Unmanned aerial vehicle searching method based on multi-strategy grey wolf algorithm

Abstract

The invention discloses an unmanned aerial vehicle searching method based on a multi-strategy grey wolf algorithm, and relates to the technical field of unmanned aerial vehicles, and the method comprises the steps: building a three-dimensional space terrain model in a task area based on the map environment of a battlefield; constructing a multi-target evaluation function including the path length, the flight height and the steering angle; setting a starting point and a target point of a search task, completing path search and generating candidate paths by using a multi-strategy grey wolf algorithm based on a three-dimensional space terrain model, and evaluating the advantages and disadvantages of the candidate paths through a multi-target evaluation function to obtain an optimal path which is used for completing the search task and meets an evaluation index; and random noise and dynamic obstacles are introduced to verify the robustness of the multi-strategy grey wolf algorithm in different environments. According to the method, the global optimization problem existing in the unmanned aerial vehicle search task in a complex battlefield environment is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned aerial vehicles (UAVs), and in particular to a UAV search method. Background Art

[0002] Battlefield drone search is a research area of ​​significant tactical significance. UAVs play an increasingly important role in battlefield environments, performing tasks such as target reconnaissance, intelligence gathering, and target location, improving military operational efficiency and protecting soldiers' lives. However, this field faces several challenges and issues. First, battlefield environments are complex and dynamic, including factors such as terrain, obstacles, and enemy defense systems, which can affect the UAV's search paths and decision-making. Second, the UAV's extensive search area requires efficient path planning and decision-making algorithms to ensure comprehensive and accurate search. Furthermore, the problem of local optimality is a key challenge: UAVs can become trapped in local optimal solutions within the search space and fail to find the global optimal solution. To address these issues, researchers are committed to developing new search strategies, path planning algorithms, and decision-making models, incorporating machine learning and artificial intelligence technologies, to improve the efficiency, accuracy, and survivability of UAV search. Such research will help enhance the capabilities of battlefield UAV search, providing better intelligence support and tactical advantages for military operations.

[0003] In the early stages of research and exploration, researchers focused on the search problem of UAVs in complex environments and attempted to propose various path planning algorithms. Early Dijkstra and A* algorithms were widely used for UAV path planning. These algorithms achieve navigation by calculating the shortest paths between nodes. However, these algorithms performed poorly in complex environments, leading to the search for more efficient path planning methods. Subsequently, a variety of advanced path planning algorithms, such as genetic algorithms, ant colony algorithms, and gray wolf algorithms, were proposed, combining biomimetic algorithms. These algorithms mimic natural evolutionary processes and swarm intelligence to optimize and adaptively adjust UAV flight paths. The gray wolf algorithm, with its simple structure, minimal parameter adjustments, strong global search capabilities, and fast convergence, has been applied to solving UAV path planning problems in complex environments. Shasha Tian et al. proposed a three-step experience-buffered deep deterministic policy gradient (TSEB-DDPG) algorithm to solve the problem of fast UAV path planning in complex urban environments. Wentao Wang et al. proposed an artificial rabbit optimization algorithm that combines reinforcement learning and a thermal-guided search strategy (RLTARO) to solve the path planning problem for UAV formations in mountainous and forested terrain. Alexios Lekidis et al. proposed a new method for automated drone infrastructure inspection, addressing the problem of power infrastructure inspection in harsh environments. Humairah Hamid et al. proposed a three-step strategy to solve the problem of drone path planning in disaster situations. Liu et al. used a Gaussian mutation strategy and a spiral function as a perturbation mechanism to help the algorithm escape local optima promptly. Dezfouli et al. proposed a new cosine transfer function (CTF) to convert the continuous Grey Wolf Optimization (GWO) algorithm into a binary form and introduced an extreme value search strategy to improve the efficiency of the converted binary solution, addressing the exploration and exploitation required for complex discrete problems. Duan et al. incorporated SCA into the position update of the leading wolf in GWO to address the premature convergence problem. Yu et al. proposed a hybrid GWO and differential evolution algorithm (HGWODE) for solving drone path planning, using a rank-based mutation strategy to promote exploitation while maintaining search capabilities. Battlefield environments are complex and changing. How to quickly and effectively complete drone search tasks is a key research issue, and there is still considerable room for research in drone path planning in complex environments.

