Unmanned aerial vehicle path planning method and device based on improved frost ice optimization algorithm

Abstract

The invention discloses an unmanned aerial vehicle path planning method and device based on an improved frost ice optimization algorithm, and the method comprises the steps: constructing a flight space according to the starting point and the terminal point of an unmanned aerial vehicle, and planning a flight path of the unmanned aerial vehicle according to an obstacle in the flight space and a comprehensive cost function of the path planning of the unmanned aerial vehicle; substituting the coordinate value of the rime particle position obtained through a multi-strategy improved frost ice optimization algorithm into the comprehensive cost function to calculate and output an optimal path; and adjusting the flight path of the unmanned aerial vehicle according to the optimal path. According to the invention, unmanned aerial vehicle path planning is realized based on the improved frost ice optimization algorithm, the length of the optimized path, the flight time, the energy consumption and other aspects are obviously improved, the path with low cost, high safety and short arrival time can be quickly found, and the task execution efficiency of the unmanned aerial vehicle is improved.

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 widespread, a core issue has gradually emerged: trajectory planning. Effective trajectory planning not only affects drone operational efficiency but also directly impacts flight safety and mission success.

[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 drone systems.

[0004] Metaheuristic algorithms, as a class of nondeterministic search strategies, demonstrate 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-constraint optimization challenges, and by simulating intelligent behaviors found in nature and society, they provide innovative solutions for drone path planning. Currently, the research and application of metaheuristic algorithms are advancing at an unprecedented pace, not only promoting the iterative upgrades of the algorithms themselves, but also opening up new avenues for expanding the boundaries of drone technology.

[0005] The application of metaheuristic algorithms in drone trajectory planning has greatly improved the efficiency and accuracy of path planning. Researchers have used these algorithms to optimize drone paths and achieved remarkable results in solving complex challenges. However, no single algorithm can achieve optimal performance for all problems. Therefore, in specific applications, it is particularly important to design specialized metaheuristic algorithms tailored to the characteristics and requirements of specific problems to ensure optimal optimization results.

[0006] The Rime Ice Optimization (RIME) algorithm, proposed by Su et al. in 2023, is a novel physics-inspired algorithm inspired by the natural growth of frost. By simulating the spread of soft frost and the solidification of hard frost, RIME constructs a soft frost search strategy and a hard frost penetration mechanism, enabling efficient transitions between exploration and exploitation. However, in some cases, RIME suffers from slow convergence, a tendency to fall into local optimal solutions, and poor performance in practical applications.

[0007] Gaoquan Gu, Jingjun Lou, and others proposed a multi-strategy improved frost and ice optimization algorithm (MIRIME). First, they initialized the population using a tent chaos map, laying the foundation for global optimization. Second, they introduced an adaptive update strategy based on leadership and dynamic centroids to encourage the population to explore in more favorable directions. To address the problem of population scarcity in later iterations, they introduced an anti-learning control strategy based on lens imaging to enhance population diversity and ensure convergence accuracy. MIRIME was applied to a 3D path planning problem for unmanned aerial vehicles (UAVs). Experimental results showed that MIRIME outperformed 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 utilized a segmented mapping elitist reverse learning population selection strategy to enhance the algorithm's population diversity. Second, they proposed an elite pool exploration strategy controlled by a random factor, making it less likely for the algorithm to fall into local optima. Finally, they proposed a hard frost penetration exploration strategy based on a sine-cosine function, enabling the algorithm to more quickly find the global optimum during exploration. They also achieved promising results in applying the algorithm to a 3D UAV path planning problem in three different terrain scenarios.

[0008] However, in the face of ever-changing environments and task requirements, continuously exploring and developing 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 adopted a Gaussian mutation perturbation strategy to increase the diversity of the search, help to escape 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 introduced 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 stages of iteration, the present invention proposes a leader-based reverse learning strategy, which selects the individual with the best position in the group as the leader, and guides other individuals to reversely learn and explore towards 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 solution quality and stability, showing great application potential.

