UAV path planning method and device based on improved frost and ice optimization algorithm

Abstract

The present invention discloses a method and device for UAV path planning based on an improved frost and ice optimization algorithm, the method comprising: constructing a flight space according to the starting point and end point of the UAV, and planning the flight path of the UAV according to the obstacles in the flight space and the comprehensive cost function of the UAV path planning; substituting the coordinate values ​​of the positions of rime particles obtained by the multi-strategy improved frost and ice optimization algorithm into the comprehensive cost function to calculate and output the optimal path; adjusting the flight path of the UAV according to the optimal path. The present invention realizes UAV path planning based on the improved frost and ice optimization algorithm, and has achieved significant improvements in the length, flight time and energy consumption of the optimized path, and can quickly find a path with low cost, high safety and short arrival time, thereby improving the efficiency of UAV task execution.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned aerial vehicle (UAV) path planning, and in particular to a method and device for UAV path planning based on an improved frost and ice optimization algorithm. Background Art

[0002] As drone technology matures and becomes more popular, a core issue has gradually emerged: trajectory planning. Effective trajectory planning is not only related to the operating efficiency of drones, but also directly related to flight safety and mission success rate.

[0003] The improvement of trajectory planning is not only reflected in path optimization, but also in its ability to achieve more refined control, ensuring that drones can perform tasks safely and efficiently in complex environments, while minimizing energy consumption and flight risks, greatly improving the overall performance of the drone system.

[0004] Metaheuristic algorithms, as a type of non-deterministic search strategy, have demonstrated unparalleled potential in solving the complex optimization problem of drone trajectory planning due to their flexibility and wide applicability. These algorithms can effectively handle multi-objective and multi-constrained optimization challenges, and provide innovative solutions for drone path planning by simulating intelligent behaviors in natural and social phenomena. At present, the research and application of metaheuristic algorithms are advancing at an unprecedented speed, which not only promotes the iterative upgrade of the algorithm itself, but also opens up new paths for expanding the boundaries of drone technology.

[0005] The application of metaheuristic algorithms in UAV trajectory planning has greatly improved the efficiency and accuracy of path planning. Researchers have used these algorithms to optimize UAV paths and have achieved remarkable results in solving complex challenges. However, no algorithm can perform optimally on all problems. Therefore, in specific applications, it is particularly important to design dedicated metaheuristic algorithms based on the characteristics and requirements of specific problems to ensure that the algorithm can achieve the best optimization effect.

[0006] The Rime Ice Optimization (RIME) algorithm is a novel physical heuristic algorithm proposed by Su et al. in 2023, which is inspired by the natural growth process of frost ice. RIME simulates the diffusion of soft frost and the solidification of hard frost, constructs a soft frost search strategy and a hard frost penetration mechanism, and realizes the efficient conversion between exploration and development of the algorithm. However, the RIME algorithm has the problems of slow convergence, easy to fall into local optimal solutions, and poor performance in practical problems in some cases.

[0007] Gaoquan Gu, Jingjun Lou and others proposed a multi-strategy improved frost and ice optimization algorithm (MIRIME). First, the tent chaos map is used to initialize the population to lay the foundation for global optimization. Secondly, an adaptive update strategy based on leadership and dynamic centroid is introduced to promote the group to develop in a more favorable direction. In order to solve the problem of population scarcity in the later iterations, an anti-learning control strategy based on lens imaging is introduced to enhance population diversity and ensure convergence accuracy. MIRIME is applied to solve the three-dimensional path planning problem of unmanned aerial vehicles. Experimental results show that MIRIME outperforms other competing algorithms in terms of solution quality and stability. Cankun Xie, Shaobo Li and others also improved the frost and ice optimization algorithm. First, they used the elite reverse learning population selection strategy of segmented mapping to enhance the population diversity of the algorithm. Secondly, an elite pool exploration strategy controlled by random factors is proposed, which makes it difficult for the algorithm to fall into the local optimum. Finally, a hard frost piercing development strategy based on sine-cosine function is proposed, which enables the algorithm to find the global optimum faster during the development process. They also achieved good results by applying the algorithm to the three-dimensional unmanned aerial vehicle path planning problem in three different terrain scenarios.

[0008] However, faced with ever-changing environments and task requirements, the continuous exploration and development of more efficient and intelligent meta-heuristic algorithms remains one of the major challenges facing this field. Summary of the invention

[0009] In view of this, the present invention proposes a UAV path planning method and device based on an improved frost and ice optimization algorithm. First, in the exploration stage, this study adopts a Gaussian mutation perturbation strategy to increase the diversity of the search, which helps to jump out of the local optimal solution, improve the convergence speed and robustness of the algorithm, and thus more effectively search for the global optimal solution. Secondly, in the algorithm development stage, the present invention introduces a random differential position update rule, which updates the positions of other individuals by randomly selecting individuals in the population and calculating their position differences to guide the algorithm to search for the optimal solution. In response to the problem that the algorithm's optimization ability weakens in the later stage of iteration, the present invention proposes a leader-based reverse learning strategy, which selects the best-positioned individual in the group as the leader, and guides other individuals to reversely learn and explore the leader's position to increase the algorithm's optimization ability, which helps to find a better solution. The present invention was experimentally compared with 7 mainstream algorithms, and it was found that the present invention is superior to other algorithms in terms of solution quality and stability, showing great application potential.

[0010] Specifically, the present invention provides the following technical solutions:

[0011] A UAV path planning method based on an improved frost optimization algorithm comprises:

[0012] S1: Construct a flight space according to the starting point and end point of the UAV, and plan the flight path of the UAV according to the obstacle set in the flight space and the comprehensive cost function of the UAV path planning;

