Unmanned aerial vehicle path planning method based on multi-strategy fusion information acquisition optimization algorithm

Abstract

The invention belongs to the technical field of unmanned aerial vehicle path planning, and particularly discloses an unmanned aerial vehicle path planning method based on a multi-strategy fusion information acquisition optimization algorithm, and the method comprises the steps: obtaining the digital elevation model map data of a target region, and constructing a three-dimensional environment space model based on a task environment; constructing a path cost function and initializing an optimization algorithm population, wherein the initialization adopts three strategy fusion mechanisms of hypercube initialization, chaos initialization and random initialization to enhance the diversity of the population; a crisscross strategy is introduced, the adaptability and stability of the algorithm in the dynamic search process are enhanced, and a sine disturbance mechanism is adopted, so that the global optimization capacity and local development precision of the algorithm are enhanced; the flight path of the unmanned aerial vehicle is constructed by optimizing the path point sequence, and the path is smoothed by introducing B spline interpolation, so that the path is ensured to have continuity and feasibility, the flight requirement of the unmanned aerial vehicle is met, and the robustness and environmental adaptability of path generation are remarkably improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of unmanned aerial vehicle path planning, and particularly relates to an unmanned aerial vehicle path planning method based on a multi-strategy fusion information acquisition optimization algorithm. BACKGROUND

[0002] An unmanned aerial vehicle (UAV) is a flight platform that can complete a flight task without relying on an on-board pilot for control, and has the characteristics of compact structure, flexible operation, convenient deployment, and low operation cost. At present, although some unmanned aerial vehicles have a certain degree of autonomous flight capability, in actual application, ground remote control operation is still the main method. This is mainly limited by factors such as sensing accuracy, path planning capability, energy endurance, and flight airspace management. With the development of flight control systems, sensor technology, wireless communication, and embedded processing platforms, unmanned aerial vehicles are increasingly widely used in multiple industries, covering logistics transportation, security inspection, agricultural plant protection, environmental monitoring, communication relay, geological exploration, and emergency rescue. In typical tasks such as natural disaster assessment, geological disaster monitoring, and border patrol, unmanned aerial vehicles often need to perform low-altitude autonomous flight tasks in complex regions with large terrain undulations, dense obstacles, and strong environmental uncertainty.

[0003] In such application scenarios, in order to ensure flight safety and task completion quality, the flight path of the unmanned aerial vehicle needs to be reasonably planned so that it can avoid terrain obstacles and potential threats while meeting the performance constraints of the aircraft and the task requirements. Traditional path planning methods are mostly based on two-dimensional simplified models or rule-based geometric models, and are difficult to truly reflect the changes in elevation, obstacle distribution, and flight accessibility in complex geographic environments, thereby limiting their adaptability and practicality in complex three-dimensional terrain.

[0004] Therefore, it is urgent to construct a path planning method for real terrain environments, combine geographic spatial data such as digital elevation models (DEM), and introduce multi-source perception mechanisms and intelligent optimization algorithms to improve the global optimization ability and environmental adaptability of path planning, and thereby enhance the autonomous flight and task execution capabilities of unmanned aerial vehicles in complex three-dimensional mountainous terrain environments.

[0005] Information Acquisition Optimizer (IAO) is a new meta-heuristic optimization algorithm, which belongs to the category of intelligent optimization algorithm. The algorithm is inspired by the behavior patterns of humans in the process of acquiring and processing information. It mainly simulates the behaviors of humans in the process of solving problems, such as collecting, filtering and evaluating information, structuring organization, and gradually guiding the population to evolve to better solutions. The information collection stage simulates the extensive exploration of the search space by the group, which is used to obtain potential effective information resources. The information filtering and evaluation stage analyzes and filters the acquired information, removes redundant or inefficient information, and enhances the convergence ability of the algorithm. The information organization and re-evaluation stage guides the search direction optimization by constructing a new information structure, and improves the local development ability. Compared with traditional swarm intelligence optimization algorithms, IAO algorithm focuses more on information-driven evolution process in search strategy. This kind of algorithm can be widely applied to the solution of complex problems such as path planning, parameter optimization, feature selection, etc.

[0006] Although IAO algorithm shows certain advantages in optimization efficiency and solution quality, there are still some limitations in practical application. On the one hand, the parameter initialization and its adaptive adjustment mechanism of the algorithm are not perfect, which can easily lead to the destruction of the balance between global search and local development, and then cause the imbalance of search behavior, affecting the final path quality and convergence performance. On the other hand, the existing researches are mostly based on idealized or simplified test environment for verification, lacking systematic evaluation in complex three-dimensional terrain and multi-constraint task scene, which makes it difficult to fully reflect its adaptability and stability in real dynamic tasks. These problems limit the wide popularization and practical application of IAO algorithm in high-dimensional, multi-constrained and dynamic environment to some extent. Therefore, how to better maintain the balance between global search and local development of IAO, and how to construct a more reasonable scene environment for unmanned aerial vehicle path planning method become the key research direction. SUMMARY

[0007] In order to solve the problems of the prior art, the present application provides a multi-strategy fusion information acquisition optimization algorithm based unmanned aerial vehicle path planning method, which can solve the problems of existing unmanned aerial vehicle path planning, such as insufficient environment modeling, insufficient algorithm optimization ability, and lack of algorithm iteration speed. The method has good performance and high optimization ability in unmanned aerial vehicle path planning in different numerical optimization problem domains and various complex mountainous scenes. The generated flight path has higher smoothness and continuity, and can realize more effective obstacle avoidance operation, thereby significantly improving the robustness and environmental adaptability of the path planning system.