[0010] Specifically, the present invention provides the following technical solutions: A UAV path planning method based on an improved frost and ice optimization algorithm, comprising: S1: Construct a flight space based on the starting and ending points of the UAV, and plan the flight path of the UAV based on the obstacle set in the flight space and the comprehensive cost function of the UAV path planning; S2: Substitute the coordinate values ​​of the rime particle positions 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, adopting 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 the 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 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. 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 to S24 until the termination condition is met, and output the optimal solution found, that is, the coordinate value of the rime particle position; S3, adjusts the flight path of the UAV according to the optimal path.

[0011] Preferably, the improved soft rime search strategy is expressed as: ; in, is the updated rime particle position after the improved soft rime search strategy. 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 represent the upper and lower bounds of the search space, respectively. Indicates the current iteration number, is the maximum number of iterations, It represents the adhesion coefficient, which affects the coagulation probability of the search individual and increases with the number of iterations. It is calculated by the following formula:

[0012] is the Gaussian distribution after the Gaussian mutation perturbation strategy is optimized, and is calculated by the following formula:

[0013] in, is the value of the Gaussian distribution probability density function, which indicates that the random variable is at a specific point The probability density at is calculated by the following formula:

[0014] in, represents the variance, which measures the degree of dispersion of data distribution. represents the mean, represents the center position of the distribution, The independent variable of the probability density function represents a specific value or position. =0, =1, Expressed as: .

[0015] Preferably, the expression of the hard rime puncture mechanism improved by the random differential position update rule is:

[0016] in, It is the position of rime particles after the hard rime penetration mechanism is updated with the improved random differential position update rule. Represents a random number between (0,1), and represents two different random individuals.

[0017] Preferably, the expression of the hard rime puncture mechanism improved by the cross strategy is:

[0018] in, This is the updated rime particle position after the cross strategy improved hard rime penetration mechanism. Indicates the optimal position of rime particles before the update. represents a random individual, Represents a random number between (0,1), take .

[0019] Preferably, the leader's reverse learning strategy is expressed as:

[0020] in, It is the position of the rime particles after being updated by the leader's reverse learning strategy.

[0021] Preferably, in the later stage of iteration, the positions of the rime particles after being updated by the hard rime puncture mechanism improved by the random differential position update rule and the positions of the rime particles after being updated by the hard rime puncture mechanism improved by the cross strategy are compared, and the individual with the best position is selected as the leader.

[0022] Preferably, in step S1, the obstacle set is represented as:

[0023] in, is the set of obstacles in the flight space; is the X-axis coordinate value of the obstacle, and y is the Y-axis coordinate value of the obstacle.

[0024] Preferably, in step S1, the calculation process of the comprehensive cost function of the UAV path planning is: The path length cost function is calculated using the following formula:

[0025] in, Indicates the first step in the UAV path planning The coordinates of the point, is the Euclidean distance, Represents the total number of points on the drone's path; The flight height cost function is calculated using the following formula:

[0026] in, Indicates that the drone is The coordinate of the point on the Z axis, is the average height of all points along the path; The smoothness cost function of the path is calculated by the following formula:

[0027] in, = ,express The turning angle of the point; The comprehensive cost function of UAV path planning is calculated by the following formula:

[0028] in, ( = 1,2,3) are the weights of each cost, calculated using the following formula:

[0029] The unmanned flight path of the drone is planned based on the obstacle set in the flight space and the comprehensive cost function of the drone path planning, which is obtained through the following model:

[0030] in, Indicates the flight path, and Represent the ground and obstacles respectively.