[0013] S2: Substitute the coordinate values ​​of the positions of the rime particles obtained by the multi-strategy improved rime optimization algorithm into the comprehensive cost function to calculate and output the optimal path; wherein, the optimal path satisfies the minimum comprehensive cost function of the UAV path planning and does not intersect with the obstacle set; the multi-strategy improved rime optimization algorithm includes: S21, initializing the relevant parameters of the multi-strategy improved rime optimization algorithm, and calculating the population matrix; S22: In the exploration stage, the Gaussian mutation perturbation strategy is used to improve the soft rime search strategy, and the global optimal solution is searched according to the improved soft rime search strategy; S23: In the development stage, a random differential position update rule is introduced, and the positions of other individuals are updated by randomly selecting individuals in the population and calculating their position differences, guiding the algorithm to search for the optimal solution, introducing the crossover strategy in the genetic algorithm, promoting information exchange and cooperation between particles, and enhancing the global search capability of the algorithm. The random differential position update rule and crossover strategy are used to improve the hard rime puncture mechanism, and development is carried out according to the improved hard rime puncture mechanism to approach the global optimal solution as soon as possible; S24: In the later stage of iteration, a leader-based reverse learning strategy is introduced. By selecting the individual with the best position in the group as the leader, and guiding other individuals to reversely learn and explore the leader's position, the algorithm's optimization ability is increased to obtain a better global optimal solution. The forward greedy mechanism is used to filter out inferior solutions and retain the best solutions. The comprehensive cost function value of the updated agent is compared with the comprehensive cost function value of the agent before the update. If the updated comprehensive cost function value is better than the comprehensive cost function value before the update, a replacement occurs, and the solution agent of the two is replaced at the same time; S25: Repeat steps S22~S24 until the termination condition is met, and output the optimal solution found, that is, the coordinate value of the position of the rime particles;

[0014] S3, adjust the flight path of the UAV according to the optimal path.

[0015] Preferably, the improved soft rime search strategy is expressed as:

[0016] ;

[0017] in, is the position of rime particles after the improved soft rime search strategy is updated. The best individual in the population Rime particles, Represents a random number between 0 and 1. is a random number between 0 and 1. Represents rounding to an integer. Indicates the adhesion between soft rime, which is a random number in the range of (0,1). and They represent the upper and lower bounds of the search space respectively, Indicates the current iteration number, is the maximum number of iterations, Represents the adhesion coefficient, which affects the condensation probability of the search individual and increases with the number of iterations. It is calculated by the following formula:

[0018]

[0019] is the Gaussian distribution after the Gaussian mutation perturbation strategy is optimized, and is calculated by the following formula:

[0020]

[0021] in, is the value of the Gaussian distribution probability density function, indicating that the random variable The probability density at is calculated by the following formula:

[0022]

[0023] in, represents the variance, which measures the degree of dispersion of data distribution. represents the mean, represents the center of the distribution, The independent variable of the probability density function represents a specific value or position. =0, =1, It is expressed as:

[0024] .

[0025] Preferably, the expression of the hard rime puncture mechanism improved by the random differential position update rule is:

[0026]

[0027] in, It is the position of rime particles after the hard rime penetration mechanism is updated by the random difference position update rule. Represents a random number between (0,1), and represents two different random individuals.

[0028] Preferably, the expression of the hard rime puncture mechanism improved by the cross strategy is:

[0029]

[0030] in, It is the position of rime particles after the cross strategy improved hard rime piercing mechanism is updated. Indicates the optimal position of rime particles before the update. represents a random individual, Represents a random number between (0,1), .

[0031] Preferably, the leader's reverse learning strategy is expressed as:

[0032]

[0033] in, It is the position of the rime particles after being updated by the leader’s reverse learning strategy.

[0034] Preferably, in the later stage of iteration, the positions of rime particles after being updated by the hard rime piercing mechanism improved by the random differential position update rule and the positions of rime particles after being updated by the hard rime piercing mechanism improved by the cross strategy are compared, and the individual with the best position is selected as the leader.

[0035] Preferably, in step S1, the obstacle set is represented as:

[0036]

[0037] in, is the set of obstacles in the flight space; is the coordinate value of the obstacle on the X axis, and y is the coordinate value of the obstacle on the Y axis.

[0038] Preferably, in step S1, the calculation process of the comprehensive cost function of the drone path planning is:

[0039] The path length cost function is calculated by the following formula:

[0040]

[0041] in, Indicates the first The coordinates of the point, is the Euclidean distance, Represents the total number of points on the drone's path;

[0042] The flight altitude cost function is calculated by the following formula:

[0043]

[0044] in, Indicates that the drone is The coordinate of the point on the Z axis, is the average height of all points on the path;

[0045] The smoothness cost function of the path is calculated by the following formula:

[0046]

[0047] in, = ,express The turning angle of the point;

[0048] The comprehensive cost function of UAV path planning is calculated by the following formula:

[0049]

[0050] in, ( = 1,2,3) is the weight of each cost, calculated by the following formula:

[0051]

[0052] The unmanned flight path of the drone is planned according to the obstacle set in the flight space and the comprehensive cost function of the drone path planning, which is obtained through the following model:

[0053]

[0054] in, Indicates the flight path. and Represent the ground and obstacles respectively.

[0055] The embodiment of the present invention also provides a UAV path planning device based on an improved frost and ice optimization algorithm, which includes:

[0056] A flight path planning unit, used to construct a flight space according to the starting point and the end point of the UAV, and plan the flight path of the UAV according to the obstacle set in the flight space and the comprehensive cost function of the UAV path planning;

[0057] The optimal path output unit is used to substitute the coordinate values ​​of the positions of the rime particles obtained by the multi-strategy improved rime optimization algorithm into the comprehensive cost function to calculate and output the optimal path; wherein, the optimal path satisfies the minimum comprehensive cost function of the UAV path planning and does not intersect with the obstacle set; the multi-strategy improved rime optimization algorithm includes: S21, initializing the relevant parameters of the multi-strategy improved rime optimization algorithm, and calculating the population matrix; S22: in the exploration stage, using the Gaussian mutation perturbation strategy to improve the soft rime search strategy, and searching for the global optimal solution according to the improved soft rime search strategy; S23: in the development stage, introducing a random differential position update rule, updating the positions of other individuals by randomly selecting individuals in the population and calculating their position differences, guiding the algorithm to search for the optimal solution, introducing the crossover strategy in the genetic algorithm, promoting information exchange and cooperation between particles, and enhancing the global search of the algorithm. Search ability, random differential position update rules and crossover strategies are used to improve the hard rime puncture mechanism, and development is carried out according to the improved hard rime puncture mechanism to approach the global optimal solution as soon as possible; S24: In the later stage of iteration, a leader-based reverse learning strategy is introduced. By selecting the individual with the best position in the group as the leader, and guiding other individuals to reversely learn and explore the leader's position, the algorithm's optimization ability is increased to obtain a better global optimal solution. A forward greedy mechanism is used to filter out inferior solutions and retain the best solutions. The comprehensive cost function value of the updated agent is compared with the comprehensive cost function value of the agent before the update. If the updated comprehensive cost function value is better than the comprehensive cost function value before the update, a replacement occurs, and the solution agent of both is replaced at the same time; S25: Repeat steps S22~S24 until the termination condition is met, and output the optimal solution found, that is, the coordinate value of the position of the rime particles;