[0008] In order to achieve the above purpose, the technical scheme adopted by the present application is:

[0009] The unmanned aerial vehicle path planning method based on multi-strategy fusion information acquisition optimization algorithm is realized based on the following steps:

[0010] S1. Three-dimensional simulation environment construction based on digital elevation model DEM: Reconstruct and design obstacles in the real environment including power transmission towers and windmills on the obtained DEM map to model the three-dimensional simulation scene, and set the environment boundary cost condition;

[0011] S2. Multi-constraint path modeling: For the unmanned aerial vehicle task scene, a path planning model considering environmental and unmanned aerial vehicle physical constraint conditions is constructed; by introducing a weighting mechanism, the threat cost and constraint are fused into a unified objective function;

[0012] S3. Continuous path generation: The discrete path points generated by the algorithm are smoothed by using B-spline interpolation, and on the basis of maintaining the starting point and target point constraint, a continuous and smooth path is generated;

[0013] S4. Intelligent optimization algorithm solving stage: Initialize the MSF-IAO algorithm parameters, generate a diversified initial population using a hybrid initialization strategy, and select high-quality individuals to construct an initial solution set; introduce a vertical and horizontal crossover strategy during the dynamic search process of the algorithm, and use a sinusoidal disturbance mechanism to enhance the global optimization ability and local development precision of the algorithm;

[0014] S5. Update selection of optimal solution: In each generation, the current global optimal solution is dynamically updated by comparing the fitness values of the population individuals; if the iteration number reaches the set upper limit, the optimization is terminated and the optimal path point sequence is output;

[0015] S6. Optimal path generation and verification: The algorithm outputs the global optimal solution after reaching the preset selection number, and evaluates the performance through convergence curves, path smoothness and other indicators to finally generate a three-dimensional path that meets multiple constraints to verify its engineering feasibility and application value.

[0016] Further, step S1 specifically includes the following content:

[0017] With the aid of remote sensing images and digital elevation model DEM data, accurate terrain elevation information of the target area is obtained; based on the obtained elevation data, gray mapping technology is used to convert the elevation value into the corresponding gray value, thereby generating a terrain gray image.

[0018] Further, step S2 specifically includes the following content:

[0019] S2-1. Obstacle constraint:

[0020] By designing obstacle constraints including power transmission towers and windmills to simulate the real scene, and modeling them, the mathematical expression is:

[0021]

[0022] where F U represents the threat cost of the obstacle region, d r is the distance from the UAV to the threat center of the obstacle region, R is the maximum detection radius of the obstacle region, (x i ,y i ,z i ) is the current position coordinate of the UAV, (x R ,y R ,z R ) is the center coordinate of the obstacle region;

[0023] S2-2. No-fly zone constraint:

[0024]

[0025] where F N represents the threat cost of the no-fly zone, and represent the lower and upper limits of the X coordinate of the no-fly zone, respectively, and represent the lower and upper limits of the Y coordinate of the no-fly zone, respectively;

[0026] S2-3. Path length cost:

[0027] The path length cost is used to measure the total distance of the UAV flight trajectory; the path length cost function is defined as follows:

[0028]

[0029] where F L is the total path length of each discrete point of the UAV, N represents the total number of discrete path points generated by the control points, l i is the distance between the i-th path point and its subsequent path point; (x s ,y s ,z s ) is the starting point coordinate of the UAV, (x g ,y g ,z g ) is the target point coordinate of the UAV, L EC represents the Euclidean distance between the starting point S(x S ,y S ,z S ) and the target point G(x G ,y G ,z G );

[0030] S2-4. Height cost:

[0031] To improve the energy efficiency and flight stability, the smoothness of the flight trajectory in the vertical direction is optimized, and a height cost model is constructed as follows: Let the path consist of m discrete points, and the height of the i-th path point be Z i The average height of the path can be expressed as:

[0032]

[0033] In the formula, F H is the height cost, M is the number of intermediate points, is the average height of the path point;

[0034] S2-5. Pitch angle and yaw angle cost:

[0035] The direction vector between adjacent path points is defined as follows:

[0036]

[0037] In the formula, is the direction vector between adjacent path points, P i is the path point, P i+1 is the coordinate of the next generation path point; x i+1 , y i+1 and z i+1 represent the coordinates of the next adjacent point; F T is the yaw angle cost; F C is the pitch angle cost, γ Ω is the set reasonable pitch angle; θ i represents the turning angle of the path at the i-th control point, represents the adjacent next generation vector; γ i represents the pitch angle of the path at the i-th control point, and represent the Euclidean norm of the current vector and the adjacent next generation vector, respectively;

[0038] S2-6. Cost function:

[0039] By linear weighting method, the UAV path planning problem is converted into an optimization modeling problem by integrating the above multiple constraint conditions, and the cost function of the UAV path planning can be expressed as:

[0040] F Whole = m1·(F U +F N )+m2·F L +m3·F H +m4·(F T +F C ) (47)

[0041] Wherein, the comprehensive cost function F Whole Composed of 4 sub-objective functions, including obstacle threat, no-fly zone threat, path length cost, height cost, yaw angle and pitch angle cost; m1, m2, m3 and m4 are weight factors of corresponding cost functions.

[0042] Further, step S3 specifically includes the following content:

[0043] In order to make the flight path more smooth, continuous and conform to the actual motion law; through the optimization of a series of path points, the path points are obtained, and a flight path of the unmanned aerial vehicle is constructed by connection, but due to the physical constraint conditions of the unmanned aerial vehicle being fixed, the obtained path cannot meet the flyable condition; therefore, the B-spline curve method is adopted to perform flight path smoothing in the flight, which can be expressed as:

[0044]

[0045] In the formula, S(u) is the point coordinate on the curve corresponding to the parameter point u in the n control points, u i , u i+1 , u i+k-1 , u i+k respectively represent the i, i+1, i+k-1, i+k parameter points; u max is the maximum value of the parameter u, P i is the control point, N i,p (u) is the b-spline basis function (the i-th, order p), N i+1,k-1 (u) is the i+1 point, and the order is k-1; U=[u0,u1,...,u n ] is the knot vector.

[0046] Further, step S4 specifically includes the following content:

[0047] S4-1. Build a basic information acquisition optimization algorithm;

[0048] S4-2. Integrate a hybrid initialization strategy;

[0049] S4-3. Introduce a cross-longitudinal strategy and add a sinusoidal disturbance mechanism.

[0050] Further, step S4-1 specifically includes the following content:

[0051] S4-1. Build an information acquisition optimization algorithm:

[0052] The information acquisition optimization algorithm is inspired by human information acquisition behavior, and information updating and iteration are performed through three key strategies of information collection, information filtering and evaluation, and information organization and evaluation:

[0053] S4-1-1. Information collection:

[0054] Individuals collect information from different sources using various methods, retaining the most relevant and reliable data;

[0055]

[0056] wherein, are two individuals randomly selected at the beginning of the algorithm, iter represents the current iteration number, and the state of the information body at the i-th iteration is the state of the information body at the i+1-th iteration is is a random number between 0 and 1, representing the influencing factors in the information collection process.

