objectives, effectively shortening the flight distance while ensuring path safety. First, a fast-expanding random tree is used to generate a feasible initial population with high quality and diversity. Second, a dynamic subpopulation division mechanism is constructed, assigning elite, intermediate, and inferior subpopulations to fine-tuning, compromise search, and diversity exploration, respectively, and dynamically adjusting the size of the three types of subpopulations over time. During the bee-like phase, the nearest path segment intersection, direction-guided mutation, altitude profile shaping, and curvature-constrained smoothing operators are applied sequentially to candidate paths to reorganize effective path segments, suppress redundant altitude oscillations, and smooth excessive turns. The altitude-aware simplification operator and the distance-bounded safety operator are respectively applied to the path length and path threat objectives, and are differentiated according to the different evolutionary states of the elite, intermediate, and inferior subpopulations. Furthermore, a leader-based information guidance strategy and a dual-source information guidance strategy are used to develop non-dominated and dominated solutions, respectively, while an individual restart strategy utilizes high-quality solutions from external archives to reconstruct stagnant individuals. In summary, this invention can effectively improve the solution quality and search efficiency of UAV multi-objective path planning in complex environments, exhibiting positive effects such as fast convergence speed, high path safety, and strong global search capability. Attached Figure Description

[0044] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0045] Figure 1 This is an overall flowchart of the UAV 3D multi-objective path planning method based on multi-operator cooperative evolution proposed in this invention; Figure 2 This is a comparison diagram of non-dominated solution sets obtained by different algorithms in one embodiment of the present invention; Figure 3 This is a convergence curve of the hypervolume index of different algorithms as a function of running time in one embodiment of the present invention. Detailed Implementation

[0046] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described below in conjunction with the accompanying drawings and embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0047] Numerous specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways than those described herein, and therefore the invention is not limited to the specific embodiments disclosed in the following specification.

[0048] In practice, existing path planning methods typically use path length as the sole optimization objective. However, when planning UAV paths in complex 3D scenarios, it is necessary to consider not only flight distance but also obstacle distribution, spatial threat areas, and flight safety. Therefore, existing single-objective path planning methods struggle to generate high-quality flight paths that balance path length and safety in complex 3D environments. This invention proposes a multi-operator co-evolutionary 3D multi-objective path planning method for UAVs. The specific implementation is as follows... Figure 1 As shown, this is mainly achieved through the following steps.

[0049] S1. Establish a discrete 3D environment model and flight angle constraint model for the UAV, and set the starting point and target point. In this invention, a discrete 3D space is used to model the UAV flight environment. The UAV flight path is represented by a discrete waypoint sequence, and a feasible path is represented as... ,in, This represents a path, where S represents the drone's starting point, T represents the target point, and each track point... From three-dimensional coordinates The maximum horizontal turn angle for adjacent flight segments is set at 45°, and the maximum vertical climb or descent turn angle is set at 30°. The constraints are as follows: , Wherein, 45° is the maximum horizontal turning angle of adjacent flight segments, and 30° is the maximum vertical climb or descent turning angle of adjacent flight segments; all newly generated or reconstructed paths must simultaneously satisfy the above flight angle constraints and obstacle collision avoidance constraints. This invention simultaneously optimizes two objectives: path length and path threat. The path length objective is obtained by accumulating the three-dimensional Euclidean distances between adjacent waypoints in the path, calculated using the following formula: ,in, Representing a path The length of the path threat target is calculated by determining the minimum distance between each path segment and the nearest obstacle. The calculation formula is: ,in, Indicates the threat level of the path. This represents the minimum distance between the path segment and the nearest obstacle. w is a display scaling constant set according to the magnitude of the 3D environment data. w is only used to unify the display scale of the two target values, does not participate in weighted optimization, and does not change the Pareto dominance relationship between individuals.

[0050] S2. Initialize algorithm parameters, including population size. Maximum number of consecutive evolutionary failures for an individual Deadline for operation; population size in this invention. Set to 50, the maximum number of consecutive evolutionary failures for an individual. Set the value to 15, and the algorithm's runtime to 60 seconds. When the algorithm's runtime reaches 60 seconds, the evolution process terminates and the non-dominated solution set is output.