[0004] Patent application number 202411578945.1 discloses a three-dimensional path planning method for drones based on an improved gray wolf algorithm. The method includes: first, environmental modeling of the three-dimensional threat area and the definition of the total cost function of the drone flight for the constraints; second, an adversarial learning strategy is added to the gray wolf initialization to increase the search range of the understanding space and to update individual positions by improving the adaptive weight factor, thereby accelerating the convergence rate; finally, to avoid falling into the local optimum, a particle swarm algorithm is introduced to balance global development and local convergence. The above patent can find a safe and feasible path. However, the above patent has problems such as insufficient algorithm adaptive adjustment and the unverified robustness of the algorithm in different environments. Summary of the Invention

[0005] To address the technical challenges of global optimization in UAV search missions under complex battlefield conditions, this paper proposes a UAV search method based on the multi-strategy Grey Wolf algorithm. This method establishes a three-dimensional spatial model based on the actual battlefield context and proposes a multi-objective evaluation function that includes path length, flight altitude, and flight turn angle, effectively evaluating candidate paths. This proposed multi-strategy Grey Wolf algorithm (AIGWO) solves the global optimization problem encountered by battlefield UAV search missions.

[0006] In order to achieve the above object, the technical solution of the present invention is achieved as follows:

[0007] A drone search method based on a multi-strategy gray wolf algorithm includes the following steps:

[0008] S1. Based on the battlefield map environment, establish a three-dimensional spatial terrain model within the mission area; construct a multi-objective evaluation function including path length, flight altitude and turning angle;

[0009] S2. Set the starting point and target point of the search task, use the multi-strategy gray wolf algorithm to complete the path search based on the three-dimensional spatial terrain model, generate candidate paths, evaluate the quality of the candidate paths using a multi-objective evaluation function, and obtain the optimal path that completes the search task and meets the evaluation criteria;

[0010] S3. Random noise and dynamic obstacles are introduced to verify the robustness of the multi-strategy gray wolf algorithm in different environments.

[0011] Specifically, the method of using the multi-strategy gray wolf algorithm to complete the path search is: iteratively solving and outputting candidate paths within the task area through the gray wolf algorithm; in the gray wolf algorithm solution, the search method is selected from the initial search, breadth search and depth search based on the adaptive adjustment of the decay factor and the position changes of the leader wolf and the target; dimensional learning is performed to construct a neighborhood space for each search agent, realize the effective sharing of neighborhood information, enable the individual hunting behavior of the gray wolf to be learned by its neighbors, and increase the candidate search update position.

[0012] Specifically, the method of iteratively solving and outputting candidate paths within the task area using the gray wolf algorithm is as follows:

[0013] Step 1: Initialize the parameters of the AIGWO algorithm: including the maximum number of iterations, the decay factor k, and the random vector and search coefficient

[0014] Step 2: Based on the current position of the UAV and the three-dimensional terrain model, randomly generate the initial population in the search space, calculate the fitness value of each individual and sort them in ascending order of fitness value, and record the top three best gray wolf positions X in the sorting results. α 、X β 、X δ and fitness values;

[0015] Step 3: Adaptively adjust and update the attenuation factor k and random vector and search coefficient Calculate the original position based on dynamic weight distribution;

[0016] Step 4: Select a search method and perform location update based on the selected search method.

[0017] Step 5: Select the optimal location update by adjusting the dynamic radius, handling empty neighborhoods, and selecting neighbor individuals using roulette wheel;

[0018] Step 6: If the preset end condition is met, stop the calculation, output the target position of the gray wolf, and obtain the candidate path; otherwise, return to step 2 to step 6.

[0019] Specifically, the attenuation factor k is expressed as:

[0020] k=k base ×(0.5+0.5×γ);

[0021] Where, the basic attenuation iter is the current number of iterations, T is the maximum number of iterations; diversity ratio Among them, the current average distance D i,jRepresents the distance matrix between the current individual i and the neighbor individual j, μ initial is the average distance at the initial iteration, n is the number of individuals;

[0022] Basic decay k base It decreases linearly with the number of iterations, but nonlinear adjustment is introduced through the diversity ratio γ. There is no need to manually set a fixed attenuation rate, and it can be automatically adjusted according to the population status. When the population diversity is high, the attenuation factor k is increased to enhance the global exploration capability. When the population diversity is low, the attenuation factor k is reduced to accelerate local development. By combining the iteration progress and population diversity, the attenuation factor k is adaptively adjusted to balance global exploration and local development.