[0057] S4-1-2. Information filtering and evaluation:

[0058] The filtering and evaluation process of information is an important mechanism for individuals to quickly identify relevant and useful information, to eliminate inaccurate and misleading information, and to improve the overall quality of information, which is represented by the formula:

[0059]

[0060] wherein, is a randomly selected individual, rand is a random number generated between 0 and 1, and Δ is the error generated when the subjective factor filters and evaluates the information, defined as:

[0061]

[0062] Ξ = 2 * mod(3.468 * v * (1 - β) * (acos(γ * 10 4 )), 1) (53)

[0063]

[0064] wherein, Ξ is the subjective influence factor, Γ is defined as the reliability factor, Max_iter is the maximum iteration number, and the mathematical model of Γ consists of three main parts: the sine function part, the logarithmic function part, and the information quality factor Φ; mod is the modulus operation; v, β, a, and γ are random numbers generated between 0 and 1. The formula of the information quality factor Φ is:

[0065]

[0066] wherein, δ is a random number generated between 0 and 1, and Φ is considered as a function of the iteration number iter;

[0067] S4-1-3. Information analysis and organization:

[0068] Information analysis and organization is to identify the existing useful information from the filtered information, and to convert the convertible information identified in the previous stage into useful information, which is expressed as:

[0069]

[0070] In the formula, represents the best information body generated in the previous iteration process, represents the average value of the best information body generated in the previous iteration process, ε, ζ, κ, ω represent random numbers generated between [0, 1], and Λ represents the control factor of analyzing and organizing information, which is defined as:

[0071]

[0072] Further, step S4-2 specifically includes the following contents:

[0073] Hybrid initialization: by combining Latin hypercube sampling, Logistic chaotic mapping and random initialization, an initial solution set is provided for the optimization algorithm; by dynamically adjusting the proportion of the three initialization methods, the initialization process is adaptively optimized according to the problem dimension and population size, that is:

[0074] p LHS = 0.4 + 0.3 * α (58)

[0075] p Logistic = 0.3 * (1-β) (59)

[0076] p Rand = 1-p lhs -p chaos (60)

[0077] In the formula, p LHS , p Rand , p LHS are the probabilities of selecting Latin hypercube sampling, Logistic chaotic mapping and random initialization, respectively, and α, β are the probability parameters of selecting Latin hypercube sampling and Logistic chaotic mapping designed by the algorithm. The number of individuals generated by each method is:

[0078] n LHS = round(N LHS ) (61)

[0079] n Logistic = round(N Logistic ) (62)

[0080] n Rand = N-nLHS -n Logistic (63)

[0081] where n LHS Select the number of individuals of Latin hypercube sampling, n Logistic Select the number of individuals of Logistic chaotic mapping, n Rand Select the number of randomly initialized individuals, round is rounding operation, and N is the number of individuals in the algorithm design. Shuffle is used to randomly shuffle the row order to avoid structural bias, and then:

[0082]

[0083] where X is the new population formed by mixing, and Shuffle is the mixing of the three populations.

[0084] Further, step S4-3 specifically includes the following contents:

[0085] S4-3-1. Cross vertical strategy:

[0086] Horizontal crossover promotes the spread of high-quality features by recombining information between individuals in the current population, enhances the same level of cooperation and search space coverage, as follows:

[0087]

[0088] wherein, is a newly generated individual, x i represents the position vector of the i-th individual in the current iteration, x i-1 represents the position vector of the i-1-th individual in the current iteration, x i+1 represents the position vector of the i+1-th individual in the current iteration; r ~ U(0,1) as a fusion factor, used to adjust the weighted proportion of feature information between two individuals; and c ~ U(-1,1) introduces a disturbance term to strengthen the differential mutation effect, thereby improving the jumping ability and local search accuracy of the individual in the solution space;

[0089] Vertical crossover is aimed at intergenerational information integration, usually by introducing historical elite solutions or global optimal solutions coupled with the current population; as follows:

[0090]

[0091] wherein, is a new individual generated by vertical crossover, is the individual of the t-th generation, d1 and d2 represent two index positions randomly selected from all dimensions of the current individual; the fusion coefficient r1 ~ U(0,1) is used to adjust the recombination weight of the feature values between the two dimensions;

[0092] S4-3-2. Sine perturbation mechanism:

[0093] The sine perturbation strategy is an adaptive mutation strategy based on perturbation and inter-individual difference guidance, and is a search mechanism with exploration and adaptability, and is expressed as:

[0094] X new (i,j) = X(i,j) + sin(r3*π)*(X(i,j)-X(a,j)), r4 < K and r5 < 0.05 (67)

[0095]

[0096] In the formula, X new (i,j) is a new individual generated by the sine perturbation, X(i,j) is the individual before the strategy is performed, t is the current iteration number, T is the maximum iteration number, X(a,j) represents any particle in the particle cluster; as the algorithm proceeds, the collision between particles becomes more frequent, so the collision probability K is controlled, and r3, r4 and r5 are random values, taking values in the range [0,1].

[0097] The present application has the beneficial effects of:

[0098] In order to improve the safety and efficiency of unmanned aerial vehicle path planning in complex mountainous scenes, the present application proposes a hybrid swarm intelligence optimization algorithm based on the fusion of information acquisition optimization algorithm (IAO) and particle collision exploration and cross strategy based on sine perturbation. Firstly, the hybrid initialization of the fusion of three strategies of hypercube initialization, chaotic initialization and random initialization according to the problem dimension and population size is adopted. Then, the candidate solutions are generated through information filtering and evaluation screening. The generated candidate solutions are corrected by selecting different learning strategies through random probability selection in the information filtering and evaluation stage and the information analysis and organization stage, and the optimal solutions are selected by judgment. At the same time, the sine perturbation strategy is integrated into the algorithm to continuously perturb and update the position of the solution. Finally, the longitudinal and transverse cross strategy is adopted to linearly combine and differentially perturb each individual and adjacent individuals and itself to construct new solutions, improve the search diversity and local search ability, and balance the local synergy and random exploration ability of the algorithm. The present application has good performance and high optimization ability in different numerical optimization problem domains and unmanned aerial vehicle path planning in various complex mountainous scenes. BRIEF DESCRIPTION OF DRAWINGS

[0099] Figure 1 The step flow chart of the present application is shown in the figure;

[0100] Figure 2 The three-dimensional graph of the unmanned aerial vehicle planning path based on the simple mountainous scene multi-strategy fusion information acquisition algorithm, sparrow search algorithm and whale optimization algorithm of the present application is shown in the figure.