[0058] Flight path adjustment unit, used to adjust the flight path of the drone according to the optimal path

[0059] Compared with the prior art, the present invention has the following beneficial effects:

[0060] The present invention applies a multi-strategy improved frost ice optimization algorithm to the path planning of unmanned aerial vehicles. The multi-strategy improved frost ice optimization algorithm integrates multiple strategies to overcome the limitation that the original frost ice algorithm is easily trapped in the local optimal solution. In order to enhance the diversity of the search process and the global exploration ability, the Gaussian mutation perturbation mechanism is adopted in the exploration stage of the algorithm, which increases the diversity of the search, significantly improves the probability of jumping out of the local minimum point, helps to jump out of the local optimal solution, improves the convergence speed and robustness of the algorithm, and enables the algorithm to more efficiently approach the true global optimal solution; in the development stage, the random differential position update rule is introduced, and the positions of other individuals are updated by randomly selecting individuals in the population and calculating their position differences to guide the algorithm to search for the optimal solution, while maintaining the dynamic balance of the population. This strategy effectively balances exploration and development, helps to avoid premature convergence, and improves the stability and timeliness of the algorithm when dealing with complex optimization problems; at the same time, the crossover strategy in the genetic algorithm is introduced to promote information exchange and cooperation between particles and enhance the global search ability of the algorithm. In order to solve the problem that the algorithm's optimization ability weakens in the later stages of iteration, a leader-based reverse learning strategy is creatively added. By identifying the best performing individual in the population as the leader, and guiding other individuals to reversely learn and explore the leader's position, that is, starting from a distance from the current state and exploring toward the leader's position, the algorithm's later optimization ability is greatly enhanced, which helps to find a better solution. The present invention has made significant improvements in the length, flight time, and energy consumption of the optimized path, and can quickly find a path with low cost, high safety, and short arrival time, thereby improving the efficiency of drone mission execution. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 This is the flowchart of the original frost algorithm;

[0062] Figure 2 A schematic diagram of a flow chart of a UAV path planning method based on an improved frost and ice optimization algorithm provided in the first embodiment of the present invention;

[0063] Figure 3 It is the specific working principle diagram of step S2;

[0064] Figure 4 is the workflow diagram of step S2;

[0065] Figure 5 is a comparative convergence curve of the ADRIME algorithm and other 7 optimization algorithms for 12 functions in the 20-dimensional case of the CEC2022 test set; the horizontal axis is the number of iterations, and the vertical axis is the mean square error;

[0066] Figure 6 Box plot comparing 12 functions of ADRIME algorithm and other 7 optimization algorithms in 20 dimensions of CEC2022 test set;

[0067] Figure 7 This is the convergence curve diagram of ADRIME algorithm and other 7 optimization algorithms in UAV planning;

[0068] Figure 8 shows the optimal path diagram of ADRIME algorithm and other 7 optimization algorithms in UAV planning;

[0069] Fig. 9 A schematic structural diagram of a UAV path planning device based on an improved frost and ice optimization algorithm provided in the second embodiment of the present invention. DETAILED DESCRIPTION

[0070] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0071] To facilitate understanding of the present invention, the algorithm principle of the original frost and ice algorithm is first introduced below:

[0072] Rime, as a product of condensation of water vapor in a low-temperature environment, is affected by multiple factors such as temperature, wind speed and humidity. Due to the unique climate and terrain conditions in specific areas, fascinating rime and ice scenery can often be formed. Rime can be divided into two categories according to its properties: soft rime and hard rime, and wind speed plays a key role in this: a breeze environment promotes soft rime, which grows slowly and is randomly distributed; while strong winds shape hard rime, which grows rapidly and has obvious directionality. Inspired by the growth mechanism of rime, researchers proposed a soft rime search strategy and a hard rime piercing mechanism, and adopted a positive greedy selection strategy. Combining these three mechanisms, a frost and ice algorithm was developed. For the convenience of comparison and recording, it is recorded as: RIME algorithm. The mathematical model of the RIME algorithm is introduced below:

[0073] 1. Population initialization

[0074] The frost ice initialization population is shown in formula 1:

[0075]

[0076] in, Represents the population matrix of frost ice, Indicates the position of rime particles.

[0077] 2. Soft rime search strategy (exploration phase)

[0078] In a breeze environment, soft rime grows randomly and covers a wide range, but grows slowly in the same direction. Inspired by this, a soft rime search strategy is proposed using the random coverage of rime, which allows the algorithm to quickly cover the search space in the early stage and avoid local optimality. Its mathematical model is shown in formula (2):

[0079]

[0080] in, is the position of the rime particles after the soft rime search strategy is updated. The best individual in the population Rime particles, Represents a random number between 0 and 1. is a random number between 0 and 1, Represents rounding to an integer. Indicates the adhesion between soft rime, which is a random number in the range of (0,1). and They represent the upper and lower bounds of the search space respectively, Indicates the current iteration number, is the maximum number of iterations, the adhesion coefficient The condensation probability that affects the search individual increases with the number of iterations, as shown in formula (3):

[0081]

[0082] 3. Hard rime puncture mechanism (development stage)

[0083] Under strong winds, hard rime grows more regularly. Its characteristics are: 1) Strong winds cause hard rime to grow rapidly in the same direction. 2) Rime growing in the same direction is easy to cross, that is, rime piercing. 3) Hard rime increases as it grows, and when the growth conditions are good, the probability of penetration is high. Therefore, inspired by the puncture phenomenon, a hard rime puncture mechanism is proposed for algorithm update, particle exchange, and improvement of algorithm convergence and ability to jump out of local optimality. The particle replacement formula is shown in formula (4):

[0084]

[0085] in, Indicates the position of rime particles after the hard rime piercing mechanism is updated. represents a random number between 0 and 1. Represents the normalized value of the current individual fitness value.