[0051] S3. An initial population is generated using a sampling-based initialization strategy, and an initial path that simultaneously satisfies obstacle avoidance and flight angle constraints is generated using a fast expanding random tree algorithm. Specifically, an initial population is generated using a sampling-based initialization strategy. Each individual represents a drone path. During the random tree expansion process, a node is only accepted if the newly added path segment does not collide with obstacles and the path after adding the new node satisfies the 45° horizontal turning angle constraint and the 30° vertical turning angle constraint, in order to improve the feasibility, quality and diversity of the initial population.

[0052] S4. Perform fast non-dominated sorting and crowding distance calculation on the population, dividing the population into elite subpopulations, intermediate subpopulations, and inferior subpopulations, and update the external archive set. Specifically, this invention adopts a dynamic subpopulation partitioning method. The elite subpopulation, intermediate subpopulation, and inferior subpopulation are respectively... The formula for calculating the size of the elite subpopulation is: ,in, For population size, Let represent the initial and final proportions of the elite subpopulation, respectively, and t represent the current time. The maximum running time is 60 seconds; the formula for calculating the size of the inferior subpopulation is: ,in, These represent the initial and final proportions of the inferior subpopulation, respectively; the size of the intermediate subpopulation is calculated as follows: Among them, the initial proportion of the elite subpopulation =0.33, final ratio =1; Initial proportion of the inferior subpopulation =0.33, final ratio =0. Subsequently, a fast non-dominated sort and crowding distance calculation are performed on the population, dividing it into different subpopulations based on non-dominated level and crowding distance. For elite subpopulations, individuals from the first frontier are prioritized; if the number is insufficient, they are supplemented from subsequent frontiers according to crowding distance from largest to smallest. Intermediate and inferior subpopulations are formed sequentially from the remaining individuals. Simultaneously, when a new non-dominated solution is generated, the external archive set is determined. Does a dominated individual exist? If so, delete the dominated individual and add the new non-dominated solution. Its size is That is, 7. The proportion of elites gradually increases from 0.33 to 1, so that the algorithm gradually transitions from the early stage of diversified exploration by three types of subpopulations to the later stage of refined optimization of bottleneck targets by more individuals; the final proportion of 1 does not mean that the individuals tend to be the same, but that all individuals adopt the elite evolution scheme.

[0053] In the S5 phase, the shortest path segment crossover operator, direction-guided mutation operator, height profile shaping operator, and curvature-constrained smoothing operator are sequentially executed on candidate individuals. Furthermore, based on the subpopulation category, individual target bottleneck, and evolutionary state, the height-aware simplification operator and distance-bounded safety operator are invoked differently, allowing the same operator pool to form different cooperative paths in different subpopulations, thus balancing global search, local development, and multi-objective equilibrium. Specifically, all individuals in the elite subpopulation participate in evolution; the intermediate subpopulation selects 50% of its individuals based on fitness values ​​and the number of successful evolutions; and the inferior subpopulation selects 50% of its individuals based on the number of successful evolutions.

[0054] Furthermore, the fitness value is obtained by summing the normalized values ​​for the path length target and the path threat target, respectively. The calculation formula is as follows: ,in and Let represent the path length and path threat value of the i-th individual, respectively. and These represent the maximum and minimum path length values ​​in the corresponding subpopulations, respectively. and These represent the maximum and minimum path threat values ​​in the corresponding subpopulations, respectively. The normalization is performed independently within each subpopulation. Subsequently, the nearest path segment crossover operator, the direction-guided mutation operator, the height profile shaping operator, and the curvature constraint smoothing operator are sequentially applied to the candidate individuals participating in the evolution.

[0055] Specifically, the input to the nearest path segment intersection operator is two parent path individuals, denoted as... and Where S represents the starting point and T represents the target point. Represent intermediate waypoints in the path, calculate the spatial distance between any pair of path segments in two parent paths, and determine the pair of path segments with the smallest distance. and If connected and as well as and If none of the line segments collide with obstacles, two candidate paths are generated by reconnecting the endpoints, and it is checked whether the candidate paths satisfy the flight angle constraint. Fast non-dominated sorting is performed on the parent path and the candidate paths, and the non-dominated solution is selected as the output; otherwise, the current path remains unchanged.