[0101] Figure 3 It is the side profile view of the unmanned aerial vehicle planning path based on the multi-strategy fusion information acquisition algorithm under the simple mountainous scene of the application;

[0102] Figure 4 It is the path length and average altitude comparison chart of the unmanned aerial vehicle planning path based on the multi-strategy fusion information acquisition algorithm, sparrow search algorithm and whale optimization algorithm under the simple mountainous scene of the application;

[0103] Figure 5 It is the optimal fitness and average fitness comparison chart of the unmanned aerial vehicle planning path based on the multi-strategy fusion information acquisition algorithm, sparrow search algorithm and whale optimization algorithm under the simple mountainous scene of the application;

[0104] Figure 6 It is the three-dimensional chart of the unmanned aerial vehicle planning path based on the multi-strategy fusion information acquisition algorithm, sparrow search algorithm and whale optimization algorithm under the complex mountainous scene of the application;

[0105] Figure 7 It is the side profile view of the unmanned aerial vehicle planning path based on the multi-strategy fusion information acquisition algorithm under the complex mountainous scene of the application;

[0106] Figure 8 It is the path length and average altitude comparison chart of the unmanned aerial vehicle planning path based on the multi-strategy fusion information acquisition algorithm, sparrow search algorithm and whale optimization algorithm under the complex mountainous scene of the application;

[0107] Figure 9 It is the optimal fitness and average fitness comparison chart of the unmanned aerial vehicle planning path based on the multi-strategy fusion information acquisition algorithm, sparrow search algorithm and whale optimization algorithm under the complex mountainous scene of the application. DETAILED DESCRIPTION

[0108] The principles and characteristics of the application will be described below in conjunction with the drawings, and the examples are only used to explain the application and not to limit the use range of the application.

[0109] As Figure 1 shown, the application proposes a multi-strategy fusion information acquisition optimization algorithm based unmanned aerial vehicle path planning method, which is realized based on the following steps:

[0110] S1. Three-dimensional simulation environment construction based on digital elevation model DEM:

[0111] Reconstruct and design the obstacles in the real environment including power transmission towers and windmills on the obtained DEM map, to model the three-dimensional simulation scene, and set the environment boundary cost conditions.

[0112] To realize the path planning based on real terrain, firstly, the geographic spatial data of the target area is acquired. In this study, the precise terrain elevation information of one island in the Chagos Archipelago in the middle of the Indian Ocean is obtained by means of remote sensing images and Digital Elevation Model (DEM) data. Based on the obtained elevation data, the gray mapping technology is adopted to convert the elevation values into corresponding gray values, so as to generate a terrain gray image. The image can intuitively express the spatial undulation characteristics of the terrain, and reflect the distribution law of the ground elevation by using the brightness difference, thereby providing a reliable visualization basis for path planning and terrain analysis.

[0113] The generated terrain gray image can be used as input data for subsequent path planning and terrain analysis modules. On the one hand, the path planning algorithm can determine the terrain undulation area by the brightness difference of the image pixels, so as to avoid high and steep obstacles or dangerous areas; on the other hand, the image can also be used to construct a cost function, and the elevation change is combined to design a path penalty term, so as to improve the feasibility and smoothness of the path.

[0114] S2. Multi-constraint path modeling:

[0115] In order to improve the feasibility and safety of the path planning result in the real environment, a complex mountain environment constraint model is constructed between the take-off point and the target point according to the task requirements, and various typical threat areas are introduced for modeling. The threat areas include but are not limited to forbidden flight areas, windmills, power transmission towers and other potential human impact areas.

[0116] For the unmanned aerial vehicle task scenario, a path planning model considering both the environment and the physical constraint conditions of the unmanned aerial vehicle itself is proposed. By introducing a weighting mechanism, the threat cost and the constraint are fused into a unified objective function, so as to improve the practicality and safety of the path generation. Specifically, the following contents are included:

[0117] S2-1. Obstacle constraint:

[0118] By designing obstacle constraints including power transmission towers and windmills, the effect of simulating real scenarios is achieved, and the modeling is performed, and the mathematical expression is as follows:

[0119]

[0120]

[0121] In the formula, F U represents the threat cost of the obstacle area, d r is the distance from the unmanned aerial vehicle to the threat center of the obstacle area, R is the maximum detection radius of the obstacle area, (x i ,y i ,z i ) is the current position coordinate of the unmanned aerial vehicle, (xR ,y R ,z R ) is the obstacle center coordinate;

[0122] S2-2. No-fly zone constraint:

[0123]

[0124] where F N represents the threat cost of the no-fly zone, and represent the lower and upper limits of the X coordinate of the no-fly zone, respectively, and represent the lower and upper limits of the Y coordinate of the no-fly zone, respectively;

[0125] S2-3. Path length cost:

[0126] The path length cost is used to measure the total distance of the UAV flight trajectory; the path length cost function is defined as follows:

[0127]

[0128] where F L is the total path length of each discrete point of the UAV, N represents the total number of discrete path points generated by the control points, l i is the distance between the i-th path point and its subsequent path point; (x s ,y s ,z s ) is the starting point coordinate of the UAV, (x g ,y g ,z g ) is the target point coordinate of the UAV, and L EC represents the Euclidean distance between the starting point S(x S ,y S ,z S ) and the target point G(x G ,y G ,z G );

[0129] S2-4. Height cost:

[0130] To improve energy efficiency and flight stability, the smoothness of the optimized flight trajectory in the vertical direction is improved, and the height cost model is constructed as follows: let the path consist of m discrete points, and the height of the i-th path point be Z i , then the average height of the path can be represented as:

[0131]

[0132] where F HH is the height of the path point, m is the number of the intermediate points, and H is the average height of the path points.

[0133] S2-5. Pitch and yaw cost:

[0134] In three-dimensional path planning, the naturalness and continuity of the steering action are important indicators for measuring the quality of the UAV path. Therefore, the direction vector between adjacent path points is defined as shown in the following formula:

[0135]

[0136] In the formula, is the direction vector between adjacent path points, P i is the path point, P i+1 is the coordinate of the next generation path point; x i+1 , y i+1 , and z i+1 represent the coordinates of the next adjacent point; F T is the yaw angle cost; F C is the pitch angle cost, γ Ω is the set reasonable pitch angle; θ i represents the steering angle of the path at the i-th control point, represents the adjacent next generation vector; γ i represents the pitch angle of the path at the i-th control point, and represent the Euclidean norm of the current vector and the adjacent next generation vector, respectively;

[0137] S2-6. Cost function:

[0138] By combining the above multiple constraint conditions, the UAV path planning problem is converted into an optimization modeling problem through linear weighting method, and the cost function of the UAV path planning can be represented as:

[0139] F Whole = m1·(F U +F N )+m2·F L +m3·F H +m4·(F T +F C ) (81)

[0140] Among them, the comprehensive cost function F Whole is composed of four sub-objective functions, including obstacle threat, forbidden area threat, path length cost, height cost, yaw angle and pitch angle cost; m1, m2, m3 and m4 are the weight factors of the corresponding cost functions.