[0031] An embodiment of the present invention further provides a UAV path planning device based on an improved frost and ice optimization algorithm, comprising: A flight path planning unit is used to 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; The optimal path output unit is used to substitute the coordinate values ​​of the rime particle positions 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 search of the algorithm. Search ability, random differential position update rule and cross 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. 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 rime particle position; Flight path adjustment unit, used to adjust the flight path of the drone according to the optimal path Compared with the prior art, the present invention has the following beneficial effects: This paper applies a multi-strategy improved Frost Ice Optimization Algorithm to UAV path planning. This multi-strategy improved Frost Ice Optimization Algorithm integrates multiple strategies to overcome the limitations of the original Frost Ice Algorithm, which is easily trapped in local optimal solutions. To enhance the diversity of the search process and global exploration capabilities, a Gaussian mutation perturbation mechanism is adopted in the algorithm's exploration phase. This increases the diversity of the search and significantly improves the probability of escaping local minima, which helps to escape local optimal solutions, improves the algorithm's convergence speed and robustness, and enables the algorithm to more efficiently approach the true global optimal solution. In the development phase, a random differential position update rule is introduced. By randomly selecting individuals in the population and calculating their position differences, the positions of other individuals are updated to guide the algorithm's search for the optimal solution while maintaining the dynamic balance of the population. This strategy effectively balances exploration and development, helps avoid premature convergence, and improves the algorithm's stability and timeliness when dealing with complex optimization problems. Furthermore, a crossover strategy, often used in genetic algorithms, is introduced to promote information exchange and cooperation between particles, enhancing the algorithm's global search capabilities. To address the problem of the algorithm's weakening optimization ability in the later stages of iteration, a leader-based reverse learning strategy was creatively incorporated. By identifying the best-performing individual in the population as the leader, and guiding other individuals to reversely learn and explore towards the leader's position, that is, starting from a distance from the current state and exploring towards the leader's position, this greatly enhances the algorithm's later optimization ability and helps discover more optimal solutions. This invention has achieved significant improvements in the length, flight time, and energy consumption of optimized paths, and can quickly find low-cost, highly secure paths with a short arrival time, thereby improving the efficiency of drone mission execution. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 This is the flowchart of the original frost algorithm; 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 a first embodiment of the present invention; Figure 3 This is a specific working principle diagram of step S2; Figure 4 This is the workflow diagram of step S2; Figure 5 shows the convergence curves of the ADRIME algorithm compared with seven other optimization algorithms for 12 functions in the 20-dimensional CEC2022 test set. The horizontal axis is the number of iterations, and the vertical axis is the mean square error. Figure 6 The box plots comparing ADRIME and seven other optimization algorithms on 12 functions in the 20-dimensional CEC2022 test set are shown. Figure 7 This is the convergence curve of ADRIME algorithm and other 7 optimization algorithms in UAV planning; Figure 8 shows the optimal path diagram of ADRIME algorithm and other seven optimization algorithms in UAV planning; Figure 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

[0033] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. 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 making creative efforts are within the scope of protection of the present invention.

[0034] To facilitate understanding of the present invention, the following first introduces the algorithm principle of the original frost and ice algorithm: 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 topographic conditions in specific areas, fascinating rime ice scenes 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 the birth of 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 puncture mechanism, and adopted a positive greedy selection strategy. Combining these three mechanisms, they developed a frost ice algorithm, which is recorded as the RIME algorithm for the convenience of comparison and record. The following introduces the mathematical model of the RIME algorithm: 1. Population initialization The frost ice initialization population is shown in formula 1:

[0035] in, Represents the population matrix of frost ice, Indicates the position of rime particles.

[0036] 2. Soft Rime Search Strategy (Exploration Phase) In a breeze, soft rime grows randomly and covers a wide area, but grows slowly in the same direction. Inspired by this, we utilize the random coverage of rime to propose a soft rime search strategy, which allows the algorithm to quickly cover the search space in the early stages and avoid local optimality. Its mathematical model is expressed as formula (2):

[0037] 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 represent the upper and lower bounds of the search space, respectively. Indicates the current iteration number, is the maximum number of iterations, adhesion coefficient The condensation probability that affects the search individual increases with the number of iterations, as shown in formula (3):

[0038] 3. Hard Rime Piercing Mechanism (Development Stage) Under strong winds, hard rime grows more regularly. Its characteristics are: 1) Strong winds cause hard rime to grow rapidly in a uniform direction. 2) Rime growing in the same direction easily intersects, i.e., rime pierces. 3) Hard rime increases in size as it grows, and when growth conditions are favorable, the probability of piercing is high. Therefore, inspired by the piercing phenomenon, a hard rime piercing mechanism is proposed for algorithm updates, enabling particle exchange and improving the algorithm's convergence and ability to escape local optima. The particle replacement formula is shown in Formula (4):

[0039] 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.