[0086] 4. Positive Greedy Selection Mechanism

[0087] Metaheuristic algorithms usually use a greedy mechanism when updating the global optimal solution and individual positions. By comparing the performance of the updated individual with the current global optimal, if the former is better, the global optimal solution is updated. This method is simple and fast, but it is lacking in improving the individual search ability. Its main function is to record the best result. In order to improve the efficiency of the algorithm, a positive greedy mechanism is proposed. This mechanism compares the performance of the individual before and after the update. If the performance after the update is better, the old individual is replaced. This approach helps excellent individuals appear more frequently, thereby improving the quality of the solution. Although changes in the positions of individuals in the population may cause the performance of some intelligent agents to decline, it generally helps the population to develop in a better direction during the iteration process. The mathematical model is shown in formulas (5) and (6):

[0088]

[0089]

[0090] in, represents the fitness value of the agent before updating, is the updated fitness value, is the global optimal fitness value, Represents the position before the update, is the updated position, represents the global optimal position of an individual.

[0091] In summary, the process of the RIME algorithm is as follows Figure 1 shown.

[0092] However, the RIME algorithm has problems such as low accuracy, slow convergence speed, and easy falling into local optimal solutions in experiments.

[0093] For this reason, please see Figure 2 The first embodiment of the present invention provides a UAV path planning method based on an improved frost and ice optimization algorithm, which includes:

[0094] S1: Construct a flight space according to the starting point and end point of the UAV, and plan the flight path of the UAV according to the obstacle set in the flight space and the comprehensive cost function of the UAV path planning.

[0095] Specifically, let the starting point of the drone be ( ), the end point is ( ); The trajectory of the drone from the starting point to the end point is composed of a set of points ( ) is composed of is any point in the trajectory, whose coordinates are ( ),

[0096] Plan the flight space based on the starting point and the end point, establish the obstacle set in the flight space based on the on-site topography, and model the obstacle set according to the following formula:

[0097]

[0098] in, is the set of obstacles in the flight space; is the coordinate value of the obstacle on the X axis, and y is the coordinate value of the obstacle on the Y axis;

[0099] Calculate the comprehensive cost function of the UAV path planning, where

[0100] The path length cost function is calculated by the following formula:

[0101]

[0102] in, Represents the path planning of the UAV The coordinates of the point, is the Euclidean distance, Represents the total number of points on the drone's path;

[0103] The flight altitude cost function is calculated by the following formula:

[0104]

[0105] in, Indicates that the drone is The coordinate of the point on the Z axis, is the average height of all points on the path;

[0106] The smoothness cost function of the path is calculated by the following formula:

[0107]

[0108] in, = ,express The turning angle of the point;

[0109] The comprehensive cost function of UAV path planning is calculated by the following formula:

[0110]

[0111] in, ( = 1,2,3) is the weight of each cost, calculated by the following formula:

[0112]

[0113] The UAV plans the flight path of the unmanned aircraft according to the obstacle set in the flight space and the comprehensive cost function of the UAV path planning, through the following model:

[0114]

[0115] in, Indicates the flight path. and Represent the ground and obstacles respectively.

[0116] S2: Substitute the coordinate values ​​of the positions of the rime particles obtained by the multi-strategy improved frost optimization algorithm into the comprehensive cost function to calculate and output the optimal path.

[0117] In this embodiment, the multi-strategy improved frost optimization algorithm can be recorded as ADRIME algorithm, such as Figure 3 and Figure 4 As shown, the ADRIME algorithm includes the following calculation steps:

[0118] S21: Initialize the relevant parameters of the frost algorithm and calculate the population matrix;

[0119] S22: In the exploration phase, the Gaussian variation perturbation strategy is used to improve the soft rime search strategy, and the global optimal solution is searched according to the improved soft rime search strategy;

[0120] S23: In the development stage, introduce the random differential position update rule, update the positions of other individuals by randomly selecting individuals in the population and calculating their position differences, guide the algorithm to search for the optimal solution, introduce the crossover strategy in the genetic algorithm, promote information exchange and cooperation between particles, enhance the global search ability of the algorithm, use the random differential position update rule and crossover strategy to improve the hard rime puncture mechanism, and develop according to the improved hard rime puncture mechanism to approach the global optimal solution as soon as possible;

[0121] S24: In the later stage of iteration, a leader-based reverse learning strategy is introduced. By selecting the best individual in the group as the leader and guiding other individuals to reversely learn and explore the leader's position, the algorithm's optimization ability is increased to obtain a better global optimal solution. A forward greedy mechanism is used to filter out inferior solutions and retain the best solutions. The fitness value of the updated agent is compared with the fitness value of the agent before the update. If the updated fitness value is better than the value before the update, a replacement occurs, and the solution agent of both agents is replaced at the same time;

[0122] S25: Repeat steps S22 to S24 until the termination condition is met, and output the optimal solution found.

[0123] Specifically, initialize the relevant parameters of the frost and ice algorithm, and calculate the population matrix according to formula (1);

[0124] In order to reduce the probability of the RIME algorithm encountering a local optimal solution trap, a Gaussian mutation perturbation strategy is introduced in the exploration phase to improve the soft rime search strategy. The core of this strategy is to force the rime particles to perform a series of instantaneous and nonlinear random movements, which significantly improves the coverage of the search space. Through this mechanism, the algorithm can effectively break the constraints of the local optimal solution and accelerate the convergence process to the global optimal solution. At the same time, it significantly enhances the stability and adaptability of the algorithm when facing complex problems. The mathematical expression of the improved soft rime search strategy is shown in formula (7):

[0125]

[0126] Among them, among them, is the position of rime particles after the improved soft rime search strategy is updated. The best individual in the population Rime particles, Represents a random number between 0 and 1. is a random number between 0 and 1. Represents rounding to an integer. Indicates the adhesion between soft rime, which is a random number in the range of (0,1). and They represent the upper and lower bounds of the search space respectively, Indicates the current iteration number, is the maximum number of iterations, Represents the adhesion coefficient, which affects the condensation probability of the search individual and increases with the number of iterations. It is calculated by the following formula:

[0127]

[0128] is the Gaussian distribution after the Gaussian mutation perturbation strategy is optimized, as shown in formula (8):

[0129]

[0130] in, is the value of the Gaussian distribution probability density function, indicating that the random variable The probability density at The expression of is shown in formula (9):

[0131]

[0132] in, represents the variance, which measures the degree of dispersion of data distribution. represents the mean, represents the center of the distribution, The independent variable of the probability density function represents a specific value or position. =0, =1, It is expressed as:

[0133]

[0134] Therefore, when When , the soft rime search strategy rime particle position is updated using formula (7).