[0141] S3. Continuous path generation:

[0142] Trajectory smoothing refers to the process of optimizing and processing the trajectory data of an aircraft (such as a UAV, missile or spacecraft) or other moving body, making the trajectory smoother, more continuous and conforming to the actual movement law. By optimizing a series of path points, path points are obtained, and a UAV flight trajectory is constructed by connecting them. However, due to the fixed physical constraint conditions of the UAV, the obtained path cannot meet the flyable conditions. Therefore, the present application uses B-spline interpolation to smooth the discrete path points generated by the algorithm, generates a continuous and smooth path while maintaining the constraints of the starting point and target point. Specifically, it can be expressed as:

[0143]

[0144] In the formula, S(u) is the point coordinate on the curve corresponding to the parameter point u in the n control points; u i , u i+1 , u i+k-1 , u i+k respectively represent the i, i+1, i+k-1, i+k parameter points; u max is the maximum value of the parameter u, P i is the control point, N i,p (u) is the b-spline basis function (the i-th, order p), N i+1,k-1 (u) is the i+1 point, and the order is k-1; U = [u0, u1,..., u n ] is the knot vector.

[0145] S4. Intelligent optimization algorithm solving stage:

[0146] A hybrid initialization strategy is adopted, which combines super-cube initialization, chaotic initialization and random initialization according to the problem dimension and population size. Then, through information filtering and evaluation screening, candidate solutions are generated. For the generated candidate solutions, different learning strategies are selected for correction through random probability selection after information filtering and evaluation stage and information analysis and organization stage. The optimal solution is selected by judgment. At the same time, the algorithm is combined with a sinusoidal disturbance strategy to constantly disturb and update the position of the solution. Finally, a vertical and horizontal crossover strategy is used to linearly combine and differentially disturb each individual and its adjacent individual and itself to construct a new solution.

[0147] Initialize the parameters of the MSF-IAO algorithm, generate a diversified initial population using the hybrid initialization strategy, and select high-quality individuals to construct an initial solution set. In the dynamic search process of the algorithm, introduce a vertical and horizontal crossover strategy and use a sinusoidal disturbance mechanism to enhance the global optimization ability and local development precision of the algorithm. Specifically, the following contents are included:

[0148] S4-1. Build a basic information acquisition optimization algorithm. Specifically:

[0149] S4-1. Building information acquisition optimization algorithm:

[0150] Information Acquisition Optimizer (IAO) is inspired by human information acquisition behavior, which updates and iterates through three key strategies: information collection, information filtering and evaluation, and information organization and evaluation:

[0151] S4-1-1. Information collection:

[0152] Individuals collect information from different sources using various methods, retaining the most relevant and reliable data;

[0153]

[0154] wherein, are two individuals randomly selected at the beginning of the algorithm, iter represents the current iteration number, and the state of the information body at the i-th iteration is The state of the information body at the i+1-th iteration is is a random number between 0 and 1, representing the influencing factors in the information collection process;

[0155] S4-1-2. Information filtering and evaluation:

[0156] The filtering and evaluation process of information is an important mechanism for individuals to quickly identify relevant and useful information, not only effectively eliminating inaccurate and misleading information, but also significantly improving the overall quality of information, which is represented by the formula:

[0157]

[0158] wherein, is a randomly selected individual, rand is a random number generated in [0,1]; Δ is the error produced when the subjective factor filters and evaluates information, defined as:

[0159]

[0160] Ξ = 2 * mod(3.468 * v * (1 - β) * (acos(γ * 10 4 )), 1) (87)

[0161]

[0162] In the formula, Ξ is a subjective influence factor, Γ is defined as a reliability factor, Max iter is the maximum number of iterations, the mathematical model of Γ is composed of three main parts of the sine function part, the logarithmic function part and the information quality factor Φ; mod is the modulus operation; v, β, a, γ are random numbers generated between [0, 1]. The formula of the information quality factor Φ is:

[0163]

[0164] In the formula, δ is a random number generated between [0, 1]; Φ is regarded as a function of the number of iterations iter;

[0165] S4-1-3. Information analysis and organization:

[0166] Information analysis and organization is to identify existing useful information from filtered information, and to convert the convertible information identified in the previous stage into useful information, and its formula is expressed as:

[0167]

[0168] In the formula, represents the best information body generated in the previous iteration process, represents the average value of the best information body generated in the previous iteration process, ε, ζ, κ, ω represent random numbers generated between [0, 1], and Λ represents the control factor of analyzing and organizing information, which is defined as:

[0169]

[0170] S4-2. Incorporate hybrid initialization strategy;

[0171] Step S4-2 specifically includes the following contents:

[0172] Hybrid initialization: By combining Latin hypercube sampling (LHS), Logistic chaotic mapping and random initialization, an initial solution set with good distribution, rich diversity and nonlinear jumping characteristics is provided for the optimization algorithm. By dynamically adjusting the proportion of the three initialization methods, the initialization process is optimized according to the problem dimension (dim) and population size (pop) to improve the performance of the optimization algorithm. Then,

[0173] p LHS = 0.4 + 0.3*α (LHS) (92)

[0174] p Logistic = 0.3*(1-β) (Logistic) (93)

[0175] p Rand = 1-plhs -p chaos (Rand) (94)

[0176] where p LHS , p Rand , p LHS are the probabilities of selecting Latin hypercube sampling, Logistic chaotic mapping and random initialization, respectively; a, b are the probability parameters of selecting Latin hypercube sampling and Logistic chaotic mapping in algorithm design. The number of individuals generated by each method is:

[0177] n LHS = round(N LHS ) (95)

[0178] n Logistic = round(N Logistic ) (96)

[0179] n Rand = N-n LHS -n Logistic (97)

[0180] where n LHS is the number of individuals of selecting Latin hypercube sampling, n Logistic is the number of individuals of selecting Logistic chaotic mapping, n Rand is the number of individuals of selecting random initialization, round is the rounding operation, and N is the number of individuals in algorithm design. Shuffle is used to randomly shuffle the row order to avoid structural bias, so:

[0181]

[0182] where X is the new population formed by mixing, and Shuffle is the mixing of the three populations.

