Unmanned aerial vehicle three-dimensional path planning method based on polygene optimization chimpanzee algorithm

Abstract

The invention belongs to the technical field of three-dimensional unmanned aerial vehicle path planning, and particularly relates to an unmanned aerial vehicle three-dimensional path planning method based on a multi-gene optimization chimpanzee algorithm, which comprises the following steps: S1, initializing information of unmanned aerial vehicles and targets, and acquiring the positions and the number of initial unmanned aerial vehicles and the target point information of the unmanned aerial vehicles before distribution is started; and the position of the target is detected. The invention provides an unmanned aerial vehicle path planning method based on an improved chimpanzee algorithm by optimizing a traditional chimpanzee search algorithm and taking minimization of unmanned aerial vehicle path planning cost as an optimization target. The improved chimpanzee algorithm is fast in optimization speed, strong in capability and not easy to fall into local convergence, and can well deal with high-dimensional complex problems. By improving the chimpanzee algorithm, the multi-unmanned aerial vehicle path planning cost is reduced, and an ideal path planning scheme can be quickly found.

Description

Technical Field

[0001] The present invention relates to the technical field of three-dimensional unmanned aerial vehicle path planning, and in particular to a three-dimensional unmanned aerial vehicle path planning method based on a multi-gene optimized chimpanzee algorithm. Background Art

[0002] Solar drones, as an aircraft that relies on solar radiation energy for powered flight, effectively utilize solar energy by converting solar energy into electrical energy through solar panels. This type of drone can adjust its flight altitude according to demand through a control system. Due to the flexibility of its flight mode, solar drones are increasingly used in many fields such as meteorological reconnaissance, search and rescue assistance, fire detection and traffic control. Therefore, accurately planning the flight path of drones is of great significance for practical operations. The essence of path planning is to explore an optimal route from a starting point to a target point in the face of diversified mission constraints. However, in complex environments, airspace restrictions often require drones to fly at low altitudes, and most existing research is limited to smaller scales or simpler scenarios. In view of this, it is particularly important to develop path planning methods suitable for large-scale and complex environments. In these complex scenarios, wind is not only a potential energy source that helps increase the flight distance and speed of drones and shorten the arrival time, but its spatial uncertainty makes planning an effective path extremely complicated. Especially in a uniform and stable wind field environment, changes in wind speed further increase the difficulty of planning. The significant impact of wind fields on aircraft and the huge state space make path planning a computationally intensive challenge. This study not only focuses on minimizing flight costs, but also explores strategies that can be applied to other optimization criteria. In recent years, path planning issues have attracted widespread attention from researchers around the world, and exploration activities in related fields have increased. Studies have shown that optimization and innovation in path planning are necessary both under special environmental conditions and in complex mission requirements. By continuously improving and adapting new solution strategies and technologies, the accuracy and efficiency of path planning can be significantly improved. Especially in multi-UAV systems, it is particularly important to seek more stable and efficient path planning methods.

[0003] In order to improve the accuracy and efficiency of path planning and reduce costs, and to solve the problem of poor stability of the solution algorithm in the process of multi-UAV path planning, we proposed a UAV three-dimensional path planning method based on the multi-gene optimized chimpanzee algorithm to solve the above problems. Summary of the invention

[0004] 1. Technical issues to be resolved

[0005] In view of the deficiencies in the prior art, the present invention provides a three-dimensional path planning method for unmanned aerial vehicles based on a multi-gene optimized chimpanzee algorithm, which solves the problems raised in the above-mentioned background technology.

[0006] (II) Technical solution

[0007] In order to achieve the above-mentioned purpose, the present invention specifically adopts the following technical solutions:

[0008] A three-dimensional path planning method for unmanned aerial vehicles based on a multi-gene optimized chimpanzee algorithm comprises the following steps:

[0009] S1: Initialize the information of the drone and the target. Before the allocation starts, obtain the location and number of the initial drones, as well as the target point information of the drones, and detect the location of the target;

[0010] S2: The impact of complex uniform wind fields on the flight speed of UAVs is taken into account in the path planning scenario; a detailed analysis of the constraints affecting multiple UAVs in complex wind fields is conducted, and a multi-solar UAV path planning optimization function is constructed;

[0011] S3: Randomly generate multiple groups of initial UAV path planning solutions based on multi-gene segment coding;

[0012] S4: Calculate the path planning cost of each solution according to the fitness function;

[0013] S5: When t=1, the initial optimal path planning scheme is calculated according to the improved IMG-CHOA algorithm, and the position of the individual with the minimum path planning cost is determined as the optimal position

[0014] S6: Generate an iterative path planning scheme based on the improved IMG-CHOA algorithm to seek the optimal path planning scheme after the information changes;

[0015] S7: Perform reverse learning and Gauss-Cauchy mutation on the global optimal position, calculate the minimum path planning cost of the optimal solution after the updated position, compare it with the original position, and retain the better one; otherwise, discard the new path planning solution;

[0016] S8: Determine whether the current number of iterations reaches the preset number of iterations. If so, output the global optimal solution, that is, the minimum path planning cost and the corresponding path planning solution; otherwise, proceed to the next iteration.

[0017] Furthermore, in S1, U={U i ,i=1,2,…,N U} represents the set of multiple drones participating in the mission T = {T i ,i=1,2,…,N U} is the set of target points that these drones need to reach, and P = {P i ,i=1,2,…,N P} is the set of existing enemy threats. For a single drone, when it moves from the starting position (starting point S i ) to the destination (target point M i ) during its flight, it will successively pass through a series of waypoints to form a complete flight path. These track segments are connected in series according to the established flight rules to form a complete track from the starting point to the target point. Each track node (in W i-k (k=1,2,…,n-1) marks) are all key positions of the UAV in the mission execution, which requires precise planning to ensure safety and efficiency.