[0135] During the development phase, the random differential position update rule was introduced to significantly improve the global search capability of the algorithm and avoid it from falling into the trap of local optimal solutions. The core idea of ​​this rule is to introduce randomness so that rime particles can jump in the solution space in an unpredictable way, thereby breaking through the limitations of local optimal solutions and exploring a wider solution domain.

[0136] Specifically, the working principle of the random differential position update rule is: randomly select a number of individuals from the current rime particle group, and generate a set of new differential vectors by calculating the position differences between these individuals. Subsequently, these differential vectors are used to update the positions of other particles. This update method not only increases the randomness and unpredictability of particle movement, but also effectively expands the search range and enhances the exploration ability of the algorithm. Since this process is based on the interaction between particles, it also promotes information exchange between particles, further improving the diversity and efficiency of the search. The expression of the hard rime puncture mechanism improved by the random differential position update rule is shown in formula (11):

[0137]

[0138] in, It is the position of rime particles after the hard rime penetration mechanism is updated by the random difference position update rule. Represents a random number between (0,1), and represents two different random individuals.

[0139] The RIME algorithm tends to focus on the evolutionary path of a single optimal particle, resulting in relatively weak cooperation and information sharing mechanisms between particles. Although this feature accelerates the convergence speed, it also brings serious limitations and makes it difficult to cross to a more optimal solution area. Therefore, the crossover operation in the genetic algorithm (GA) is introduced as an improvement strategy to promote information exchange and cooperation between particles and enhance the global search capability of the algorithm. The crossover strategy in the genetic algorithm is a mechanism that simulates the gene recombination phenomenon in biological genetics. The crossover strategy is applied to FOA, enabling it to effectively exchange key information carried by non-optimal particles, such as saddle points, local optimal solutions, etc.

[0140] Specifically, in each generation of evolution, multiple particles are randomly selected for pairing and a crossover operation is performed. This operation divides each paired particle into two parts with a certain probability, and then recombines the first half of one particle with the second half of another particle, and vice versa. In this way, the information originally belonging to different particles is effectively mixed together to form new particles, which carry richer and more diverse information, helping the algorithm to explore a wider solution space. The expression of the hard rime puncture mechanism improved by the crossover strategy is shown in formula (12):

[0141]

[0142] in, It is the position of rime particles after the cross strategy improved hard rime piercing mechanism is updated. Indicates the optimal position of rime particles before the update. represents a random individual, Represents a random number between (0,1), .

[0143] Therefore, when When the hard rime piercing mechanism rime particle position is updated by formula (11) or formula (12), the rime particle position after the hard rime piercing mechanism is updated by the improved random difference position update rule and the rime particle position after the hard rime piercing mechanism is updated by the improved cross strategy are compared, and the individual with the best position is selected.

[0144] In the iterative process of the RIME algorithm, as the number of iterations increases, the particle swarm tends to gather around the known local optimal solution, thereby reducing the algorithm's ability to explore the unknown solution space. In order to solve this problem, the leader-based reverse learning strategy (LRLS) is introduced in the later stage of the iteration, aiming to enhance the algorithm's optimization ability in the later stage of the iteration by stimulating the collective wisdom of the particle swarm, so as to be more likely to find a better or even global optimal solution. The core idea of ​​LRLS is to identify and utilize the most competitive individuals in the group, the so-called "leader". This leader is the particle with the best position (i.e., the optimal solution or a position close to the optimal solution) among the individuals, and it represents the best state that the group can achieve in the current iteration state. Once the leader is determined, other particles will no longer roam blindly in the solution space, but turn to leader-centered guided learning, and promote the evolution of the entire group towards a better solution by imitating and surpassing the leader's position.

[0145] In specific implementation, the LRLS strategy requires each particle to calculate the difference between its current position and the leader's position, and then adjust its own movement direction and speed based on this difference in order to follow the leader more closely. However, unlike the traditional following strategy, LRLS also includes a reverse learning component, which means that the particles will not only approach the leader, but also move in the opposite direction within a certain range to explore the neighborhood of the leader's position and increase the diversity of solutions. This strategy helps to avoid the particle swarm from being too concentrated in the leader's position and forming a search blind spot, ensuring that the algorithm can still maintain strong exploration and development capabilities in the later stages of iteration. In mathematical model, the implementation process of the leader's reverse learning strategy is described by formula (13):

[0146]

[0147] in, is the position of the rime particles after being updated by the leader’s reverse learning strategy. It is the position of the rime particles after the improved hard rime piercing mechanism is updated. Specifically, the position of the rime particles after the hard rime piercing mechanism is updated by the random difference position update rule and the position of the rime particles after the hard rime piercing mechanism is updated by the cross strategy, and the individual with the best position is selected as the leader. Represents the best individual in the population before hard rime penetration Rime particles.

[0148] A forward greedy mechanism is used to filter out inferior solutions and retain the best solutions. The fitness value of the agent after the update is compared with the fitness value of the agent before the update. If the fitness value after the update is better than the value before the update, a replacement occurs. At the same time, the solution agent of both agents is replaced. The formula of the forward greedy mechanism is as follows: Formula (5) and Formula (6). Repeat the above steps until the termination condition is met and output the optimal solution found. .

[0149] The following is a simulation experiment analysis of the ADRIME algorithm.

[0150] Test case 1: Benchmark function

[0151] Benchmark functions are key tools for evaluating algorithm performance, providing a unified platform to test and compare different optimization algorithms. In this work, we use the CEC2022 test suite to evaluate the performance of the proposed ADRIME algorithm with a test dimension of 20. This test suite can effectively test the global optimization ability of the algorithm. The specific details of CEC2022 are shown in Table 1.

[0152] Table 1 CEC2022 test functions

[0153]

[0154] Test Example 2: Comparison of Algorithm Parameter Settings

[0155] ADRIME is compared with seven other optimization algorithms, including PO, HLOA, PSO, HEOA, NRBO, GWO and RIME. To ensure the fairness and effectiveness of the comparison, the experimental conditions are set uniformly. Table 2 gives the parameter settings of these algorithms. The maximum number of iterations of all algorithms is fixed to 500 times, and the population size is set to 30 individuals. This setting is intended to simulate the common parameter scale in actual optimization problems, while giving the algorithm enough iterations to fully demonstrate its convergence characteristics. To reduce the influence of accidental factors, each algorithm is run independently 30 times to ensure the reliability and representativeness of the statistical results. The experimental results are quantitatively analyzed by calculating the average value (Ave) and standard deviation (Std) of each run. The average value reflects the speed at which an algorithm finds the optimal solution within a specific number of iterations. The smaller the value, the faster the algorithm converges and the closer the result to the optimal solution can be found in fewer iterations. The standard deviation measures the stability of the algorithm performance, that is, the consistency of the results in multiple independent runs. The smaller the standard deviation, the better the robustness of the algorithm and the lower the sensitivity to different initial conditions and random perturbations.