[0040] 4. Positive Greedy Selection Mechanism 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 lacks in improving the individual search ability. Its main function is to record the best results. In order to improve the efficiency of the algorithm, a positive greedy mechanism is proposed, which 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 individual positions in the population may cause the performance of some intelligent agents to decline, it helps the population as a whole to develop in a better direction during the iteration process. The mathematical model is shown in formulas (5) and (6):

[0041]

[0042] 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.

[0043] In summary, the process of the RIME algorithm is as follows Figure 1 shown.

[0044] However, the RIME algorithm has problems such as low accuracy, slow convergence speed, and easy falling into local optimal solutions in experiments.

[0045] For this reason, 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: S1: Construct a flight space based on the starting and ending points of the UAV, and plan the flight path of the UAV based on the obstacle set in the flight space and the comprehensive cost function of the UAV path planning.

[0046] Specifically, let the starting point of the UAV 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 ( ), Plan the flight space based on the starting and ending points, establish the obstacle set in the flight space based on the on-site terrain, and model the obstacle set according to the following formula:

[0047] in, is the set of obstacles in the flight space; is the X-axis coordinate value of the obstacle, and y is the Y-axis coordinate value of the obstacle; Calculate the comprehensive cost function of the UAV path planning, where The path length cost function is calculated using the following formula:

[0048] 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; The flight height cost function is calculated using the following formula:

[0049] in, Indicates that the drone is The coordinate of the point on the Z axis, is the average height of all points along the path; The smoothness cost function of the path is calculated by the following formula:

[0050] in, = ,express The turning angle of the point; The comprehensive cost function of UAV path planning is calculated by the following formula:

[0051] in, ( = 1,2,3) are the weights of each cost, calculated using the following formula:

[0052] The UAV plans its flight path based on the obstacle set in the flight space and the comprehensive cost function of the UAV path planning, through the following model:

[0053] in, Indicates the flight path, and Represent the ground and obstacles respectively.

[0054] S2: Substituting 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.

[0055] 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 computational steps: S21: Initialize the relevant parameters of the frost algorithm and calculate the population matrix; 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 based on the improved soft rime search strategy; S23: During the development phase, a random differential position update rule was introduced. By randomly selecting individuals in the population and calculating their position differences, the positions of other individuals were updated to guide the algorithm in searching for the optimal solution. The crossover strategy from the genetic algorithm was introduced to promote information exchange and cooperation between particles, enhancing the algorithm's global search capability. The random differential position update rule and crossover strategy were used to improve the hard rime puncture mechanism. Development was carried out based on the improved hard rime puncture mechanism to approach the global optimal solution as quickly as possible. S24: In the later stage of iteration, a leader-based reverse learning strategy is introduced. By selecting the best-positioned individual in the group as the leader and guiding other individuals to reversely learn and explore towards the leader's position, the algorithm's optimization ability is enhanced 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. S25: Repeat steps S22 to S24 until the termination condition is met, and output the optimal solution found.

[0056] Specifically, initialize the relevant parameters of the frost and ice algorithm and calculate the population matrix according to formula (1); 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):

[0057] Among them, among them, is the updated rime particle position after the improved soft rime search strategy. 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 represent the upper and lower bounds of the search space, respectively. Indicates the current iteration number, is the maximum number of iterations, It represents the adhesion coefficient, which affects the coagulation probability of the search individual and increases with the number of iterations. It is calculated by the following formula:

[0058] is the Gaussian distribution after the Gaussian mutation perturbation strategy is optimized, as shown in formula (8):

[0059] in, is the value of the Gaussian distribution probability density function, which indicates that the random variable is at a specific point The probability density at The expression of is shown in formula (9):

[0060] in, represents the variance, which measures the degree of dispersion of data distribution. represents the mean, represents the center position of the distribution, The independent variable of the probability density function represents a specific value or position. =0, =1, Expressed as:

[0061] Therefore, when When , the soft rime search strategy rime particle position is updated using formula (7).

[0062] During the development phase, a random differential position update rule was introduced to significantly enhance the algorithm's global search capabilities and prevent it from falling into the trap of local optimal solutions. The core idea of ​​this rule is to introduce randomness, allowing rime particles to jump in the solution space in an unpredictable way, thereby breaking through the limitations of local optimal solutions and exploring a wider solution domain.