[0023] Specifically, if the selected search method is initial search, when updating the position, the weights of α, β, and δ wolves are assigned according to the dominant position of α. The expression for position updating is:

[0024]

[0025] If the selected search method is breadth search, a wider field of view is used to explore the location of the prey and determine the approximate range of the prey. The expression for position update is:

[0026]

[0027] If the selected search method is depth search, after finding the prey, track the prey at the same height as the ground, and the expression for position update is:

[0028]

[0029] Where Levy(D) is the Levy flight distribution function, D represents the dimension, and the calculation formula is as follows:

[0030]

[0031] in, Indicates the position after (iter+1) iterations, Respectively represent the updated positions of α gray wolf, β gray wolf, and δ gray wolf; Indicates the position of wolf α after the iter-th iteration; represents the average position of the population in the ζ dimension; rand is a random number in the interval [0, 1]; s is a fixed constant, τ is a random number in [0, 2]; u is a random number with a mean of 0 and a standard deviation of σ u The normal distribution of v is 0 and the standard deviation is 1; N(μ,σ 2 ) is the normal distribution function, is the position of the mth gray wolf after the iterth iteration, Dim is the dimension;

[0032] When the wolf pack is at the outermost edge, an initial search is used to move the wolf pack toward a better solution; when the wolf pack is at the innermost edge, a breadth search is used to prevent the wolf pack from falling into a local optimum; when the wolf pack is in the middle, a depth search is used, and the α gray wolves can be redistributed based on Levy jumps to prevent the loss of population diversity.

[0033] Specifically, the method for adjusting the dynamic radius is:

[0034] The search range is controlled by parameterized decay, and the initial search radius is set according to the spatial range of the upper and lower bounds of the variable:

[0035] R initial =‖u b -l b ‖2;

[0036] Among them, R initial is the initial search radius, u b and l b are the upper and lower bound vectors of the variable respectively;

[0037] As the number of iterations increases, the search radius shrinks exponentially:

[0038]

[0039] Where R current is the search radius, λ is the decay rate coefficient, exp is the exponential function, iter is the current number of iterations, and T is the maximum number of iterations;

[0040] Define a minimum radius constraint:

[0041] R min =0.05·R initial ;

[0042] R current =mmax(R current ,R min );

[0043] R min is the minimum radius;

[0044] All agents use the same dynamic radius r. The expression for adjusting the dynamic radius r is:

[0045] r=R current ·l n×1 ;

[0046] Among them, l n×1 is a vector of all 1s.

[0047] Specifically, the method for processing the empty neighborhood is:

[0048] Precompute the global ordering and define dynamic neighborhoods:

[0049] Q sorted =argsort(F);

[0050]

[0051] Among them, argsort function is used to return the index of the sorted array, F = [F1, F2, ..., F n ] is the fitness value vector of all individuals, Q sorted is an index list sorted in ascending order by fitness value, and n is the number of individuals;

[0052] Fix the top 10% elite individuals as backup neighbors:

[0053] N θ ={j|||X L -X j ||2≤R(iter), j∈{1, 2,...,n}};

[0054] Among them, N θ is the dynamic radius neighborhood, R(iter) is the search radius of the current iteration, X L is the position of individual L, X j is the location of neighbor individual j;

[0055]

[0056] Where K is the number of individuals in the top 10% globally, and L is the index of the current individual. When the neighborhood is empty, it automatically switches to the globally optimal individual.