[0156] Table 2 Comparison of algorithm parameter settings

[0157]

[0158] Test case 3: Analysis of algorithm numerical results

[0159] In order to comprehensively evaluate and confirm the competitiveness and effectiveness of the ADRIME algorithm in the field of optimization, a rigorous and systematic experimental verification process was adopted. First, the CEC2022 test set was selected to perform a performance test on the algorithm in a 20-dimensional space. This dimensional setting not only reflects the algorithm's ability to handle high-dimensional optimization problems, but is also one of the commonly used benchmarks in current optimization algorithm research.

[0160] The experimental results are shown in Table 3. Through a detailed analysis of the performance of the ADRIME algorithm on the CEC2022 test set, it is found that ADRIME has achieved optimal or near-optimal results on most test functions, which not only proves its excellent optimization ability, but also demonstrates the stability and robustness of the algorithm when facing complex optimization problems. (The optimal value is marked in bold)

[0161] Table 3 Comparison of numerical optimization results of CEC2022 test set

[0162]

[0163] In order to further quantify and verify the performance difference between ADRIME and other algorithms, the nonparametric rank sum test, a statistical analysis tool, is used. The nonparametric rank sum test can effectively detect whether there is a significant difference in the distribution of two sets of data without assuming that the data obeys a specific distribution form. Therefore, it is very practical when comparing algorithm performance. When the p-value obtained by the test is less than 0.05, there is reason to believe that there is a significant difference in the performance of the two algorithms, that is, in a statistical sense, the performance of ADRIME is significantly better than other algorithms. On the contrary, if the p-value is greater than or equal to 0.05, it indicates that the performance difference between the two algorithms on the test function is not statistically significant.

[0164] Table 4 shows the comparison results obtained by nonparametric rank sum test. It can be seen that ADRIME has significant differences with other algorithms on most test functions, which means that in these test cases, the performance of ADRIME algorithm is significantly better than other competing algorithms.

[0165] Table 4 Wilcoxon rank sum test p value

[0166]

[0167] Finally, in order to more comprehensively compare the overall performance of different algorithms, the nonparametric Friedman ranking average rank test is used. This is a commonly used method for comparing multiple groups of data, which can comprehensively rank the performance of multiple algorithms on multiple test functions. Table 5 lists the algorithm ranking results based on the Friedman average rank test. From the results, the ADRIME algorithm ranks first in the test function the most times and has the lowest average ranking, which shows that among all the algorithms involved in the comparison, ADRIME has the best overall performance when solving the optimization problem on the test set.

[0168] Table 5 Friedman test results

[0169]

[0170] In summary, through comprehensive testing and in-depth analysis on the CEC2022 test set, the ADRIME algorithm has demonstrated excellent performance in terms of optimization ability, robustness, and statistical performance comparison. This series of experimental results fully demonstrates the competitiveness of the ADRIME algorithm in the field of optimization and lays a solid theoretical foundation for its promotion and deployment in practical applications.

[0171] Test Example 4: Comparative Analysis of Algorithm Convergence Curves

[0172] In order to deeply compare the convergence differences of different optimization algorithms in solving complex problems, we used 12 representative test functions in the CEC2022 test set to draw detailed convergence curves, which intuitively demonstrated the performance of each algorithm in the optimization process.

[0173] As shown in Figure 5, the horizontal axis represents the number of iterations, and the vertical axis represents the objective function value, so as to intuitively show the convergence trend of the algorithm. In this chart, the trend of the curve directly reflects the process of the algorithm gradually approaching the optimal solution as the number of iterations increases, and the position of the curve reflects the solution quality of the algorithm at different iteration stages, that is, the size of the objective function value. The smaller the objective function value, the higher the search accuracy of the algorithm, and the more effectively it can approach the optimal solution of the problem. It can be seen from the figure that the convergence curve of the ADRIME algorithm is obviously below all the comparison algorithms, which means that under the same number of iterations, the ADRIME algorithm can achieve a lower objective function value and show better optimization performance. This result not only confirms the significant advantage of the ADRIME algorithm in the optimization value, but also shows its overall improvement in convergence speed and accuracy. Compared with a variety of comparison algorithms, the convergence curve of the ADRIME algorithm shows a more gentle and stable downward trend on most test functions, which shows that its performance in the optimization process is more stable, not easily affected by initial conditions or random disturbances, and has stronger robustness.

[0174] like Figure 6 As shown in the figure, the horizontal axis represents different algorithms, the vertical axis represents the objective function value, and the function value distribution on the vertical axis indicates the cumulative number of iterations of the algorithm at different function values. Figure 6 Comparison of the box plots of different algorithms shows that the convergence degree of the ADRIME algorithm is significantly better than that of other algorithms or close to the algorithm with the best convergence.

[0175] S3, adjust the flight path of the UAV according to the optimal path.

[0176] In this embodiment, the coordinate values ​​of the positions of rime particles obtained by the multi-strategy improved frost optimization algorithm are substituted into the comprehensive cost function of the UAV flight to calculate and output the optimal path, and the flight path of the UAV can be adjusted according to the optimal path.

[0177] The following experiments will explore the performance of the ADRIME algorithm in the UAV path planning problem:

[0178] Test Example 5: UAV trajectory planning experiment

[0179] In order to further explore the performance of the ADRIME algorithm in the UAV path planning problem, seven mainstream optimization algorithms were selected as comparison benchmarks. Each algorithm underwent 30 independent runs, and the experimental results are recorded in detail in Table 6. The ADRIME algorithm stood out in the Friedman ranking and ranked first, which strongly proved that it surpassed the seven mainstream optimization algorithms in the robustness and efficiency of the optimization results.

[0180] Table 6 Experimental results of UAV trajectory planning

[0181]

[0182] like Figure 7 The convergence curve shows that the ADRIME algorithm not only has a faster convergence speed, but also has excellent convergence accuracy, which means that it can find a path closer to the optimal solution in a shorter time, significantly improving the efficiency and accuracy of UAV path planning.