[0063] Specifically, the working principle of the random differential position update rule is: randomly select several 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 motion, but also effectively expands the search range and enhances the algorithm's exploration ability. 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):

[0064] in, It is the position of rime particles after the hard rime penetration mechanism is updated with the improved random differential position update rule. Represents a random number between (0,1), and represents two different random individuals.

[0065] The RIME algorithm tends to focus on the evolutionary path of a single optimal particle, resulting in relatively weak inter-particle collaboration and information sharing mechanisms. While this characteristic accelerates convergence, it also imposes significant limitations, making it difficult to cross over to more optimal solutions. Therefore, the crossover operation in the genetic algorithm (GA) is introduced as an improvement strategy to promote information exchange and collaboration between particles, enhancing the algorithm's global search capabilities. The crossover strategy in the genetic algorithm simulates the genetic recombination phenomenon in biological genetics. Applying the crossover strategy to the FOA enables it to effectively exchange critical information carried by non-optimal particles, such as saddle points and local optima.

[0066] Specifically, during each generation of evolution, multiple particles are randomly selected for pairing and a crossover operation is performed. This operation splits 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. They carry richer and more diverse information, which helps the algorithm explore a wider solution space. The expression of the hard rime puncture mechanism improved by the crossover strategy is shown in formula (12):

[0067] in, This is the updated rime particle position after the cross strategy improved hard rime penetration mechanism. Indicates the optimal position of rime particles before the update. represents a random individual, Represents a random number between (0,1), take .

[0068] Therefore, when When , the position of rime particles of the hard rime puncture mechanism is updated using formula (11) or formula (12), and the updated position of rime particles of the hard rime puncture mechanism improved by the random difference position update rule is compared with the updated position of rime particles of the hard rime puncture mechanism improved by the cross strategy, and the individual with the best position is selected.

[0069] During the iterative process of the RIME algorithm, as iterations increase, the particle swarm tends to cluster around known local optima, reducing the algorithm's ability to explore the unknown solution space. To address this issue, a leader-based reverse learning strategy (LRLS) is introduced in the later stages of the iterations. This strategy aims to stimulate the collective intelligence of the particle swarm, enhancing the algorithm's optimization capabilities in the later stages of the iterations and increasing the likelihood of discovering even better or even global optimal solutions. The core idea of ​​LRLS is to identify and leverage the most competitive individuals in the swarm, known as "leaders." This leader is the particle with the best position (i.e., the optimal solution or a position close to the optimal solution) and represents the best state the swarm can achieve at the current iteration. Once the leader is identified, other particles no longer blindly roam the solution space but instead engage in guided learning centered on the leader. By imitating and surpassing the leader's position, the entire swarm evolves towards a more optimal solution.

[0070] 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 traditional following strategies, LRLS also includes a reverse learning component, which means that the particles will not only move closer to 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):

[0071] 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 puncture mechanism is updated. Specifically, the position of the rime particles after the hard rime puncture mechanism is updated by the random difference position update rule and the position of the rime particles after the hard rime puncture mechanism is updated by the cross strategy, and the individual with the best position is selected as the leader. The best individual in the population before rime penetration Rime particles.

[0072] 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 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. .

[0073] The following is a simulation experiment analysis of the ADRIME algorithm.

[0074] Test Example 1: Benchmark Function Benchmark functions are key tools for evaluating algorithm performance, providing a unified platform for testing and comparing different optimization algorithms. In this work, we evaluated the performance of the proposed ADRIME algorithm using the CEC2022 test suite, with a test dimension of 20. This test suite effectively verifies the algorithm's global optimization capabilities. The details of CEC2022 are shown in Table 1.