[0018] Furthermore, the construction of a multi-solar UAV path planning optimization function in S2 includes the following sub-steps:

[0019] Sub-step S2.1: Coordination constraints refer to a series of regulations that ensure that all members of the entire multi-UAV formation can complete the task smoothly and in a coordinated manner while ensuring that individual UAVs comply with their individual path constraints. This constraint involves adjusting the spatiotemporal relationship between UAVs in the formation to avoid mutual collisions, ensure mission efficiency, and optimize the flight path of the entire formation;

[0020] If the drone's flight altitude does not meet the specified minimum or maximum limits, its path planning can be adjusted by setting a penalty function to ensure that the drone remains at an appropriate flight altitude. The penalty functions are:

[0021]

[0022] Among them, H max The maximum flight altitude is H. min Minimum flight altitude allowed, Q i is the scale factor;

[0023] Spatial coordination constraints, also known as anti-collision constraints, are core requirements for ensuring that when multiple drones work together, the distance between them must exceed the preset minimum safe flight interval. This constraint ensures that each drone can safely maintain sufficient spatial separation when performing tasks to avoid collisions with each other, namely:

[0024] d i-j …d m (2)

[0025] Among them, marked as d i-j The variable represents the shortest distance between the track nodes of the i-th UAV and its j-th successor UAV in the flight sequence; and d m It specifically refers to the minimum safe flight interval that any two drones need to maintain;

[0026] In this study, the specified time for the drone to arrive at the destination is set as tu And through time coordination constraints, we can ensure the time synchronization of the UAV when performing tasks. According to the maximum and minimum speed limits of the UAV and the actual flight path length, we can calculate the estimated time interval for the UAV to reach the target location. In this way, the actual arrival time of the UAV needs to meet the following range:

[0027]

[0028] In this formula, the symbol v max With v min They represent the maximum and minimum flight speeds allowed, and L i It accurately reflects the total length of the actual navigation path of the i-th unmanned aerial vehicle (UAV);

[0029] In addition, the flight distance of the solar drone is limited by its energy reserve and flight time allocation, and has a maximum range parameter. The maximum track length is set to L. Therefore, the distance of each flight segment needs to meet the following conditions: The length of each flight segment does not exceed L. This constraint ensures that the drone can effectively complete the scheduled route under limited energy supply. Then the distance of each flight segment should meet:

[0030] ∑l i , ,L max (4)

[0031] According to the above conditions, the number of nodes in the drone's path planning is limited by its performance and cannot exceed a specific range. In addition, the cost of path planning also includes energy consumption. If the energy cost of a path is too high and exceeds the acceptable range, then this path will be considered infeasible. This setting ensures that the drone can effectively complete its mission within its energy limit.

[0032] The evaluation function of multi-UAV path planning expands the coordinated adjustment of multiple UAVs in time and space on the basis of the basic path planning function. In addition, it also includes the consideration of the threat cost that may be encountered in specific environments such as uniform wind fields. Therefore, the evaluation formula of multi-UAV path planning integrates these key factors, as follows:

[0033]

[0034] The formula f L-i , f H-i , f T-i , f m-i , f Z-i , f W-irepresents the energy consumption of the i-th unmanned aerial vehicle (UAV) under the path planning scheme, including flight altitude, time consumption, potential threats, collision risks, and additional threat costs caused by the wind field environment; parameter γ i Then they correspond to the trade-off coefficients of the above-mentioned various costs respectively, and G is the total number of UAVs participating in the mission;

[0035] Through the analysis of time coordination constraints, the time cost can be expressed as:

[0036]

[0037] Sub-step S2.2: Under the assumption that the wind field that the drone enters is uniform and stable, it is sufficient to use a kinematic model to describe its motion. The kinematics of steady-state straight-line flight includes the effect of thrust. However, it is subsequently extended to stable turning flight. Specifically, the kinematics of the drone is described as follows:

[0038]

[0039] where v w is the air speed, ε is the path angle when the aircraft is in a stable state entering the wind field, α is the heading angle of the UAV, and the forces parallel and perpendicular to the flight path are equal, and the equation is as follows:

[0040]

[0041] Where β is the sideslip angle of the drone entering the wind field, θ is the roll angle of the aircraft, and γ is the angle of incidence of the thrust vector with the flight path (note that if the thrust axis is aligned with the x-axis of the aircraft fuselage, then γ = 0, the angle of attack of the aircraft). Assuming γ = 0 (i.e., the thrust is aligned with the track angle, so that the thrust perpendicular to the flight path can be ignored), the equation is as follows:

[0042]

[0043] The lift coefficient is defined as: According to the above formula:

[0044]

[0045] The drag coefficient can be expressed as a polynomial function of the lift coefficient. This relationship reflects the dependence between lift and drag and provides an important basis for the analysis and design of flight dynamics.

[0046]

[0047] And through the formula According to the above formula, the aircraft path angle is

[0048] By combining the drag coefficient and the horizontal component of the vertical force on the flight path, the turn rate can be calculated. Based on these factors, the aircraft's kinematic equations are adjusted accordingly. This approach effectively combines the drag dynamics with the turn dynamics, providing a more accurate model for flight control and performance analysis. The aircraft kinematic equations become:

[0049]

[0050] Assume that V 0X V 0Y V 0Z is the velocity component of the UAV when it enters the wind field. The velocity change of the UAV when entering the wind field is

[0051]

[0052] Furthermore, in S3, this study effectively reduces the computational complexity of the path planning problem by adopting a multi-gene segment encoding method. This encoding method uses different gene segments to represent the paths of multiple unmanned aerial vehicles (UAVs), reduces the search operation amount and improves the optimization efficiency. In this model, if the formation consists of G UAVs, each gene segment will contain G gene segments. This strategy selects the gene segment with the lowest cost in each iteration of the algorithm, optimizes the processing speed of the algorithm by accumulating and storing track segments, and ensures the quality of the solution. In the gene segment encoding, not only the three-dimensional spatial positioning information of the track point is included, but also a state identifier p is specially added. i The key role of this identifier is to comprehensively record the various environmental constraints and state changes encountered by the drone during the execution of the track segment, especially the special constraints in complex operation scenarios. This coding method helps to systematically plan and optimize the paths of multi-UAV formations and ensure the efficiency and safety of coordinated flight.

[0053] Furthermore, in S4, this paper uses the objective function of the model as the fitness function:

[0054]

[0055] Further, the improved sparrow search algorithm in S5 includes the following sub-steps:

[0056] Sub-step S5.1: This study intends to develop a novel update strategy for the attacker, surround, and driver steps in the chimpanzee algorithm. This strategy can achieve adaptive and nonlinear adjustment of the parameter w according to the algorithm's iterative process t, that is, the number of iterations, in order to achieve better optimization results. In order to prevent the algorithm from falling into a local optimal solution, iteration thresholds t1 and t2 are introduced. In order to ensure that the algorithm has a strong global exploration efficiency at the initial stage, the inertia weight needs to be maintained at a high level. For this reason, this study uses the cosine function as the strategy model for dynamic adaptation of the inertia weight, and finely adjusts the weight value through nonlinear changes. The specific mathematical expression is as follows:

[0057] In the above expression, w max Represent the upper limit of inertia weight, w min Symbolizes its lower limit, T max Indicates the maximum number of algorithm iterations. In addition, this study also conceived a quadratic polynomial function. When t∈(t1, t2) satisfies the conditions, by increasing the value of w, the algorithm's global search potential can be significantly enhanced, effectively preventing it from converging to a suboptimal solution prematurely, and ensuring the comprehensiveness and effectiveness of the search process: w(t)=2A1t 2 +A2t+2A3, A is a constant, and the w(t) function passes through the point (t1,w(t1)), ((t1+t2) / 2,w max ),(t2,w(t1)), so we can get the values ​​of A1A2A3 respectively:

[0058]

[0059] The quadratic function is:

[0060]

[0061] In this expression, the inertia weight w(t1) is the value at a specific time point t1 and is calculated according to formula (15). The parameters t1 and t2 allow their values ​​to be determined according to human fine-tuning of specific instances. Based on the in-depth analysis of a wide range of experimental data sets, the studied algorithm achieves a stable convergence state when the number of iterations exceeds 240. In order to prevent the algorithm from locking into a local minimum prematurely, we set the values ​​of t1 and t2 to 3·T respectively. max / 10 and 5·T max / 10, so for this situation, formula (19) is changed to:

[0062]

[0063] In summary, the adaptive inertia weight adjustment strategy with the addition of the hyperbolic tangent function is:

[0064]

[0065] The update formula for attackers, besiegers, and expellers becomes:

[0066] X1=w·X a -A1·|C1·X a -m1·X| (22)

[0067] X2=w·X b -A2·|C2·X b -m2·X| (23)

[0068] X3=w·X c -A3·|C3·X c -m3·X| (24)

[0069] Where: X a , X b , X c Respectively represent the position vectors of the attacker, the besieger, and the expeller, A is a random vector; m is a chaotic mapping vector, and C is a random number between [0, 2];

[0070] Sub-step S5.2: To prevent the algorithm from falling into the local optimum, this study optimizes the chaser search step in the chimpanzee algorithm, uses random particles for selection, and applies fusion refraction and symbiosis and mutual benefit to the particle position. The strategy based on convex lens imaging can be obtained from formula (25):

[0071]

[0072] In the symbiotic search algorithm, mutually beneficial operation is one of the components of the symbiotic search algorithm. j is a randomly selected individual from the population, represented by X i and X j , mutually beneficial operations produce new individuals:

[0073]

[0074] In this study, the chimpanzee chaser step is integrated into the refraction reverse learning symbiotic algorithm, and the mutually beneficial operations in the symbiotic algorithm are integrated according to the reverse position of the optimal position in the refraction reverse learning, and then the individuals are updated:

[0075]

[0076] The particle update formula of the chimpanzee algorithm is:

[0077]

[0078] Furthermore, in S7, in order to enable individuals to better find the optimal solution, the reverse learning strategy is integrated into the algorithm, and the mathematical representation is as follows: In order to enable individuals to approach the optimal solution more efficiently, we have taken the innovative measure of embedding the reverse learning strategy into the chimpanzee social optimization algorithm, and its mathematical model can be expressed as:

[0079]

[0080] X b ' est (t) indicates the inverse solution corresponding to the current optimal solution when evolving to the tth generation. The variables ub and lb respectively indicate the upper and lower limits of the solution space, while r is a random number matrix that follows the standard uniform distribution law in the (0,1) interval. The parameter b1 is assigned the role of the information exchange regulation factor:

[0081]

[0082] This study proposes a Cauchy-Gaussian mutation mechanism, which can make good use of the advantages of the two distributions. The Cauchy mutation mechanism is used in the early stage of algorithm iteration, and the Gaussian mutation mechanism is used in the later stage of algorithm iteration. It can take into account the different mutation range requirements of different search stages of the algorithm. The mathematical definition of the Cauchy-Gaussian mutation mechanism is shown in the formula:

[0083]

[0084] represents the position of the optimal individual after mutation; Cauchy(x0,γ) and Gauss(μ,σ 2 ) are two random variables that follow the Cauchy distribution and Gaussian distribution. In order to significantly enhance the optimization performance of the algorithm, this paper adopts a flexible dynamic decision-making mechanism to innovate target positioning, that is, under the control of the preset probability, periodically switching between the reverse learning strategy and the Cauchy mutation operator perturbation mechanism to dynamically optimize the target position. Specifically, the target position update strategy depends on the selection probability P. s The quantitative expression of this probability parameter follows the following formula:

[0085]

[0086] In the above expression, Σ is used as the adjustment factor, and its recommended setting value is 0.05. The specific selection process is as follows: When the random number rand is less than P s , the algorithm will enable the reverse learning mechanism to update the position; otherwise, if rand is greater than or equal to P s, then the Cauchy-Gaussian mixture mutation perturbation strategy is selected to update the target position. After the position undergoes perturbation mutation, we further introduce the greedy criterion to compare the fitness evaluation of the new and old positions to determine whether it is necessary to perform position update. The implementation method of the greedy criterion follows the following formula:

[0087]

[0088] (III) Beneficial effects

[0089] Compared with the prior art, the present invention provides a method for three-dimensional path planning of unmanned aerial vehicles based on a multi-gene optimized chimpanzee algorithm, which has the following beneficial effects:

[0090] The present invention optimizes the traditional chimpanzee search algorithm, takes minimizing the cost of UAV path planning as the optimization goal, and proposes a UAV path planning method based on the improved chimpanzee algorithm. The improved chimpanzee algorithm has fast optimization speed, strong ability and is not easy to fall into local convergence, and can deal with high-dimensional complex problems well. By improving the chimpanzee algorithm, the cost of multi-UAV path planning is reduced, and the ideal path planning solution can be quickly found. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] Figure 1 This is a flow chart of the UAV path planning algorithm of the present invention;

[0092] Figure 2 It is the coding map of the multi-gene segment of the present invention;

[0093] Figure 3 This is the GWO algorithm UAV path planning diagram of the present invention;

[0094] Figure 4 This is the path planning diagram of the drone using the CHOA algorithm of the present invention;

[0095] Figure 5 The MCHOA algorithm UAV path planning diagram of the present invention;

[0096] Figure 6 This is the UAV path planning diagram of the IMG-CHOA algorithm of the present invention;

[0097] Figure 7 This is a comparison chart of performance indicators of different algorithms of the present invention;

[0098] Figure 8 This is a comparison chart of the energy cost and time cost of drones with different algorithms in the present invention.