[0183] S4-3. Introduce crossover horizontal-vertical strategy and add sine perturbation mechanism. Specifically, it includes:

[0184] S4-3-1. Crossover horizontal-vertical strategy:

[0185] Crossover horizontal-vertical strategy (Crossover-horizontal-vertical strategy) achieves the coordinated regulation of global exploration and local development by fusing horizontal and vertical information interaction, which can enhance the adaptability and stability of the algorithm, effectively improve the population diversity and algorithm convergence speed.

[0186] Horizontal crossover promotes the propagation of high-quality features by recombining the information between individuals in the current population, enhances the same level of collaboration and search space coverage, as follows:

[0187]

[0188] where, is the newly generated individual, x i represents the position vector of the i-th individual in the current iteration, x i-1 represents the position vector of the i-1-th individual in the current iteration, x i+1 represents the position vector of the i+1-th individual in the current iteration; r ~ U(0, 1) is used as a fusion factor to adjust the weighted proportion of feature information between the two individuals; and c ~ U(-1, 1) introduces a disturbance term to strengthen the differential mutation effect, thereby improving the jumping ability and local search precision of the individual in the solution space.

[0189] Longitudinal cross information integration is usually achieved by introducing historical elite solutions or global optimal solutions coupled with the current population; as follows:

[0190]

[0191] where, is the newly generated individual, is the individual of the t-th generation, d1, d2 represent two index positions randomly selected from all dimensions of the current individual; the fusion coefficient r1 ~ U(0, 1) is used to adjust the recombination weight of the feature values between the two dimensions;

[0192] S4-3-2. Sinusoidal disturbance mechanism:

[0193] The sinusoidal disturbance strategy is an adaptive mutation strategy based on disturbance and inter-individual difference guidance, which is a search mechanism with exploration and adaptability, represented as:

[0194] X new (i,j) = X(i,j) + sin(r3*π)*(X(i,j)-X(a,j)), r4

[0195]

[0196] where, X new (i,j) is the newly generated individual, X(i,j) is the individual before the strategy, t is the current iteration number, T is the maximum iteration number, X(a,j) represents any particle in the particle cluster; as the algorithm proceeds, the collision between particles becomes more frequent, so the collision probability K is used for control, r3, r4 and r5 are random values, taking values in the range [0, 1]; the purpose is to increase the change of the periodicity of the sine function to ensure the randomness of the solution generated by the strategy.

[0197] S5. Update selection of optimal solution:

[0198] In each generation, the current global optimal solution is dynamically updated by comparing the fitness values of the population individuals; if the number of iterations reaches the set upper limit, the optimization is terminated and the optimal path point sequence is output.

[0199] In this embodiment, the path optimization is solved by an iterative optimization algorithm based on swarm intelligence. In the initial stage, a certain number of individuals are generated to form a population, and each individual represents a candidate path from the takeoff point to the target point. In each iteration, the quality of each individual's path is evaluated by calculating its fitness value, and the fitness function considers factors such as path length, terrain undulation, threat area avoidance ability, and path smoothness. On this basis, the current global optimal solution is dynamically compared and updated to ensure that the population evolves towards the high-quality solution space. Then, the population is guided according to the set search strategy, balancing global search and local development to improve search efficiency and stability.

[0200] When the number of iterations reaches the set maximum upper limit T, or the predefined convergence criteria are met, the optimization process is terminated, and the current recorded global optimal path point sequence is output. This path serves as the final optimization result and can be used for subsequent path smoothing processing and flight control system execution, ensuring that the UAV can achieve safe and efficient autonomous flight in complex mountainous environments.

[0201] S6. Optimal path generation and verification:

[0202] The algorithm outputs the global optimal solution after reaching the preset number of generations, and evaluates its performance through convergence curves, path smoothness, and other indicators to generate a three-dimensional path that meets multiple constraints, thereby verifying its engineering feasibility and application value.

[0203] Simulation experiment:

[0204] As shown in Figures 2-9 Compared with traditional classical algorithms, the multi-strategy fusion information acquisition optimization algorithm designed in the present application has significant advantages in path optimization and convergence speed. Specifically, the hybrid initialization mechanism effectively improves the diversity of population distribution, providing a good initial selection for the algorithm; the cross and horizontal strategy improves the diversity maintenance and convergence efficiency of swarm intelligence optimization algorithm in solving complex problems, effectively enhancing the adaptability and stability of the algorithm in the dynamic search process; the sinusoidal perturbation mechanism considers the information difference between individuals, nonlinear adjustment of perturbation amplitude, and dynamic change of perturbation probability, and is a search mechanism with exploration and adaptability.

[0205] As shown in Figures 2-9The experimental results shown in the figures verify the superior performance of the fusion algorithm in complex mountainous terrain and multi-obstacle environment. The generated flight path has higher smoothness and continuity, and can realize more effective obstacle avoidance operation. Compared with the existing single path planning algorithm, the path length optimization, trajectory smoothing processing and obstacle avoidance strategy rationality are more outstanding. The technical scheme significantly improves the robustness and environmental adaptability of the path planning system, overcomes the problems of easy falling into local optimum and poor path quality in the prior art, and has good engineering application prospect and popularization value.

[0206] In summary, the multi-strategy fusion algorithm MSF-IAO based on the information acquisition optimizer (IAO) designed in the present application is compared with the mainstream method, and the trajectory planning in different terrains and complex mountainous scenes is compared. The results show that the method can perform superior path planning performance and optimization ability in diversified optimization problems and complex mountainous environments. Moreover, the method can perform superior path planning performance and optimization ability in diversified optimization problems and complex mountainous environments, has high practical value and environmental adaptability, and can significantly improve the safety and efficiency of unmanned aerial vehicle trajectory planning in complex mountainous scenes.

[0207] The algorithm terminates optimization after reaching the preset maximum number of iterations and outputs the currently recorded global optimal solution path. To comprehensively evaluate the algorithm performance, convergence curves, path smoothness, obstacle avoidance effect and other indicators are introduced for analysis to verify the performance of the algorithm in optimization efficiency and path quality. Finally, the obtained path is subjected to feasibility test to ensure that it meets multiple constraint conditions such as aircraft dynamics constraints, environmental threat avoidance and terrain adaptability, thereby generating a three-dimensional flight path that can be used for actual task execution, embodying the engineering feasibility and application value of the proposed method.