[0056] The input to the direction-guided mutation operator is the path output by the nearest path segment intersection operator, with intermediate waypoints randomly selected. And construct its predecessor node. With successor nodes The straight line L between them; when When located below L, make Move upwards along the height direction without crossing L, when When located above L, make Move downwards along the height direction without crossing L to obtain candidate nodes. Only when and Only when both the obstacle avoidance constraints and the reconstructed path satisfy the flight angle constraints will the better path be selected as the output between the original path and the new path.

[0057] The height profile shaping operator is used to coordinately adjust the height distribution of local path segments, randomly selecting two intermediate waypoints. and ,in Keeping the horizontal coordinates of each waypoint between the two unchanged, in order to and The height is used as the boundary, and a linear reference height is established based on the cumulative path distance; for trackpoints Its height is updated according to the following formula: , ,in, for waypoints The original height, From to The cumulative path length, To adjust the intensity coefficient, obstacle collision detection and flight angle constraint detection are performed on the entire path after the update, and the better path is selected between the original path and the new path to suppress unnecessary altitude oscillations.

[0058] The curvature-constrained smoothing operator first calculates the horizontal and vertical turning angles at each intermediate track point, and then determines the track point N with the largest vertical turning angle. i and the track point with the largest horizontal turning angle For each of the aforementioned waypoints, auxiliary waypoints are inserted on its two adjacent path segments. The distance between the auxiliary waypoints and the aforementioned waypoints is one-third of the length of the corresponding path segment. The local path is reconstructed using the auxiliary waypoints. The reconstructed path is only accepted when the obstacle collision avoidance constraint and flight angle constraint are satisfied, so as to distribute the directional changes concentrated on a single node to multiple continuous path segments.

[0059] After completing the nearest path segment intersection, direction-guided mutation, height profile shaping, and curvature constraint smoothing, a goal-oriented operator is applied based on the evolutionary state of different subpopulations. For individuals in the elite subpopulation, a normalized comparison of path length and path threat is performed to identify their bottleneck targets. The calculation formula is as follows: ,in, For the bottleneck objective of the i-th individual, when the normalized result corresponding to the path length objective is large, only the high-aware simplification operator is executed; when the normalized result corresponding to the path threat objective is large, only the distance-bounded safety operator is executed. For individuals in the intermediate subpopulation, the high-aware simplification operator and the distance-bounded safety operator are executed sequentially to optimize both objectives simultaneously. For individuals in the disadvantaged subpopulation, a random number between 0 and 1 is generated using the random function rand(). ,when If the value is less than 0.5, the height-sensing simplification operator is executed; otherwise, the distance-bounded safety operator is executed to enhance the diversity of the population's exploration directions.

[0060] The height-aware simplified operator is an operator oriented towards path length targets. First, the original path is projected onto a vertical plane aligned with the direction of the line connecting the starting point S to the target point T, and the intersection point of the projected path and the starting and ending point lines is determined. If an intersection exists, the path is divided into two parts based on whether the projected path is above or below the straight line. The proportion of each part projected onto the starting and ending straight lines is calculated, and the part with the smaller proportion is selected as a redundant path segment and deleted. The predecessor node of the deleted path segment is used as the reference point. As the starting point for connection, in its adjacent intersection point A new waypoint is generated at the midpoint between them. If the projected path is completely located on one side of the origin-end line, a redundant intermediate track point is randomly deleted and its predecessor node is directly connected to its successor node. The path is accepted only if the reconstructed path satisfies both obstacle avoidance constraints and flight angle constraints.

[0061] The distance-bounded safety operator is an operator oriented towards path-threatening targets. It first identifies the intermediate waypoint with the minimum clearance distance to the obstacle. And calculate its distance d to the nearest obstacle, while constructing and Local connection line L between, when When located below L, make Move randomly upwards along the height direction, with a displacement not exceeding d and the new node must not cross L; when When positioned above L, it is still moved upwards, but the maximum displacement is limited to 0.5d. This upward movement is only permitted if the reconstructed path satisfies obstacle avoidance and flight angle constraints. replace This is to increase the clearance distance from obstacles while suppressing excessive height fluctuations.