[0075] Table 1 CEC2022 test functions

[0076] Test Example 2: Comparison of Algorithm Parameter Settings ADRIME was compared with seven other optimization algorithms, including PO, HLOA, PSO, HEOA, NRBO, GWO, and RIME. To ensure a fair and effective comparison, the experimental conditions were standardized. Table 2 lists the parameter settings for these algorithms. The maximum number of iterations for all algorithms was fixed at 500, and the population size was set to 30 individuals. This setting aims to simulate the parameter scale commonly encountered in real-world optimization problems while providing the algorithms with a sufficient number of iterations to fully demonstrate their convergence characteristics. To reduce the influence of random factors, each algorithm was independently run 30 times to ensure the reliability and representativeness of the statistical results. The experimental results were quantitatively analyzed by calculating the mean (Ave) and standard deviation (Std) of each run. The mean reflects the speed at which an algorithm finds the optimal solution within a specific number of iterations. A smaller value indicates faster convergence and a closer-to-optimal solution within a fewer number of iterations. The standard deviation measures the stability of the algorithm's performance, namely the consistency of the results across multiple independent runs. A smaller standard deviation indicates greater robustness and less sensitivity to different initial conditions and random perturbations.

[0077] Table 2 Comparison of algorithm parameter settings

[0078] Test case 3: Analysis of algorithm numerical results 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 implemented. First, the algorithm's performance was tested within a 20-dimensional space using the CEC2022 test set. This dimensionality not only demonstrates the algorithm's ability to handle high-dimensional optimization problems but is also a commonly used benchmark in current optimization algorithm research.

[0079] The experimental results are shown in Table 3. A detailed analysis of the ADRIME algorithm's performance on the CEC2022 test set reveals that ADRIME achieves optimal or near-optimal results on most test functions. This demonstrates not only its superior optimization capabilities but also its stability and robustness when faced with complex optimization problems. (Optimal values ​​are in bold.) Table 3 Comparison of numerical optimization results on the CEC2022 test set

[0080] To further quantify and verify the performance differences between ADRIME and other algorithms, we used the nonparametric rank-sum test, a statistical analysis tool. This test effectively detects significant differences in the distribution of two data sets without assuming a specific distribution. Therefore, it is highly practical for comparing algorithm performance. When the p-value obtained is less than 0.05, there is reason to believe that the performance of the two algorithms differs significantly, indicating that ADRIME significantly outperforms the other algorithms in a statistically significant manner. Conversely, if the p-value is greater than or equal to 0.05, the performance difference between the two algorithms on the test function is not statistically significant.

[0081] Table 4 shows the comparison results obtained by the nonparametric rank sum test. It can be seen that ADRIME has significant differences with other algorithms on the vast majority of test functions, which means that in these test cases, the performance of the ADRIME algorithm is significantly better than other competing algorithms.

[0082] Table 4 Wilcoxon rank sum test p values

[0083] Finally, to more comprehensively compare the overall performance of different algorithms, we used the nonparametric Friedman mean rank test, a commonly used method for comparing multiple sets of data. This method allows for a comprehensive ranking of the performance of multiple algorithms on multiple test functions. Table 5 lists the algorithm ranking results based on the Friedman mean rank test. The results show that the ADRIME algorithm ranked first most frequently on test functions and had the lowest average ranking, indicating that among all the algorithms compared, ADRIME achieved the best overall performance when solving optimization problems on the test set.

[0084] Table 5 Friedman test results

[0085] In summary, through comprehensive testing and in-depth analysis on the CEC2022 test set, the ADRIME algorithm demonstrated outstanding performance in optimization, robustness, and statistically significant performance comparisons. 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.

[0086] Test Example 4: Comparative Analysis of Algorithm Convergence Curves 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 during the optimization process.

[0087] As shown in Figure 5, the horizontal axis represents the number of iterations, and the vertical axis represents the objective function value, visually demonstrating the algorithm's convergence trend. In this chart, the curve directly reflects the algorithm's progress in approaching the optimal solution as the number of iterations increases, while the position of the curve reflects the quality of the solution at different iteration stages, namely, the magnitude of the objective function value. A smaller objective function value indicates a higher search accuracy and a more effective approach to the optimal solution. As can be seen from the figure, the convergence curve of the ADRIME algorithm is significantly lower than that of all the compared algorithms. This means that with the same number of iterations, the ADRIME algorithm can achieve a lower objective function value, demonstrating superior optimization performance. This result not only confirms the significant advantage of the ADRIME algorithm in terms of optimal value, but also demonstrates its overall improvement in convergence speed and accuracy. Compared to various compared algorithms, the ADRIME algorithm's convergence curve exhibits a more gradual and stable downward trend on most test functions, indicating that its performance is more stable during the optimization process, less susceptible to initial conditions or random perturbations, and possesses greater robustness.