[0208] Obviously, the above-described embodiments are only part of the embodiments of the present application, and are not all the embodiments. The preferred embodiments of the present application are shown in the drawings, but do not limit the patent scope of the present application. The present application can be realized in many different forms, and on the contrary, the purpose of providing these embodiments is to make the disclosure of the present application more thorough and comprehensive. Although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments, or equivalently replace some technical features. Any equivalent structure made by using the contents of the specification and drawings, directly or indirectly applied to other related technical fields, is also within the scope of the patent protection of the present application.

Claims

1. A UAV path planning method based on a multi-strategy fusion information acquisition optimization algorithm, characterized in that: This method is implemented based on the following steps: S1. Construction of a 3D simulation environment based on a digital elevation model (DEM): Reconstruct and design obstacles in the real environment, including transmission towers and windmills, on the acquired DEM map to model the 3D simulation scene and set environmental boundary cost conditions. S2. Multi-constraint path modeling: For UAV mission scenarios, a path planning model is constructed that takes into account both environmental and UAV physical constraints; by introducing a weighting mechanism, threat costs and constraints are integrated into a unified objective function; S3. Continuous Path Generation: B-spline interpolation is used to smooth the discrete path points generated by the algorithm, generating a continuous and smooth path while maintaining the constraints between the starting point and the target point. S4. Intelligent Optimization Algorithm Solution Stage: Initialize MSF-IAO algorithm parameters, generate diverse initial populations using a hybrid initialization strategy, and select high-quality individuals to construct the initial solution set; A cross-sectional strategy is introduced during the algorithm's dynamic search process, and a sinusoidal perturbation mechanism is adopted to enhance the algorithm's global optimization capability and local development accuracy. S5. Optimal Solution Update Selection: In each iteration, the current global optimal solution is dynamically updated by comparing the fitness values ​​of individuals in the population; if the number of iterations reaches the set upper limit, the optimization is terminated and the optimal path point sequence is output. S6. Optimal Path Generation and Verification: After reaching the preset number of iterations, the algorithm outputs the global optimal solution and evaluates its performance through indicators such as convergence curve and path smoothness. Finally, it generates a three-dimensional path that satisfies multiple constraints to verify its engineering feasibility and application value.

2. The UAV path planning method based on a multi-strategy fusion information acquisition optimization algorithm according to claim 1, characterized in that: Step S1 specifically includes the following: Using remote sensing imagery and digital elevation model (DEM) data, accurate topographic elevation information of the target area is obtained. Based on the obtained elevation data, grayscale mapping technology is used to convert the elevation values ​​into corresponding grayscale values, thereby generating a grayscale topographic image.

3. The UAV path planning method based on a multi-strategy fusion information acquisition optimization algorithm according to claim 1, characterized in that: Step S2 specifically includes the following: S2-1. Obstacle Constraints: By designing obstacle constraints including transmission towers and wind turbines, the effect of simulating a real-world scenario is achieved, and a model is created. The mathematical expression is as follows: In the formula, F U d represents the threat cost of the obstacle area. r R is the distance from the UAV to the center of the threat in the obstacle area, and R is the maximum detection radius of the obstacle area. i ,y i ,z i (x) represents the current position coordinates of the drone. R ,y R ,z R () represents the coordinates of the obstacle center; S2-2. No-fly zone constraints: In the formula, F N This indicates the cost of the threat posed by a no-fly zone. and These represent the lower and upper limits of the no-fly zone in the X-coordinate, respectively. and These represent the lower and upper limits of the no-fly zone in the Y-coordinate, respectively; S2-3. Path length cost: Path length cost is used to measure the total distance of the UAV's flight path; the path length cost function is defined as follows: In the formula, F L It is the sum of the path lengths of each discrete point of the UAV, where N represents the total number of discrete path points generated by the control points, l i The distance between the i-th path point and its subsequent path points; (x s ,y s ,z s (x) represents the coordinates of the drone's starting point. g ,y g ,z g ) represents the coordinates of the UAV target point, L EC Indicates the starting point S(x) S ,y S ,z S ) and target point G(x) G ,y G ,z G The Euclidean distance between them; S2-4. Cost of Height: To improve energy efficiency and flight stability, and optimize the smoothness of the flight trajectory in the vertical direction, an altitude cost model is constructed as shown in the following equation: Assume the path consists of m discrete points, and the altitude of the i-th path point is Z. i The average height of the path can then be expressed as: In the formula, F H The cost is the height, and M is the number of intermediate points. The average height of the path points; S2-5. Costs of pitch and yaw angles: The direction vector between adjacent path points is defined as follows: In the formula, P is the direction vector between adjacent path points. i P is a path point. i+1 These are the coordinates of the next-generation pathpoints; x i+1 y i+1 and z i+1 F represents the coordinates of the next adjacent point; T For yaw angle cost; F C For the cost of pitch angle, γ Ω To set a reasonable pitch angle; θ i This represents the turning angle of the path at the i-th control point. Represents the next-generation vector of adjacent neighbors; γ i This represents the pitch angle of the path at the i-th control point. and Let represent the Euclidean norms of the current vector and its neighboring next-generation vector, respectively. S2-6. Cost Function: Considering the above constraints, the UAV path planning problem is transformed into an optimization modeling problem using the linear weighting method. Therefore, the cost function for UAV path planning can be expressed as: F Whole =m1·(F U +F N )+m2·F L +m3·F H +m4·(F T +F C ) (13) Among them, the comprehensive cost function F Whole It consists of four sub-objective functions, including obstacle threat, no-fly zone threat, path length cost, altitude cost, yaw angle cost, and pitch angle cost; m1, m2, m3, and m4 are the weighting factors of the corresponding cost functions.