[0062] S6. During the observation bee phase, a leader-based information guidance strategy is implemented for non-dominated solutions, and a dual-source information guidance strategy is implemented for dominant solutions to improve the convergence ability of high-quality solutions and the development ability of dominant solutions. Specifically, firstly, a fast non-dominated sorting is performed on the new population generated in the mercenary bee phase, dividing the population into non-dominated solution sets. With Dominant Solution Set Specifically, for the non-dominated solution set, a leader-based information guidance strategy is adopted. First, a leader individual is selected from the non-dominated solution set using a roulette wheel method based on crowding distance. Individuals with larger crowding distances are located in sparser regions of the solution space, and are therefore more likely to be selected as leaders, thus guiding the population to evolve into less explored regions. Subsequently, for each individual in the non-dominated solution set... The update formula is adopted: New individuals are generated, among which, Let 'a' be a random number ranging from [-1, 1], and 'a' be an adjustment parameter ranging from [0, 1]. This applies to the newly generated individuals after the update. Simultaneously, obstacle avoidance detection and flight angle constraint detection are performed; when both types of constraints are satisfied, a selection is made between the old and new individuals based on the dominance relationship.

[0063] Furthermore, the dual-source information guidance strategy is used to update the dominant solution. It selects the optimal individual for the path length target and the optimal individual for the path threat target from the current non-dominated solution set as reference individuals, where the optimal individual for the path length target is denoted as... The optimal individual for the path threat target is denoted as For the dominant individual currently awaiting update The update formula is adopted: Generate new candidate individuals, among which To guide the weighting coefficients, all are random numbers in the range of [0,1]. Then, obstacle avoidance detection and flight angle constraint detection are performed simultaneously on the newly generated individuals after the update. When both types of constraints are satisfied, a selection is made between the old and new individuals based on the dominance relationship.

[0064] S7, the scout bee phase, involves implementing an individual restart strategy for individuals that have been stagnant for a long time without updating, in order to maintain population activity and avoid the algorithm getting trapped in local optima. When the number of consecutive evolutionary failures of an individual exceeds a preset threshold... When this occurs, the individual is classified as a stagnant individual, indicating that it is unlikely to achieve further effective improvement under the current evolutionary direction. =15. Specifically, let the number of consecutive evolutionary failures of an individual be . ,when Greater than At this point, the individual is considered to have entered a stagnant state. First, the new population output from the observation bee stage is subjected to another fast non-dominated sorting, dividing the new population into non-dominated and dominated solution sets. For stagnant non-dominated solution individuals, from the external archive set... A high-quality individual is randomly selected to replace the current stagnant individual, in order to inherit information about historical high-quality solutions; for the dominant solution individual in the stagnant process, from... Two individuals are randomly selected, and the nearest path segment crossover operator is executed to generate a new individual; the replacement is only performed when the new individual satisfies the obstacle avoidance constraint and flight angle constraint, so as to balance the preservation of high-quality information and the restoration of population diversity.

[0065] S8. Determine if the termination condition is met. If it is, output the non-dominated solution set; otherwise, return to step S4.

[0066] This invention proposes a multi-operator co-evolutionary UAV 3D multi-objective path planning method, which combines an improved artificial bee colony algorithm with the path planning problem, named MS-ABC. This method generates an initial population that satisfies collision avoidance and flight angle constraints through a sampling-based initialization strategy. In the mercenary bee phase, it enhances global search and target-oriented optimization through six operators: nearest path segment intersection, direction-guided mutation, altitude profile shaping, curvature constraint smoothing, altitude-aware simplification, and distance-bounded safety. In the observer bee phase, it improves the efficiency of developing non-dominated and dominated solutions through leader-based and dual-source information guidance strategies. In the scout bee phase, it restores population activity by utilizing an individual restart strategy based on external archives, thereby obtaining a Pareto path set that balances path length, path threat, and flight feasibility.

[0067] Next, a specific case will be used to further describe and illustrate the invention. The invention will be compared and analyzed experimentally with the Improved Artificial Bee Colony Algorithm (IABC), the Multi-Strategy Evolutionary Artificial Bee Colony Algorithm (MSEL-ABC), the Hybrid Gray Wolf Optimization Algorithm (HSGWO-MSOS), the Two-Stage Knowledge-Assisted Co-evolutionary Algorithm (TSKAC-NSGAII), and the Reinforcement Learning-Guided Multi-Objective Particle Swarm Optimization Algorithm (MCMOPSO-RL). The simulation experiments and results are as follows: In this complex 3D scene, the invention and the five existing algorithms were run independently, each for 60 seconds, to ensure the fairness and stability of the experimental results. The obtained non-dominated solution set is as follows: Figure 2 As shown, the convergence results based on the hypervolume index are as follows: Figure 3 As shown.