[0088] like Figure 6 As shown in the figure, the horizontal axis represents different algorithms, the vertical axis represents the target function value, and the function value distribution on the vertical axis shows the cumulative number of iterations of the algorithm at different function values. Figure 6 Comparing the box plots of different algorithms, we can see 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.

[0089] S3, adjusts the flight path of the UAV according to the optimal path.

[0090] In this embodiment, the coordinate values ​​of the rime particle positions 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.

[0091] The following experiments will explore the performance of the ADRIME algorithm in the UAV path planning problem: Test Example 5: UAV trajectory planning experiment To further explore the performance of the ADRIME algorithm for UAV path planning, we selected seven mainstream optimization algorithms as benchmarks. Each algorithm underwent 30 independent runs, and the experimental results are detailed in Table 6. The ADRIME algorithm stood out in the Friedman ranking, ranking first, which strongly demonstrates that it surpasses the seven mainstream optimization algorithms in terms of robustness and efficiency of optimization results.

[0092] Table 6 UAV trajectory planning experimental results

[0093] like Figure 7 The convergence curve shows that the ADRIME algorithm not only has a faster convergence speed, but also has excellent convergence accuracy. This 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.

[0094] Figure 8 also provides a more intuitive visual comparison of the eight algorithms in optimizing paths. By observing the paths of each algorithm, it is clear that the path planned by the ADRIME algorithm is smoother, more direct, and more efficient, reflecting its meticulous considerations and intelligent decision-making capabilities in path planning.

[0095] Combined with the quantitative data in Table 6 and Figure 7 The qualitative analysis in Figure 8 demonstrates that the ADRIME algorithm demonstrates unparalleled optimization performance in the field of UAV path planning. Not only does it achieve breakthroughs in both speed and accuracy, but it also demonstrates strong adaptability and robustness in practical applications, opening up new possibilities for the future development of UAV technology. This series of experimental results reinforces the effectiveness and practicality of the ADRIME algorithm and indicates its enormous potential for solving complex optimization problems.

[0096] This paper applies a multi-strategy improved Frost Ice Optimization Algorithm to UAV path planning. This multi-strategy improved Frost Ice Optimization Algorithm integrates multiple strategies to overcome the limitations of the original Frost Ice Algorithm, which is easily trapped in local optimal solutions. To enhance the diversity of the search process and global exploration capabilities, a Gaussian mutation perturbation mechanism is adopted in the algorithm's exploration phase. This increases the diversity of the search and significantly improves the probability of escaping local minima, which helps to escape local optimal solutions, improves the algorithm's convergence speed and robustness, and enables the algorithm to more efficiently approach the true global optimal solution. In the development phase, a random differential position update rule is introduced. By randomly selecting individuals in the population and calculating their position differences, the positions of other individuals are updated to guide the algorithm's search for the optimal solution while maintaining the dynamic balance of the population. This strategy effectively balances exploration and development, helps avoid premature convergence, and improves the algorithm's stability and timeliness when dealing with complex optimization problems. Furthermore, a crossover strategy, often used in genetic algorithms, is introduced to promote information exchange and cooperation between particles, enhancing the algorithm's global search capabilities. To address the problem of the algorithm's weakening optimization ability in the later stages of iteration, a leader-based reverse learning strategy was creatively incorporated. By identifying the best-performing individual in the population as the leader, and guiding other individuals to reversely learn and explore towards the leader's position, that is, starting from a distance from the current state and exploring towards the leader's position, this greatly enhances the algorithm's later optimization ability and helps discover more optimal solutions. This invention has achieved significant improvements in the length, flight time, and energy consumption of optimized paths, and can quickly find low-cost, highly secure paths with a short arrival time, thereby improving the efficiency of drone mission execution.

[0097] See also Figure 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: 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 to 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 220 is used to substitute the coordinate values ​​of the rime particle positions 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 based on the improved hard rime puncture mechanism to approach the global optimal solution as quickly 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 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 rime particle position; The flight path adjustment unit 230 is used to adjust the flight path of the UAV according to the optimal path.

[0098] 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 scope of protection 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 1 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.

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