[0099] Fig. 9 is the fitness difference of the last 60 iterations of the present invention;

[0100] Fig.10This is a force model diagram of the UAV wind field of the present invention. DETAILED DESCRIPTION

[0101] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0102] Example

[0103] like Figure 1-10 As shown, an embodiment of the present invention proposes a method for three-dimensional path planning of a UAV based on a multi-gene optimized chimpanzee algorithm, comprising the following steps:

[0104] S1: Initialize the information of the drone and the target. Before the allocation starts, obtain the location and number of the initial drones, as well as the target point information of the drones, and detect the location of the target;

[0105] S2: The impact of complex uniform wind fields on the flight speed of UAVs is taken into account in the path planning scenario; a detailed analysis of the constraints affecting multiple UAVs in complex wind fields is conducted, and a multi-solar UAV path planning optimization function is constructed;

[0106] S3: Randomly generate multiple groups of initial UAV path planning solutions based on multi-gene segment coding;

[0107] S4: Calculate the path planning cost of each solution according to the fitness function;

[0108] S5: When t=1, the initial optimal path planning scheme is calculated according to the improved IMG-CHOA algorithm, and the position of the individual with the minimum path planning cost is determined as the optimal position

[0109] S6: Generate an iterative path planning scheme based on the improved IMG-CHOA algorithm to seek the optimal path planning scheme after the information changes;

[0110] S7: Perform reverse learning and Gauss-Cauchy mutation on the global optimal position, calculate the minimum path planning cost of the optimal solution after the updated position, compare it with the original position, and retain the better one; otherwise, discard the new path planning solution;

[0111] S8: Determine whether the current number of iterations reaches the preset number of iterations. If so, output the global optimal solution, that is, the minimum path planning cost and the corresponding path planning solution; otherwise, proceed to the next iteration.

[0112] In this embodiment, in S1, U={U i ,i=1,2,…,N U} represents the set of multiple drones participating in the mission T = {T i ,i=1,2,…,N U} is the set of target points that these drones need to reach, and P = {P i ,i=1,2,…,N P} is the set of existing enemy threats. For a single drone, when it moves from the starting position (starting point S i ) to the destination (target point M i ) during its flight, it will successively pass through a series of waypoints to form a complete flight path. These track segments are connected in series according to the established flight rules to form a complete track from the starting point to the target point. Each track node (in W i-k (k=1,2,…,n-1) marks) are all key positions of the drone in the mission execution, which requires precise planning to ensure safety and efficiency.

[0113] In this embodiment, the construction of a multi-solar UAV path planning optimization function in S2 includes the following sub-steps:

[0114] Sub-step S2.1: Coordination constraints refer to a series of regulations that ensure that all members of the entire multi-UAV formation can complete the task smoothly and in a coordinated manner while ensuring that individual UAVs comply with their individual path constraints. This constraint involves adjusting the spatiotemporal relationship between UAVs in the formation to avoid mutual collisions, ensure mission efficiency, and optimize the flight path of the entire formation;

[0115] If the drone's flight altitude does not meet the specified minimum or maximum limits, its path planning can be adjusted by setting a penalty function to ensure that the drone remains at an appropriate flight altitude. The penalty functions are:

[0116]

[0117] Among them, H max The maximum flight altitude is H. min Minimum flight altitude allowed, Q i is the scale factor;

[0118] Spatial coordination constraints, also known as anti-collision constraints, are core requirements for ensuring that when multiple drones work together, the distance between them must exceed the preset minimum safe flight interval. This constraint ensures that each drone can safely maintain sufficient spatial separation when performing tasks to avoid collisions with each other, namely:

[0119] d i-j ...d m(2)

[0120] Among them, marked as d i-j The variable represents the shortest distance between the track nodes of the i-th UAV and its j-th successor UAV in the flight sequence; and d m It specifically refers to the minimum safe flight interval that any two drones need to maintain;

[0121] In this study, the specified time for the drone to arrive at the destination is set as t u And through time coordination constraints, we can ensure the time synchronization of the UAV when performing tasks. According to the maximum and minimum speed limits of the UAV and the actual flight path length, we can calculate the estimated time interval for the UAV to reach the target location. In this way, the actual arrival time of the UAV needs to meet the following range:

[0122]

[0123] In this formula, the symbol v max With v min They represent the maximum and minimum flight speeds allowed, and L i It accurately reflects the total length of the actual navigation path of the i-th unmanned aerial vehicle (UAV);

[0124] In addition, the flight distance of the solar drone is limited by its energy reserve and flight time allocation, and has a maximum range parameter. The maximum track length is set to L. Therefore, the distance of each flight segment needs to meet the following conditions: The length of each flight segment does not exceed L. This constraint ensures that the drone can effectively complete the scheduled route under limited energy supply. Then the distance of each flight segment should meet:

[0125] ∑l i , ,L max (4)

[0126] According to the above conditions, the number of nodes in the drone's path planning is limited by its performance and cannot exceed a specific range. In addition, the cost of path planning also includes energy consumption. If the energy cost of a path is too high and exceeds the acceptable range, then this path will be considered infeasible. This setting ensures that the drone can effectively complete its mission within its energy limit.

[0127] The evaluation function of multi-UAV path planning expands the coordinated adjustment of multiple UAVs in time and space on the basis of the basic path planning function. In addition, it also includes the consideration of the threat cost that may be encountered in specific environments such as uniform wind fields. Therefore, the evaluation formula of multi-UAV path planning integrates these key factors, as follows:

[0128]

[0129] The formula f L-i , f H-i , f T-i , f m-i , f Z-i , f W-i represents the energy consumption of the i-th unmanned aerial vehicle (UAV) under the path planning scheme, including flight altitude, time consumption, potential threats, collision risks, and additional threat costs caused by the wind field environment; parameter γ i Then they correspond to the trade-off coefficients of the above-mentioned various costs respectively, and G is the total number of UAVs participating in the mission;

[0130] Through the analysis of time coordination constraints, the time cost can be expressed as:

[0131]

[0132] Sub-step S2.2: Under the assumption that the wind field that the drone enters is uniform and stable, it is sufficient to use a kinematic model to describe its motion. The kinematics of steady-state straight-line flight includes the effect of thrust. However, it is subsequently extended to stable turning flight. Specifically, the kinematics of the drone is described as follows:

[0133]

[0134] where v w is the air speed, ε is the path angle when the aircraft is in a stable state entering the wind field, α is the heading angle of the UAV, and the forces parallel and perpendicular to the flight path are equal, and the equation is as follows:

[0135]

[0136] Where β is the sideslip angle of the drone entering the wind field, θ is the roll angle of the aircraft, and γ is the angle of incidence of the thrust vector with the flight path (note that if the thrust axis is aligned with the x-axis of the aircraft fuselage, then γ = 0, the angle of attack of the aircraft). Assuming γ = 0 (i.e., the thrust is aligned with the track angle, so that the thrust perpendicular to the flight path can be ignored), the equation is as follows:

[0137]

[0138] The lift coefficient is defined as: According to the above formula:

[0139]

[0140] The drag coefficient can be expressed as a polynomial function of the lift coefficient. This relationship reflects the dependence between lift and drag and provides an important basis for the analysis and design of flight dynamics.