[0068] Among them, Figure 2 In the diagram, the horizontal axis represents the path threat value, and the vertical axis represents the path length value. Figure 2 It can be seen that the non-dominated solution set generated by the MS-ABC algorithm proposed in this invention is closer to the lower left region of the coordinate system, indicating that this invention can simultaneously obtain shorter paths and lower path threat values, thus yielding a higher quality solution set. Furthermore, compared to other comparative algorithms, the solution set generated by this invention has a more uniform distribution, demonstrating that this invention can effectively improve the solution set distribution performance.

[0069] exist Figure 3 In the graph, the horizontal axis represents the algorithm's running time, and the vertical axis represents the hypervolume value. The hypervolume metric measures the overall performance of the non-dominated solution set, and its value ranges from [0,1]. A larger hypervolume value indicates better overall algorithm performance. Figure 3 It can be seen that the MS-ABC algorithm initially converges faster in the test cases. As the algorithm iterates, its hypervolume value is generally higher than other comparative algorithms, and it eventually achieves a better convergence result. This indicates that the six operators—nearest path segment intersection, direction-guided mutation, height profile shaping, curvature constraint smoothing, height-aware simplification, and distance-bounded safety—can effectively enhance global search capabilities, suppress unnecessary height fluctuations, and improve path safety. Meanwhile, the leader-based information guidance strategy, the dual-source information guidance strategy, and the individual restart strategy can improve local exploitation capabilities and reduce the probability of the population getting trapped in local optima.

[0070] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments for application in other fields. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A multi-operator co-evolutionary method for UAV three-dimensional multi-objective path planning, characterized in that, Includes the following steps: S1. Establish a discrete 3D environment model and flight angle constraint model for the UAV, and set the starting point and target point; S2. Initialize algorithm parameters, including population size. Maximum number of consecutive evolutionary failures for an individual Deadline for operation; S3. An initial population is generated using a sampling-based initialization strategy, and an initial path that simultaneously satisfies obstacle avoidance constraints and flight angle constraints is generated using a fast expanding random tree algorithm. S4. Perform fast non-dominated sorting and crowding distance calculation on the population, divide the population into elite subpopulations, intermediate subpopulations and inferior subpopulations, and update the external archive set. S5, the stage of hiring bees, executes the nearest path segment crossover operator, the direction-guided mutation operator, the height profile shaping operator, and the curvature constraint smoothing operator in sequence for candidate individuals. Based on the subpopulation category, individual target bottleneck, and evolutionary state, the height-aware simplification operator and the distance-bounded safety operator are called in a differentiated manner, so that the same operator pool forms different cooperative paths in different subpopulations, so as to take into account global search, local development and multi-objective balance. S6. During the observation phase, a leader-based information guidance strategy is implemented for non-dominated solutions, and a dual-source information guidance strategy is implemented for dominant solutions to improve the convergence ability of high-quality solutions and the development ability of dominant solutions. S7, the scout bee phase, implements an individual restart strategy for individuals that have been stagnant for a long time without updating, in order to maintain population activity and avoid the algorithm getting trapped in local optima; S8. Determine if the termination condition is met. If it is, output the non-dominated solution set; otherwise, return to step S4.

2. The method for UAV three-dimensional multi-objective path planning based on multi-operator co-evolution as described in claim 1, characterized in that, In step S1, a discrete 3D path representation method is used to model the UAV flight path, and a feasible path is represented as follows: ,in, This represents a path, where S represents the drone's starting point and T represents the target point. Each track point is represented by three-dimensional coordinates. express; Flight angle constraints include horizontal turning angle constraints and vertical turning angle constraints. Let the projection vectors of adjacent path segments onto the horizontal plane be... The horizontal turning angle between two consecutive segments is Let the vertical component of the path segment be... The vertical turning angle between two consecutive segments is Then the constraint relationship is: ， ， Among them, 45° is the maximum horizontal turning angle of adjacent flight segments, and 30° is the maximum vertical climb or descent turning angle of adjacent flight segments; all newly generated or reconstructed paths must simultaneously satisfy the above flight angle constraints and obstacle collision avoidance constraints.