[0183] In addition, Figure 8 provides a more intuitive visual presentation, comparing the differences in the optimization paths of the eight algorithms. By observing the path trajectories of each algorithm, it can be clearly seen that the path planned by the ADRIME algorithm is smoother, more direct and more effective, which reflects its careful consideration and intelligent decision-making ability in path planning.

[0184] Combining the quantitative data in Table 6 and Figure 7, and the qualitative analysis in Figure 8 shows that the ADRIME algorithm has demonstrated unparalleled optimization performance in the field of UAV path planning. It has not only achieved a double breakthrough in speed and accuracy, but also demonstrated strong adaptability and robustness in practical applications, opening up new possibilities for the future development of UAV technology. This series of experimental results strengthens the effectiveness and practicality of the ADRIME algorithm, indicating its great potential in solving complex optimization problems.

[0185] The present invention applies a multi-strategy improved frost ice optimization algorithm to the path planning of unmanned aerial vehicles. The multi-strategy improved frost ice optimization algorithm integrates multiple strategies to overcome the limitation that the original frost ice algorithm is easily trapped in the local optimal solution. In order to enhance the diversity of the search process and the global exploration ability, the Gaussian mutation perturbation mechanism is adopted in the exploration stage of the algorithm, which increases the diversity of the search, significantly improves the probability of jumping out of the local minimum point, helps to jump out of the local optimal solution, improves the convergence speed and robustness of the algorithm, and enables the algorithm to more efficiently approach the true global optimal solution; in the development stage, the random differential position update rule is introduced, and the positions of other individuals are updated by randomly selecting individuals in the population and calculating their position differences to guide the algorithm to search for the optimal solution, while maintaining the dynamic balance of the population. This strategy effectively balances exploration and development, helps to avoid premature convergence, and improves the stability and timeliness of the algorithm when dealing with complex optimization problems; at the same time, the crossover strategy in the genetic algorithm is introduced to promote information exchange and cooperation between particles and enhance the global search ability of the algorithm. In order to solve the problem that the algorithm's optimization ability weakens in the later stages of iteration, a leader-based reverse learning strategy is creatively added. By identifying the best performing individual in the population as the leader, and guiding other individuals to reversely learn and explore the leader's position, that is, starting from a distance from the current state and exploring toward the leader's position, the algorithm's later optimization ability is greatly enhanced, which helps to find a better solution. The present invention has made significant improvements in the length, flight time, and energy consumption of the optimized path, and can quickly find a path with low cost, high safety, and short arrival time, thereby improving the efficiency of drone mission execution.

[0186] See also Fig. 9 The second embodiment of the present invention further provides a UAV path planning device based on an improved frost and ice optimization algorithm, which includes:

[0187] A flight path planning unit 210 is used to construct a flight space according to the starting point and the end point of the UAV, and plan the flight path of the UAV according to the obstacle set in the flight space and the comprehensive cost function of the UAV path planning;

[0188] The optimal path output unit 220 is used to substitute the coordinate values ​​of the positions of the rime particles obtained by the multi-strategy improved rime optimization algorithm into the comprehensive cost function to calculate and output the optimal path; wherein, the optimal path satisfies the minimum comprehensive cost function of the UAV path planning and does not intersect with the obstacle set; the multi-strategy improved rime optimization algorithm includes: S21, initializing the relevant parameters of the multi-strategy improved rime optimization algorithm, and calculating the population matrix; S22: in the exploration stage, using the Gaussian mutation perturbation strategy to improve the soft rime search strategy, and searching for the global optimal solution according to the improved soft rime search strategy; S23: in the development stage, introducing a random differential position update rule, by randomly selecting individuals in the population and calculating their position differences to update the positions of other individuals, guiding the algorithm to search for the optimal solution, introducing the crossover strategy in the genetic algorithm, promoting information exchange and cooperation between particles, and enhancing the global optimal solution of the algorithm. Search capability, using random differential position update rules and crossover strategies to improve the hard rime puncture mechanism, and developing according to the improved hard rime puncture mechanism to approach the global optimal solution as soon as possible; S24: In the later stage of iteration, a leader-based reverse learning strategy is introduced, by selecting the best individual in the group as the leader, and guiding other individuals to reversely learn and explore the leader's position to increase the algorithm's optimization ability and obtain a better global optimal solution. A forward greedy mechanism is used to filter out inferior solutions and retain the best solutions. The comprehensive cost function value of the updated agent is compared with the comprehensive cost function value of the agent before the update. If the updated comprehensive cost function value is better than the comprehensive cost function value before the update, a replacement occurs, and the solution agent of both is replaced at the same time; S25: Repeat steps S22~S24 until the termination condition is met, and output the optimal solution found, that is, the coordinate value of the position of the rime particles;

[0189] The flight path adjustment unit 230 is used to adjust the flight path of the UAV according to the optimal path.

[0190] Although the present invention has been described in detail with reference to the aforementioned embodiments, it is still possible for those skilled in the art to modify the technical solutions described in the aforementioned embodiments, or to make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A UAV path planning method based on an improved frost optimization algorithm, characterized in that: include: S1: Construct a flight space according to the starting point and end point of the UAV, and plan the flight path of the UAV according to the obstacle set in the flight space and the comprehensive cost function of the UAV path planning; S2: Substitute the coordinate values ​​of the positions of the rime particles obtained by the multi-strategy improved rime optimization algorithm into the comprehensive cost function to calculate and output the optimal path; wherein, the optimal path satisfies the minimum comprehensive cost function of the UAV path planning and does not intersect with the obstacle set; the multi-strategy improved rime optimization algorithm includes: S21, initializing the relevant parameters of the multi-strategy improved rime optimization algorithm, and calculating the population matrix; S22: In the exploration stage, the Gaussian mutation perturbation strategy is used to improve the soft rime search strategy, and the global optimal solution is searched according to the improved soft rime search strategy; S23: In the development stage, a random differential position update rule is introduced, and the positions of other individuals are updated by randomly selecting individuals in the population and calculating their position differences, guiding the algorithm to search for the optimal solution, introducing the crossover strategy in the genetic algorithm, promoting information exchange and cooperation between particles, and enhancing the global search capability of the algorithm. The random differential position update rule and crossover strategy are used to improve the hard rime puncture mechanism, and development is carried out according to the improved hard rime puncture mechanism to approach the global optimal solution as soon as possible; S24: In the later stage of iteration, a leader-based reverse learning strategy is introduced. By selecting the individual with the best position in the group as the leader, and guiding other individuals to reversely learn and explore the leader's position, the algorithm's optimization ability is increased to obtain a better global optimal solution. The forward greedy mechanism is used to filter out inferior solutions and retain the best solutions. The comprehensive cost function value of the updated agent is compared with the comprehensive cost function value of the agent before the update. If the updated comprehensive cost function value is better than the comprehensive cost function value before the update, a replacement occurs, and the solution agent of the two is replaced at the same time; S25: Repeat steps S22~S24 until the termination condition is met, and output the optimal solution found, that is, the coordinate value of the position of the rime particles; S3, adjust the flight path of the UAV according to the optimal path.