[0141]

[0142] And through the formula According to the above formula, the aircraft path angle is

[0143]

[0144] By combining the drag coefficient and the horizontal component of the vertical force on the flight path, the turn rate can be calculated. Based on these factors, the aircraft's kinematic equations are adjusted accordingly. This approach effectively combines the drag dynamics with the turn dynamics, providing a more accurate model for flight control and performance analysis. The aircraft kinematic equations become:

[0145]

[0146] Assume that V 0X V 0Y V 0Z is the velocity component of the UAV when it enters the wind field. The velocity change of the UAV when entering the wind field is

[0147]

[0148] In this embodiment, in S3, this study effectively reduces the computational complexity of the path planning problem by adopting a multi-gene segment encoding method. This encoding method uses different gene segments to represent the paths of multiple unmanned aerial vehicles (UAVs), reduces the search operation amount and improves the optimization efficiency. In this model, if the formation consists of G UAVs, each gene segment will contain G gene segments. This strategy selects the gene segment with the lowest cost in each iteration of the algorithm, optimizes the processing speed of the algorithm by accumulating and storing track segments, and ensures the quality of understanding. In the gene segment encoding, not only the three-dimensional spatial positioning information of the track point is included, but also a state identifier p is specially added. i The key role of this identifier is to comprehensively record the various environmental constraints and state changes encountered by the drone during the execution of the track segment, especially the special constraints in complex operation scenarios. This coding method helps to systematically plan and optimize the paths of multi-UAV formations and ensure the efficiency and safety of coordinated flight.

[0149] In this embodiment, in S4, the objective function of the model is used as the fitness function:

[0150]

[0151] In this embodiment, the improved sparrow search algorithm in S5 includes the following sub-steps:

[0152] Sub-step S5.1: This study intends to develop a novel update strategy for the attacker, surround, and driver steps in the chimpanzee algorithm. This strategy can achieve adaptive and nonlinear adjustment of the parameter w according to the algorithm's iterative process t, that is, the number of iterations, in order to achieve better optimization results. In order to prevent the algorithm from falling into a local optimal solution, iteration thresholds t1 and t2 are introduced. In order to ensure that the algorithm has a strong global exploration efficiency at the initial stage, the inertia weight needs to be maintained at a high level. For this reason, this study uses the cosine function as the strategy model for dynamic adaptation of the inertia weight, and finely adjusts the weight value through nonlinear changes. The specific mathematical expression is as follows:

[0153] In the above expression, w max Represent the upper limit of inertia weight, w min Symbolizes its lower limit, T max Indicates the maximum number of algorithm iterations. In addition, this study also conceived a quadratic polynomial function. When t∈(t1, t2) satisfies the conditions, by increasing the value of w, the algorithm's global search potential can be significantly enhanced, effectively preventing it from converging to a suboptimal solution prematurely, and ensuring the comprehensiveness and effectiveness of the search process: w(t)=2A1t 2 +A2t+2A3, A is a constant, and the w(t) function passes through the point (t1,w(t1)), ((t1+t2) / 2,w max ),(t2,w(t1)), so we can get the values ​​of A1A2A3 respectively:

[0154]

[0155] The quadratic function is:

[0156]

[0157] In this expression, the inertia weight w(t1) is the value at a specific time point t1 and is calculated according to formula (15). The parameters t1 and t2 allow their values ​​to be determined according to human fine-tuning of specific instances. Based on the in-depth analysis of a wide range of experimental data sets, the studied algorithm achieves a stable convergence state when the number of iterations exceeds 240. In order to prevent the algorithm from locking into a local minimum prematurely, we set the values ​​of t1 and t2 to 3·T respectively. max / 10 and 5·T max / 10, so for this situation, formula (19) is changed to:

[0158]

[0159] In summary, the adaptive inertia weight adjustment strategy with the addition of the hyperbolic tangent function is:

[0160]

[0161] The update formula for attackers, besiegers, and expellers becomes:

[0162] X1=w·X a -A1·|C1·X a -m1·X| (22)

[0163] X2=w·X b -A2·|C2·X b -m2·X| (23)

[0164] X3=w·X c -A3·|C3·X c -m3·X| (24)

[0165] Where: X a , X b , X c Respectively represent the position vectors of the attacker, the besieger, and the expeller, A is a random vector; m is a chaotic mapping vector, and C is a random number between [0, 2];

[0166] Sub-step S5.2: To prevent the algorithm from falling into the local optimum, this study optimizes the chaser search step in the chimpanzee algorithm, uses random particles for selection, and applies fusion refraction and symbiosis and mutual benefit to the particle position. The strategy based on convex lens imaging can be obtained from formula (25):

[0167]

[0168] In the symbiotic search algorithm, mutually beneficial operation is one of the components of the symbiotic search algorithm. j is a randomly selected individual from the population, represented by X i and X j , mutually beneficial operations produce new individuals:

[0169]

[0170] In this study, the chimpanzee chaser step is integrated into the refraction reverse learning symbiotic algorithm, and the mutually beneficial operations in the symbiotic algorithm are integrated according to the reverse position of the optimal position in the refraction reverse learning, and then the individuals are updated:

[0171]

[0172] The particle update formula of the chimpanzee algorithm is:

[0173]

[0174] In this embodiment, in S7, in order to enable individuals to better find the optimal solution, the reverse learning strategy is integrated into the algorithm, and the mathematical representation is as follows: In order to enable individuals to approach the optimal solution more efficiently, we have taken the innovative measure of embedding the reverse learning strategy into the chimpanzee social optimization algorithm, and its mathematical model can be expressed as:

[0175]

[0176] X b ' est (t) indicates the inverse solution corresponding to the current optimal solution when evolving to the tth generation. The variables ub and lb respectively indicate the upper and lower limits of the solution space, while r is a random number matrix that follows the standard uniform distribution law in the (0,1) interval. The parameter b1 is assigned the role of the information exchange regulation factor:

[0177]