3. The method for UAV three-dimensional multi-objective path planning based on multi-operator co-evolution as described in claim 1, characterized in that, In step S1, the UAV path planning model simultaneously uses path length and path threat as optimization objectives. The path length objective is obtained by accumulating the three-dimensional Euclidean distances between adjacent waypoints along the path, and the calculation formula is as follows: ,in, Representing a path The length of the path threat target is calculated by determining the minimum distance between each path segment and the nearest obstacle. The calculation formula is: ,in, Indicates the threat level of the path. This represents the minimum distance between the path segment and the nearest obstacle. w is a display scaling constant set according to the magnitude of the 3D environment data. w is only used to unify the display scale of the two target values, does not participate in weighted optimization, and does not change the Pareto dominance relationship between individuals. The multi-objective path planning problem for unmanned aerial vehicles (UAVs) involves determining the path length while satisfying obstacle avoidance and flight angle constraints. Path threats Perform Pareto minimization.

4. The method for UAV three-dimensional multi-objective path planning based on multi-operator co-evolution as described in claim 1, characterized in that, In step S3, the sampling-based initialization strategy uses a fast expanding random tree algorithm to randomly sample and expand from the starting point to the target point. When generating a new node, it is determined whether the connection between nodes collides with an obstacle, and whether the newly added path segment satisfies the horizontal turning angle and vertical turning angle constraints. Only when both the collision avoidance constraint and the flight angle constraint are satisfied is the new node added to the path until a complete feasible path is generated.

5. The method for UAV three-dimensional multi-objective path planning based on multi-operator co-evolution as described in claim 1, characterized in that, In step S4, the fast non-dominated sorting method compares the dominance relationships of individuals in the population based on path length and path threat objectives, and assigns individuals to different frontiers. The crowding distance calculation method calculates the crowding distance of individuals within the same frontier in the target space, prioritizing the retention of individuals with larger crowding distances to improve the evenness of population distribution. Furthermore, step S4 employs a dynamic subpopulation size adjustment mechanism: the size of the elite subpopulation gradually increases as the algorithm runs, while the size of the inferior subpopulation gradually decreases. The size of the intermediate subpopulation is determined based on the total population size and the sizes of the other two subpopulations, allowing the algorithm to gradually transition from early diversified exploration to later refined optimization of bottleneck objectives. The formula for calculating the elite subpopulation size is: ,in, For population size, Let represent the initial and final proportions of the elite subpopulation, respectively, and t represent the current time. The maximum running time; the formula for calculating the size of the inferior subpopulation is: ,in, These represent the initial and final proportions of the inferior subpopulation, respectively; the size of the intermediate subpopulation is calculated as follows: ; After completing the fast non-dominated sorting, individuals are first selected from the first frontier to construct an elite subpopulation. When the number of individuals in the first frontier exceeds the preset size of the elite subpopulation, individuals with larger crowding distances are selected to join the elite subpopulation through crowding distance sorting. When the number of individuals in the first frontier is insufficient, individuals are selected from subsequent frontiers in descending order of dominance level, with priority given to retaining individuals with larger crowding distances, until the preset size of the elite subpopulation is reached. After the elite subpopulation is divided, an intermediate subpopulation is constructed based on the remaining individuals. The intermediate subpopulation is selected according to the non-dominance level and crowding distance, prioritizing the retention of individuals with higher dominance levels and larger crowding distances, until the preset size of the intermediate subpopulation is reached. After the elite subpopulation and intermediate subpopulation are divided, the remaining unselected individuals constitute the inferior subpopulation. An external archive set is used to store high-quality non-dominated solutions. When a new non-dominated solution is generated, it is checked whether a dominated individual exists in the external archive set. If it does, the dominated individual is deleted, and the new non-dominated solution is added to the external archive set, which has a size of [size missing]. .