4. The UAV path planning method based on a multi-strategy fusion information acquisition optimization algorithm according to claim 1, characterized in that: Step S3 specifically includes the following: To make the flight path smoother, more continuous, and more consistent with actual motion patterns, a series of path points were optimized to obtain path points, which were then connected to construct a flight path for the UAV. However, due to the fixed physical constraints of the UAV, the obtained path did not meet the flight requirements. Therefore, the B-spline curve method was adopted to smooth the flight path during flight, which can be represented as: In the formula, S(u) represents the coordinates of the point on the curve corresponding to the parameter point u among the n control points, u i u i+1 u i+k-1 u i+k These represent the i-th, i+1, i+k-1, and i+k parameter points, respectively; u max P is the maximum value of parameter u. i N is the control point; i,p (u) is the b-spline basis function; N i+1,k-1 (u) is the (i+1)th point, with an order of k-1; U = [u0, u1, ..., u n ] is the junction vector.

5. The UAV path planning method based on a multi-strategy fusion information acquisition optimization algorithm according to claim 1, characterized in that: Step S4 specifically includes the following: S4-1. Establish a basic information acquisition optimization algorithm; S4-2. Incorporating a hybrid initialization strategy; S4-3. Introduce a cross-sectional and cross-sectional strategy and add a sinusoidal perturbation mechanism.

6. The UAV path planning method based on a multi-strategy fusion information acquisition optimization algorithm according to claim 5, characterized in that: Step S4-1 specifically includes the following: S4-1. Build an optimized information acquisition algorithm: Information acquisition optimization algorithms are inspired by human information acquisition behavior, and update and iterate information through three key strategies: information collection, information filtering and evaluation, and information organization and evaluation. S4-1-1. Information Gathering: Individuals use various methods to collect information from different sources, retaining the most relevant and reliable data; In the formula, iter represents the current iteration number, and the state of the information body at the i-th iteration is... The state of the information body at the (i+1)th iteration is θ is a random number between [0,1], used to characterize the influencing factors in the information collection process; and Two individuals were randomly selected at the beginning of the algorithm; S4-1-2. Information Filtering and Evaluation: The process of filtering and evaluating information is an important mechanism for individuals to quickly identify relevant and useful information. It is used to eliminate inaccurate and misleading information and improve the overall quality of information. Its formula can be expressed as: In the formula, For randomly selected individuals, rand is a random number generated in [0,1]; Δ is the error generated when subjective factors filter and evaluate information, defined as: Ξ=2*mod(3.468*v*(1-β)*(acos(γ*10 4 ))),1) (19) In the formula, Ξ represents the subjective influence factor, Γ is defined as the reliability factor, Max_iter is the maximum number of iterations, and the mathematical model of Γ consists of three main parts: a sine function, a logarithmic function, and the information quality factor Φ; mod is the modulo operation; v, β, a, and γ are all random numbers generated between [0,1], and the formula for the information quality factor Φ is: In the formula, δ is a random number generated between [0,1]; Φ is considered as a function of the iteration number iter; S4-1-3. Information Analysis and Organization: Information analysis and organization aim to identify existing useful information from filtered information and transform the convertible information identified in the previous stage into useful information. The formula is expressed as: In the formula, This represents the best information body generated in the previous iteration. The average value of the best information body generated in the previous iteration is represented by ε, ζ, κ, and ω, which are random numbers generated between [0,1]. Λ represents the control factors for analyzing and organizing information, defined as:

7. The UAV path planning method based on a multi-strategy fusion information acquisition optimization algorithm according to claim 6, characterized in that: Step S4-2 specifically includes the following: Hybrid initialization: By combining Latin hypercube sampling, Logistic chaotic mapping, and random initialization, an initial solution set is provided for the optimization algorithm. By dynamically adjusting the proportions of the three initialization methods, the initialization process is adaptively optimized according to the problem dimension and population size, resulting in: p LHS ＝0.4+0.3*α (24) p Logistic ＝0.3*(1-β) (25) p Rand =1-p LHS -p Logistic (26) In the formula, p LHS p Rand p LHS Here, α and β represent the probabilities of selecting Latin hypercube sampling, Logistic chaotic mapping, and random initialization, respectively; α and β are the probability parameters for selecting Latin hypercube sampling and Logistic chaotic mapping in the algorithm design; the number of individuals generated by each method is: n LHS =round(N LHS ) (27) n Logistic =round(N Logistic ) (28) n Rand =N-n LHS -n Logistic (29) In the formula, n LHS Choose the number of individuals for Latin hypercube sampling, n Logistic Choose the number of individuals in the Logistic chaotic mapping, n Rand We choose to randomly initialize the number of individuals, where `round` is the floor function, and `N` is the number of individuals in the algorithm design; by randomly shuffling the row order to avoid structural bias, we have: In the formula, X represents the new population formed by the mixture, and Shuffle represents the mixing of the three populations.

8. The UAV path planning method based on a multi-strategy fusion information acquisition optimization algorithm according to claim 7, characterized in that: Step S4-3 specifically includes the following: S4-3-1. Cross-sectional and cross-sectional strategy: Horizontal crossover promotes the spread of superior traits by reorganizing information among individuals within the current population, enhancing synergy at the same level and search space coverage, as shown in the following equation: In the formula, For the newly generated individual, x i Let x represent the position vector of the i-th individual in the current iteration. i-1 Let x represent the position vector of the (i-1)th individual in the current iteration. i+1 represents the position vector of the (i+1)th individual in the current iteration; r ~ U(0,1) is used as a fusion factor to adjust the weighting of feature information between two individuals; while c ~ U(-1,1) introduces a perturbation term to strengthen the differential mutation effect, thereby improving the individual's jumping ability and local search accuracy in the solution space; Vertical cross-fertilization, aimed at intergenerational information integration, typically involves coupling historical elite solutions or globally optimal solutions with the current population; as shown in the following equation: in, For new individuals generated by vertical intersection, For an individual in generation t, d1 and d2 represent two index positions randomly selected from all dimensions of the current individual; the fusion coefficient r1 ~ U(0,1) is used to adjust the recombination weight of the feature values ​​between these two dimensions; S4-3-2. Sinusoidal perturbation mechanism: The sinusoidal perturbation strategy is an adaptive mutation strategy guided by perturbations and inter-individual differences. It is an exploratory and adaptive search mechanism, represented as: X new (i,j)=X(i,j)+sin(r3*π)*(X(i,j)-X(a,j)),r4<K and r5<0.05 (33) In the formula, X new (i,j) represents the new individual generated by the sinusoidal perturbation, X(i,j) represents the individual before the strategy was implemented, t represents the current iteration number, T represents the maximum iteration number, and X(a,j) represents any particle in the particle cluster. As the algorithm progresses, collisions between particles become more frequent, so they are controlled by the collision probability K. r3, r4 and r5 are random values, ranging from [0,1].

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