[0178] This study proposes a Cauchy-Gaussian mutation mechanism, which can make good use of the advantages of the two distributions. The Cauchy mutation mechanism is used in the early stage of algorithm iteration, and the Gaussian mutation mechanism is used in the later stage of algorithm iteration. It can take into account the different mutation range requirements of different search stages of the algorithm. The mathematical definition of the Cauchy-Gaussian mutation mechanism is shown in the formula:

[0179]

[0180] represents the position of the optimal individual after mutation; Cauchy(x0,γ) and Gauss(μ,σ 2 ) are two random variables that follow the Cauchy distribution and Gaussian distribution. In order to significantly enhance the optimization performance of the algorithm, this paper adopts a flexible dynamic decision-making mechanism to innovate target positioning, that is, under the control of the preset probability, periodically switching between the reverse learning strategy and the Cauchy mutation operator perturbation mechanism to dynamically optimize the target position. Specifically, the target position update strategy depends on the selection probability P. s The quantitative expression of this probability parameter follows the following formula:

[0181]

[0182] In the above expression, Σ is used as the adjustment factor, and its recommended setting value is 0.05. The specific selection process is as follows: When the random number rand is less than P s , the algorithm will enable the reverse learning mechanism to update the position; otherwise, if rand is greater than or equal to P s, then the Cauchy-Gaussian mixture mutation perturbation strategy is selected to update the target position. After the position undergoes perturbation mutation, we further introduce the greedy criterion to compare the fitness evaluation of the new and old positions to determine whether it is necessary to perform position update. The implementation method of the greedy criterion follows the following formula:

[0183]

[0184] In the simulation experiment, an air formation consisting of four unmanned aerial vehicles corresponds to four designated target objects distributed on the ground. This experiment stipulates that the maximum total path length of the drone shall not exceed 1.5 times the straight-line distance from the starting point to the target point, and the minimum path segment length is set to 2 kilometers. The maximum flight altitude of the drone is 100 kilometers, the maximum turning angle is 60 degrees, and the maximum climb / dive angle is also 60 degrees. The scheduled target arrival time of the drone is set to 6900 seconds. In addition, the population size of the algorithm is set to 60, and the number of iterations is 300. For the IMG-CHOA algorithm used in this study, considering that path planning requires the integration of six evaluation indicators, the number of cost indicators for storing gene segments is set to 6. As for the wind field threat area, clockwise and counterclockwise wind fields were used in the experiment to interfere with the flight of the drone.

[0185] Figures 3 to 6 The image shows the search process of four unmanned aerial vehicles (UAVs) in three-dimensional space using path planning performed by different algorithms in a complex wind environment. In the figure, the blue area represents the minefield threat area, and the black area represents the strong wind area. From the image analysis, it can be seen that the four UAVs under the guidance of the improved algorithms IMG-CHOA and MCHOA successfully avoided the minefield threat area and successfully reached the target destination. In particular, the algorithm IMG-CHOA guided the UAV to choose a path through the clockwise wind field. In contrast, the four UAVs controlled by the basic algorithms CHOA and GWO failed to effectively avoid the minefield threat area.

[0186] Figure 7 The average performance indicators of different algorithms in the scene are compared, and it can be seen that the algorithm IMG-CHOA has the advantage in multi-UAV path planning. Figure 8The energy cost and time cost of path planning by different algorithms in a complex wind field environment are shown. In particular, the IMG-CHOA algorithm selects a path through a stable and unchanging clockwise wind field. The analysis shows that the path selection of the IMG-CHOA algorithm optimizes the flight speed and arrival time of the UAV positively, thereby reducing the time coordination cost in path planning to zero, while not significantly increasing the fuel cost. Therefore, the total cost is significantly reduced. Compared with other algorithms, the IMG-CHOA algorithm shows significant advantages in both fuel cost and time cost. This shows that choosing a suitable wind field path is crucial to optimizing the trajectory planning of the UAV, which can not only save costs but also improve the efficiency of task execution.

[0187] like Fig. 9 It reveals an optimization trajectory that depicts the evolution of the evaluation function as the iteration progresses. From this curve, we can clearly observe a progressive optimization process: in regular iterations, the overall cost overhead shows a continuous downward trend with the accumulation of iteration rounds, and finally converges to an equilibrium state. This dynamic transformation strongly proves the practical value and high efficiency of the IMG-CHOA algorithm in the field of path planning. It shows a comparison chart of the fitness difference of each algorithm relative to the basic algorithm GWO in the last 60 iterations. From Fig. 9 The data shows that the IMG-CHOA algorithm reduces the cost by 27% compared to the GWO algorithm, 20% compared to the CHOA algorithm, and 17% compared to the MCHOA algorithm when dealing with collaborative path planning of multiple drones in complex scenarios. These data highlight the significant advantages of the IMG-CHOA algorithm in reducing the total cost of multi-drone path planning, especially in complex environments. This cost optimization not only improves the economic benefits of the algorithm, but also enhances its practicality and feasibility.

[0188] Experiments have shown that the IMG-CHOA optimization algorithm has significant advantages in dealing with multi-modal optimization challenges. Its flexibility is sufficient to adapt to the needs of route calculation in various environmental backgrounds, thereby achieving efficient and accurate path planning. Nevertheless, current research still has limitations in comprehensively considering the complex influencing factors of multi-UAV collaborative operations. In order to further meet the application requirements of the real world, subsequent work will be committed to deepening model optimization and enhancing its applicability and robustness in actual scenarios.

[0189] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein by equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A three-dimensional path planning method for unmanned aerial vehicles based on a multi-gene optimized chimpanzee algorithm, characterized in that: The following steps are involved: S1: Initialize the information of the drone and the target. Before the allocation starts, obtain the location and number of the initial drones, as well as the target point information of the drones, and detect the location of the target; S2: The impact of complex uniform wind fields on the flight speed of UAVs is taken into account in the path planning scenario; a detailed analysis of the constraints affecting multiple UAVs in complex wind fields is conducted, and a multi-solar UAV path planning optimization function is constructed; S3: Randomly generate multiple groups of initial UAV path planning solutions based on multi-gene segment coding; S4: Calculate the path planning cost of each solution according to the fitness function; S5: When t=1, the initial optimal path planning scheme is calculated according to the improved IMG-CHOA algorithm, and the position of the individual with the minimum path planning cost is determined as the optimal position S6: Generate an iterative path planning scheme based on the improved IMG-CHOA algorithm to seek the optimal path planning scheme after the information changes; S7: Perform reverse learning and Gauss-Cauchy mutation on the global optimal position, calculate the minimum path planning cost of the optimal solution after the updated position, compare it with the original position, and retain the better one; otherwise, discard the new path planning solution; S8: Determine whether the current number of iterations reaches the preset number of iterations. If so, output the global optimal solution, that is, the minimum path planning cost and the corresponding path planning solution; otherwise, proceed to the next iteration.