6. The method for UAV three-dimensional multi-objective path planning based on multi-operator co-evolution as described in claim 1, characterized in that, In step S5, all individuals in the elite subpopulation participate in evolution; some individuals in the intermediate subpopulation participate in evolution based on their fitness value and the number of successful evolutions; and some individuals in the inferior subpopulation participate in evolution based on the number of successful evolutions. The fitness value is obtained by summing the normalized values ​​for path length and path threat targets, respectively. The calculation formula is as follows: ,in and Let represent the path length and path threat value of the i-th individual, respectively. and These represent the maximum and minimum path length values ​​in the corresponding subpopulations, respectively. and These represent the maximum and minimum path threat values ​​in the corresponding subpopulations, respectively.

7. The method for UAV three-dimensional multi-objective path planning based on multi-operator co-evolution as described in claim 1, characterized in that, In step S5: The input to the nearest path segment intersection operator is two parent path individuals, denoted as . and Where S represents the starting point and T represents the target point. Represent intermediate waypoints in the path, calculate the spatial distance between any pair of path segments in two parent paths, and determine the pair of path segments with the smallest distance. and If connected and as well as and If none of the line segments collide with obstacles, two candidate paths are generated by reconnecting the endpoints, and it is checked whether the candidate paths satisfy the flight angle constraint. Fast non-dominated sorting is performed on the parent path and the candidate paths, and the non-dominated solution is selected as the output; otherwise, the current path is kept unchanged. The input to the direction-guided mutation operator is the path output by the nearest path segment intersection operator, with intermediate waypoints randomly selected. And construct its predecessor node. With successor nodes The straight line L between them; when When located below L, make Move upwards along the height direction without crossing L, when When located above L, make Move downwards along the height direction without crossing L to obtain candidate nodes. Only when and Only when both the obstacle collision avoidance constraints and the reconstructed path satisfy the flight angle constraints will the better path between the original path and the new path be selected as the output. The height profile shaping operator is used to coordinately adjust the height distribution of local path segments, randomly selecting two intermediate waypoints. and ,in Keeping the horizontal coordinates of each waypoint between the two unchanged, in order to and The height is used as the boundary, and a linear reference height is established based on the cumulative path distance; for trackpoints Its height is updated according to the following formula: , ,in, for waypoints The original height, From to The cumulative path length, To adjust the intensity coefficient, obstacle collision detection and flight angle constraint detection are performed on the entire path after the update, and the better path is selected between the original path and the new path; The curvature-constrained smoothing operator first calculates the horizontal and vertical turning angles at each intermediate track point, and then determines the track point N with the largest vertical turning angle. i and the track point with the largest horizontal turning angle For each of the aforementioned waypoints, auxiliary waypoints are inserted on its two adjacent path segments. The distance between the auxiliary waypoints and the aforementioned waypoints is one-third of the length of the corresponding path segment. The local path is reconstructed using the auxiliary waypoints. The reconstructed path is only accepted when the obstacle collision avoidance constraint and flight angle constraint are satisfied, so as to distribute the directional changes concentrated on a single node to multiple continuous path segments.