2. The UAV path planning method based on the improved frost and ice optimization algorithm according to claim 1 is characterized in that: The expression of the improved soft rime search strategy is: ； in, is the position of rime particles after the improved soft rime search strategy is updated. The best individual in the population Rime particles, Represents a random number between 0 and 1. is a random number between 0 and 1. Represents rounding to an integer. Indicates the adhesion between soft rime, which is a random number in the range of (0,1). and They represent the upper and lower bounds of the search space respectively, Indicates the current iteration number, is the maximum number of iterations, Represents the adhesion coefficient, which affects the condensation probability of the search individual and increases with the number of iterations. It is calculated by the following formula: is the Gaussian distribution after the Gaussian mutation perturbation strategy is optimized, and is calculated by the following formula: in, is the value of the Gaussian distribution probability density function, indicating that the random variable The probability density at is calculated by the following formula: in, represents the variance, which measures the degree of dispersion of data distribution. represents the mean, represents the center of the distribution, The independent variable of the probability density function represents a specific value or position. =0, =1, It is expressed as: 。 3. The UAV path planning method based on the improved frost and ice optimization algorithm according to claim 2 is characterized in that: The expression of the hard rime penetration mechanism improved by random differential position update rule is: in, It is the position of rime particles after the hard rime penetration mechanism is updated by the random difference position update rule. Represents a random number between (0,1), and represents two different random individuals.

4. The UAV path planning method based on the improved frost and ice optimization algorithm according to claim 3 is characterized in that: The expression of the hard rime penetration mechanism improved by the cross strategy is: in, It is the position of rime particles after the cross strategy improved hard rime piercing mechanism is updated. Indicates the optimal position of rime particles before the update. represents a random individual, Represents a random number between (0,1), .

5. The UAV path planning method based on the improved frost and ice optimization algorithm according to claim 4 is characterized in that: The leader's reverse learning strategy is expressed as: in, It is the position of the rime particles after being updated by the leader’s reverse learning strategy.

6. The UAV path planning method based on the improved frost and ice optimization algorithm according to claim 5 is characterized in that: In the later stage of iteration, the positions of rime particles after being updated by the hard rime piercing mechanism improved by the random differential position update rule and the positions of rime particles after being updated by the hard rime piercing mechanism improved by the crossover strategy are compared, and the individual with the best position is selected as the leader.

7. The UAV path planning method based on the improved frost and ice optimization algorithm according to claim 1 is characterized in that: In step S1, the obstacle set is represented as: in, is the set of obstacles in the flight space; is the coordinate value of the obstacle on the X axis, and y is the coordinate value of the obstacle on the Y axis.

8. The UAV path planning method based on the improved frost and ice optimization algorithm according to claim 7 is characterized in that: In step S1, the calculation process of the comprehensive cost function of the UAV path planning is: The path length cost function is calculated by the following formula: in, Indicates the first The coordinates of the point, is the Euclidean distance, Represents the total number of points on the drone's path; The flight altitude cost function is calculated by the following formula: in, Indicates that the drone is The coordinate of the point on the Z axis, is the average height of all points on the path; The smoothness cost function of the path is calculated by the following formula: in, = ,express The turning angle of the point; The comprehensive cost function of UAV path planning is calculated by the following formula: in, ( = 1,2,3) is the weight of each cost, calculated by the following formula: The unmanned flight path of the drone is planned according to the obstacle set in the flight space and the comprehensive cost function of the drone path planning, which is obtained through the following model: in, Indicates the flight path. and Represent the ground and obstacles respectively.

9. A UAV path planning device based on an improved frost optimization algorithm, characterized in that: include: A flight path planning unit, used to construct a flight space according to the starting point and the end point of the UAV, and plan the flight path of the UAV according to the obstacle set in the flight space and the comprehensive cost function of the UAV path planning; The optimal path output unit is used to substitute the coordinate values ​​of the positions of the rime particles obtained by the multi-strategy improved rime optimization algorithm into the comprehensive cost function to calculate and output the optimal path; wherein, the optimal path satisfies the minimum comprehensive cost function of the UAV path planning and does not intersect with the obstacle set; the multi-strategy improved rime optimization algorithm includes: S21, initializing the relevant parameters of the multi-strategy improved rime optimization algorithm, and calculating the population matrix; S22: in the exploration stage, using the Gaussian mutation perturbation strategy to improve the soft rime search strategy, and searching for the global optimal solution according to the improved soft rime search strategy; S23: in the development stage, introducing a random differential position update rule, updating the positions of other individuals by randomly selecting individuals in the population and calculating their position differences, guiding the algorithm to search for the optimal solution, introducing the crossover strategy in the genetic algorithm, promoting information exchange and cooperation between particles, and enhancing the global search of the algorithm. Search ability, random differential position update rules and crossover strategies are used to improve the hard rime puncture mechanism, and development is carried out according to the improved hard rime puncture mechanism to approach the global optimal solution as soon as possible; S24: In the later stage of iteration, a leader-based reverse learning strategy is introduced. By selecting the individual with the best position in the group as the leader, and guiding other individuals to reversely learn and explore the leader's position, the algorithm's optimization ability is increased to obtain a better global optimal solution. A forward greedy mechanism is used to filter out inferior solutions and retain the best solutions. The comprehensive cost function value of the updated agent is compared with the comprehensive cost function value of the agent before the update. If the updated comprehensive cost function value is better than the comprehensive cost function value before the update, a replacement occurs, and the solution agent of both is replaced at the same time; S25: Repeat steps S22~S24 until the termination condition is met, and output the optimal solution found, that is, the coordinate value of the position of the rime particles; The flight path adjustment unit is used to adjust the flight path of the UAV according to the optimal path.

Images