2. The method for three-dimensional path planning of unmanned aerial vehicle based on multi-gene optimized chimpanzee algorithm according to claim 1, characterized in that: In S1, let U = {U i ,i=1,2,…,N U } represents the set of multiple drones participating in the mission T = {T i ,i=1,2,…,N U } is the set of target points that these drones need to reach, and P = {P i ,i=1,2,…,N P } is the set of existing enemy threats. For a single drone, when it moves from the starting position (starting point S i ) to the destination (target point M i ) during its flight, it will successively pass through a series of waypoints to form a complete flight path. These track segments are connected in series according to the established flight rules to form a complete track from the starting point to the target point. Each track node (in W i-k (k=1,2,…,n-1) marks) are all key positions of the drone in the mission execution, which requires precise planning to ensure safety and efficiency.

3. The method for three-dimensional path planning of unmanned aerial vehicle based on multi-gene optimized chimpanzee algorithm according to claim 2, characterized in that: The S2 constructs a multi-solar UAV path planning optimization function including the following sub-steps: Sub-step S2.1: Coordination constraints refer to a series of regulations that ensure that all members of the entire multi-UAV formation can complete the task smoothly and in a coordinated manner while ensuring that individual UAVs comply with their individual path constraints. This constraint involves adjusting the spatiotemporal relationship between UAVs in the formation to avoid mutual collisions, ensure mission efficiency, and optimize the flight path of the entire formation; If the drone's flight altitude does not meet the specified minimum or maximum limits, its path planning can be adjusted by setting a penalty function to ensure that the drone remains at an appropriate flight altitude. The penalty functions are: Among them, H max The maximum flight altitude is H. min Minimum flight altitude allowed, Q i is the scale factor; Spatial coordination constraints, also known as anti-collision constraints, are core requirements for ensuring that when multiple drones work together, the distance between them must exceed the preset minimum safe flight interval. This constraint ensures that each drone can safely maintain sufficient spatial separation when performing tasks to avoid collisions with each other, namely: d i-j …d m (2) Among them, marked as d i-j The variable represents the shortest distance between the track nodes of the i-th UAV and its j-th successor UAV in the flight sequence; and d m It specifically refers to the minimum safe flight interval that any two drones need to maintain; In this study, the specified time for the drone to arrive at the destination is set as t u And through time coordination constraints, we can ensure the time synchronization of the UAV when performing tasks. According to the maximum and minimum speed limits of the UAV and the actual flight path length, we can calculate the estimated time interval for the UAV to reach the target location. In this way, the actual arrival time of the UAV needs to meet the following range: In this formula, the symbol v max With v min They represent the maximum and minimum flight speeds allowed, and L i It accurately reflects the total length of the actual navigation path of the i-th unmanned aerial vehicle (UAV); In addition, the flight distance of the solar drone is limited by its energy reserve and flight time allocation, and has a maximum range parameter. The maximum track length is set to L. Therefore, the distance of each flight segment needs to meet the following conditions: The length of each flight segment does not exceed L. This constraint ensures that the drone can effectively complete the scheduled route under limited energy supply. Then the distance of each flight segment should meet: ∑l i ，，L max (4) According to the above conditions, the number of nodes in the drone's path planning is limited by its performance and cannot exceed a specific range. In addition, the cost of path planning also includes energy consumption. If the energy cost of a path is too high and exceeds the acceptable range, then this path will be considered infeasible. This setting ensures that the drone can effectively complete its mission within its energy limit. The evaluation function of multi-UAV path planning expands the coordinated adjustment of multiple UAVs in time and space on the basis of the basic path planning function. In addition, it also includes the consideration of the threat cost that may be encountered in specific environments such as uniform wind fields. Therefore, the evaluation formula of multi-UAV path planning integrates these key factors, as follows: The formula f L-i , f H-i , f T-i , f m-i , f Z-i , f W-i represents the energy consumption of the i-th unmanned aerial vehicle (UAV) under the path planning scheme, including flight altitude, time consumption, potential threats, collision risks, and additional threat costs caused by the wind field environment; the parameter γi corresponds to the trade-off coefficient of the above-mentioned various costs, and G is the total number of UAVs participating in the mission; Through the analysis of time coordination constraints, the time cost can be expressed as: Sub-step S2.2: Under the assumption that the wind field that the drone enters is uniform and stable, it is sufficient to use a kinematic model to describe its motion. The kinematics of steady-state straight-line flight includes the effect of thrust. However, it is subsequently extended to stable turning flight. Specifically, the kinematics of the drone is described as follows: where v w is the air speed, ε is the path angle when the aircraft is in a stable state entering the wind field, α is the heading angle of the UAV, and the forces parallel and perpendicular to the flight path are equal, and the equation is as follows: Where β is the sideslip angle of the drone entering the wind field, θ is the roll angle of the aircraft, and γ is the angle of incidence of the thrust vector with the flight path (note that if the thrust axis is aligned with the x-axis of the aircraft fuselage, then γ = 0, the angle of attack of the aircraft). Assuming γ = 0 (i.e., the thrust is aligned with the track angle, so that the thrust perpendicular to the flight path can be ignored), the equation is as follows: The lift coefficient is defined as: According to the above formula: The drag coefficient can be expressed as a polynomial function of the lift coefficient. This relationship reflects the dependence between lift and drag and provides an important basis for the analysis and design of flight dynamics. And through the formula According to the above formula, the aircraft path angle is By combining the drag coefficient and the horizontal component of the vertical force on the flight path, the turn rate can be calculated. Based on these factors, the aircraft's kinematic equations are adjusted accordingly. This approach effectively combines the drag dynamics with the turn dynamics, providing a more accurate model for flight control and performance analysis. The aircraft kinematic equations become: Assume that V 0X V 0Y V 0Z is the velocity component of the UAV when it enters the wind field. The velocity change of the UAV when entering the wind field is 4. The method for three-dimensional path planning of unmanned aerial vehicle based on multi-gene optimized chimpanzee algorithm according to claim 3 is characterized in that: In the S3, this study effectively reduces the computational complexity of the path planning problem by adopting a multi-gene segment encoding method. This encoding method uses different gene segments to represent the paths of multiple unmanned aerial vehicles (UAVs), reduces the search operation amount and improves the optimization efficiency. In this model, if the formation consists of G UAVs, each gene segment will contain G gene segments. This strategy selects the gene segment with the lowest cost in each iteration of the algorithm, optimizes the processing speed of the algorithm by accumulating and storing track segments, and ensures the quality of the solution. In the gene segment encoding, not only the three-dimensional spatial positioning information of the track point is included, but also a state identifier p is specially added. i The key role of this identifier is to comprehensively record the various environmental constraints and state changes encountered by the drone during the execution of the track segment, especially the special constraints in complex operation scenarios. This coding method helps to systematically plan and optimize the paths of multi-UAV formations and ensure the efficiency and safety of coordinated flight.