8. The method for UAV three-dimensional multi-objective path planning based on multi-operator co-evolution as described in claim 1, characterized in that, In step S5, for the selected candidate individuals in the elite subpopulation, intermediate subpopulation, and inferior subpopulation, the nearest path segment crossover operator, direction-guided mutation operator, height profile shaping operator, and curvature constraint smoothing operator are executed sequentially. Subsequently, based on the subpopulation to which the individual belongs and its target performance, a target-oriented operator is applied. For individuals in the elite subpopulation, the bottleneck target is determined based on the normalized results of the path length target and the path threat target, and its calculation formula is as follows: ,in, For the bottleneck target of the i-th individual, when the normalized result corresponding to the path length target is large, only the high-awareness simplification operator is executed; when the normalized result corresponding to the path threat target is large, only the distance-bounded safety operator is executed, thus prioritizing the improvement of the weaker target and preserving the existing advantages of the other target as much as possible. For individuals in the intermediate subpopulation, after completing the four basic evolutionary operators—the nearest path segment crossover operator, the direction-guided mutation operator, the height profile shaping operator, and the curvature-constrained smoothing operator—the height-aware simplification operator and the distance-bounded safety operator are executed sequentially to simultaneously explore the trade-off between path length and path threat. For individuals in the disadvantaged subpopulation, after completing the aforementioned four basic evolutionary operators, the height-aware simplification operator or the distance-bounded safety operator is randomly selected for operation to conduct extensive exploration from different target directions and introduce new diversity into the population. The height-aware simplified operator is an operator oriented towards path length targets. First, the original path is projected onto a vertical plane aligned with the direction of the line connecting the starting point S to the target point T, and the intersection point of the projected path and the starting and ending point lines is determined. If an intersection exists, the path is divided into two parts based on whether the projected path is above or below the straight line. The proportion of each part projected onto the starting and ending straight lines is calculated, and the part with the smaller proportion is selected as a redundant path segment and deleted. The predecessor node of the deleted path segment is used as the reference point. As the starting point for connection, in its adjacent intersection point A new waypoint is generated at the midpoint between them. If the projected path is completely located on one side of the origin-end line, a redundant intermediate track point is randomly deleted and its predecessor node and successor node are directly connected. The path is accepted only if the reconstructed path satisfies both obstacle avoidance constraints and flight angle constraints. The distance-bounded safety operator is an operator oriented towards path-threatening targets. It first identifies the intermediate waypoint with the minimum clearance distance to the obstacle. And calculate its distance d to the nearest obstacle, while constructing and Local connection line L between, when When located below L, make Move randomly upwards along the height direction, with a displacement not exceeding d and the new node must not cross L; when When positioned above L, it is still moved upwards, but the maximum displacement is limited to 0.5d. This upward movement is only permitted if the reconstructed path satisfies obstacle avoidance and flight angle constraints. replace This is to increase the clearance distance from obstacles while suppressing excessive height fluctuations.

9. The method for UAV three-dimensional multi-objective path planning based on multi-operator co-evolution as described in claim 1, characterized in that, Step S6 includes: A leader-based information guidance strategy is used to update non-dominated solutions. A roulette wheel method is used to select a leader individual based on the crowding distance of individuals in the non-dominated solution set, denoted as […]. Individuals with larger crowding distances are located in sparser areas of the target space, making them more likely to be selected as leaders. This leads the population to search for less-explored areas, which is beneficial for non-dominant individuals currently awaiting updates. The update formula is adopted: New individuals are generated, among which, Let 'a' be a random number ranging from [-1, 1], and 'a' be an adjustment parameter ranging from [0, 1]. This applies to the newly generated individuals after the update. Simultaneously perform obstacle avoidance detection and flight angle constraint detection; when both types of constraints are satisfied, select between the old and new individuals based on the dominance relationship; The dual-source information guidance strategy is used to update the dominated solution. It selects the optimal individual for the path length target and the optimal individual for the path threat target from the current non-dominated solution set as reference individuals. The optimal individual for the path length target is denoted as... The optimal individual for the path threat target is denoted as For the dominant individual currently awaiting update The update formula is adopted: Generate new candidate individuals, among which To guide the weighting coefficients, all are random numbers in the range of [0,1]. Then, obstacle avoidance detection and flight angle constraint detection are performed simultaneously on the newly generated individuals after the update. When both types of constraints are satisfied, a selection is made between the old and new individuals based on the dominance relationship.

10. The method for UAV three-dimensional multi-objective path planning based on multi-operator co-evolution according to claim 1, characterized in that, In step S7, the individual restart strategy is used to handle long-term stagnant individuals in the population. When the number of consecutive evolutionary failures of an individual exceeds a preset threshold... When an individual is identified as a stagnant individual, it indicates that it is unlikely to continue to make effective improvements under the current evolutionary direction. In order to improve the population activity and avoid the algorithm from getting trapped in local optima, different restart and update methods are adopted for non-dominated solutions and dominated solutions respectively. For long-term stagnant non-dominated individuals, a high-quality solution is randomly selected from the external archive to replace it, so that the restarted individual inherits the effective path information from the historical high-quality solutions; For a dominant individual that has been stagnant for a long period, two high-quality solutions are first randomly selected from the external archive set, denoted as follows: and Subsequently and Execute the nearest path segment crossover operator to generate new candidate individuals. When a newly generated individual satisfies both obstacle avoidance constraints and flight angle constraints, the corresponding stationary dominant individual is replaced with the new individual.

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