5. The method for three-dimensional path planning of unmanned aerial vehicle based on multi-gene optimized chimpanzee algorithm according to claim 4 is characterized in that: In S4, this paper uses the objective function of the model as the fitness function:

6. The method for three-dimensional path planning of unmanned aerial vehicle based on multi-gene optimized chimpanzee algorithm according to claim 5, characterized in that: The improved sparrow search algorithm in S5 comprises the following sub-steps: Sub-step S5.1: This study intends to develop a novel update strategy for the attacker, surround, and driver steps in the chimpanzee algorithm. This strategy can achieve adaptive and nonlinear adjustment of the parameter w according to the algorithm's iterative process t, that is, the number of iterations, in order to achieve better optimization results. In order to prevent the algorithm from falling into a local optimal solution, iteration thresholds t1 and t2 are introduced. In order to ensure that the algorithm has a strong global exploration efficiency at the initial stage, the inertia weight needs to be maintained at a high level. For this reason, this study uses the cosine function as the strategy model for dynamic adaptation of the inertia weight, and finely adjusts the weight value through nonlinear changes. The specific mathematical expression is as follows: In the above expression, w max Represent the upper limit of inertia weight, w min Symbolizes its lower limit, T max Indicates the maximum number of algorithm iterations. In addition, this study also conceived a quadratic polynomial function. When t∈(t1, t2) satisfies the conditions, by increasing the value of w, the algorithm's global search potential can be significantly enhanced, effectively preventing it from converging to a suboptimal solution prematurely, and ensuring the comprehensiveness and effectiveness of the search process: w(t)=2A1t 2 +A2t+2A3, A is a constant, and the w(t) function passes through the point (t1,w(t1)), ((t1+t2) / 2,w max ),(t2,w(t1)), so we can get the values ​​of A1A2A3 respectively: The quadratic function is: In this expression, the inertia weight w(t1) is the value at a specific time point t1 and is calculated according to formula (15). The parameters t1 and t2 allow their values ​​to be determined according to human fine-tuning of specific instances. Based on the in-depth analysis of a wide range of experimental data sets, the studied algorithm achieves a stable convergence state when the number of iterations exceeds 240. In order to prevent the algorithm from locking into a local minimum prematurely, we set the values ​​of t1 and t2 to 3·T respectively. max / 10 and 5·T max / 10, so for this situation, formula (19) is changed to: In summary, the adaptive inertia weight adjustment strategy with the addition of the hyperbolic tangent function is: The update formula for attackers, besiegers, and expellers becomes: X1=w·X a -A1·|C1·X a -m1·X| (22) X2=w·X b -A2·|C2·X b -m2·X| (23) X3=w·X c -A3·|C3·X c -m3·X| (24) Where: X a , X b , X c Respectively represent the position vectors of the attacker, the besieger, and the expeller, A is a random vector; m is a chaotic mapping vector, and C is a random number between [0, 2]; Sub-step S5.2: To prevent the algorithm from falling into the local optimum, this study optimizes the chaser search step in the chimpanzee algorithm, uses random particles for selection, and applies fusion refraction and symbiosis and mutual benefit to the particle position. The strategy based on convex lens imaging can be obtained from formula (25): In the symbiotic search algorithm, mutually beneficial operation is one of the components of the symbiotic search algorithm. j is a randomly selected individual from the population, represented by X i and X j , mutually beneficial operations produce new individuals: In this study, the chimpanzee chaser step is integrated into the refraction reverse learning symbiotic algorithm, and the mutually beneficial operations in the symbiotic algorithm are integrated according to the reverse position of the optimal position in the refraction reverse learning, and then the individuals are updated: The particle update formula of the chimpanzee algorithm is:

7. The method for three-dimensional path planning of unmanned aerial vehicle based on multi-gene optimized chimpanzee algorithm according to claim 6, characterized in that: In order to enable individuals to better find the optimal solution, the reverse learning strategy is integrated into the algorithm in S7. The mathematical representation is as follows: In order to enable individuals to approach the optimal solution more efficiently, we have taken the innovative measure of embedding the reverse learning strategy into the chimpanzee social optimization algorithm. Its mathematical model can be expressed as: X b ' est (t) indicates the inverse solution corresponding to the current optimal solution when evolving to the tth generation. The variables ub and lb respectively indicate the upper and lower limits of the solution space, while r is a random number matrix that follows the standard uniform distribution law in the (0,1) interval. The parameter b1 is assigned the role of the information exchange regulation factor: This study proposes a Cauchy-Gaussian mutation mechanism, which can make good use of the advantages of the two distributions. The Cauchy mutation mechanism is used in the early stage of algorithm iteration, and the Gaussian mutation mechanism is used in the later stage of algorithm iteration. It can take into account the different mutation range requirements of different search stages of the algorithm. The mathematical definition of the Cauchy-Gaussian mutation mechanism is shown in the formula: represents the position of the optimal individual after mutation; Cauchy(x0,γ) and Gauss(μ,σ 2 ) are two random variables that follow the Cauchy distribution and Gaussian distribution. In order to significantly enhance the optimization performance of the algorithm, this paper adopts a flexible dynamic decision-making mechanism to innovate target positioning, that is, under the control of the preset probability, periodically switching between the reverse learning strategy and the Cauchy mutation operator perturbation mechanism to dynamically optimize the target position. Specifically, the target position update strategy depends on the selection probability P. s The quantitative expression of this probability parameter follows the following formula: In the above expression, Σ is used as the adjustment factor, and its recommended setting value is 0.

05. The specific selection process is as follows: When the random number rand is less than P s , the algorithm will enable the reverse learning mechanism to update the position; otherwise, if rand is greater than or equal to P s , then the Cauchy-Gaussian mixture mutation perturbation strategy is selected to update the target position. After the position undergoes perturbation mutation, we further introduce the greedy criterion to compare the fitness evaluation of the new and old positions to determine whether it is necessary to perform position update. The implementation method of the greedy criterion follows the following formula:

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