[0057] Specifically, the roulette wheel method for selecting neighbor individuals is:

[0058] By probabilistically selecting excellent neighbor individuals, the fitness information is converted into a guiding signal for the search direction, and the objective function value is used to dynamically adjust the selected individuals:

[0059]

[0060] Among them, N θ is the dynamic radius neighborhood, F j is the original fitness value of neighbor individual j, ∈2 is a very small positive number;

[0061] The selection probability of neighbor individual j is:

[0062]

[0063] like or ∑p j ≤0, then force normalization to uniform distribution:

[0064]

[0065] Where V is the index of the selected neighbor individuals in dimension d, d = Dim is the dimension, and the number of selected neighbors is controlled by adjusting d to balance centralized development and decentralized exploration; Multinomial represents probability-based multinomial sampling;

[0066] r1=Permute([1,2,...,n]);

[0067] Permute indicates random permutation operation, r1 indicates random permutation index;

[0068] X DLH =X (x，d) +η·(X (V，d )-X (ρ，d) );

[0069] X (χ，d) is the original position of the current individual χ in the dth dimension, X (v，d) represents the position of the neighbor individual in the dth dimension, ρ = r1(iter) is the random individual index corresponding to individual χ in the random permutation index r1, and η~U(0,1) is a uniformly distributed random number;

[0070] By X (V，d) With X (ρ，d) The difference vector of adds perturbations to the current position to expand the search range; each dimension selects the neighbor individual index V separately, allowing different dimensions to explore in different directions and avoiding inefficient searches caused by coupling between dimensions; the random number η dynamically adjusts the perturbation intensity, η→0 tends to local development, and η→1 tends to global exploration;

[0071]

[0072] X DLH is the position updated by the candidate update strategy, X GWO The updated position of the individual using the GWO algorithm;

[0073] Compare two candidates X GWO and X DLH The fitness value is used to select the optimal solution, which is the next updated position.

[0074] Specifically, the three-dimensional terrain model includes a digital terrain model and other terrain models;

[0075] The expression of the digital terrain model is:

[0076] z=sin(y+Ψ1)+Ψ2·sin(x)+Ψ3·cos(ψ4(y 2 +x 2 ))+Ψ5·cos(ψ6(y 2 +x 2 ))+Ψ7·cos(y)

[0077] Where (x, y) is the horizontal coordinate, z is the horizontal height corresponding to the horizontal coordinate; ψ1, ψ2, ψ3, ψ4, ψ5, ψ6, ψ7 are all coefficients;

[0078] The other terrain models include a threat area terrain model and a mountain terrain model. The expression of the threat area terrain model is:

[0079] ((xx threat ) 2 +(yy threat ) 2 =r threat 2 )∩(z=[0,h]);

[0080] In the formula, (x threat ,y threat ) represents the location coordinates of the threat area, r threat represents the radius of the threat area, and h represents the height of the threat area;

[0081] The expression of the mountain terrain model is:

[0082]

[0083] Where h(x, y) is the height of the mountain corresponding to the horizontal coordinate; h e represents the altitude of the peak; B1 and B2 are the horizontal coordinates corresponding to the highest point of the peak; b1 and b2 represent the variables of the slope of the peak along the x and y directions, and exp is the exponential function; E is the total number of peaks, h0 is the lowest position of the peak, and the subscript e is the sequence number of the peak.

[0084] Specifically, the expression of the multi-objective evaluation function is:

[0085] f=f1*P+f2*H+f3*C;

[0086] Among them, f1 is the weight coefficient of the path length P, f2 is the weight coefficient of the flight height H, and f3 is the weight coefficient of the flight turning angle C; the value of the flight height H is obtained by calculating the square root of the difference between each element and the mean, and then summing all the results; the value of the flight height H is obtained by calculating the square root of the difference between each element and the mean, and then summing all the results; the flight turning angle C is obtained by calculating and summing the cosine values ​​of the angles between all adjacent differential vectors.

[0087] Compared with the prior art, the present invention has the following beneficial effects:

[0088] The present invention establishes a three-dimensional space model based on the actual battlefield background, proposes a multi-objective evaluation function including path length, flight altitude and flight turning angle, and effectively evaluates the quality of candidate paths. The proposed multi-strategy gray wolf algorithm (AIGWO) solves the global optimization problem existing in battlefield drones when performing search tasks. The multi-strategy gray wolf algorithm first selects the search method based on the adaptive adjustment of the decay factor and the changes in the position of the leader wolf and the target, balances the breadth and depth of the search, and speeds up the search speed; secondly, it performs dimensional learning, increases the candidate search update position, and ensures the diversity of the search; then it guides the multi-strategy gray wolf algorithm to search for the optimal solution, improving the algorithm's local optimization ability; finally, it constructs a dynamic obstacle motion model, establishes a path planning simulation environment under random noise interference, and verifies the robustness of the AIGWO algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0090] Figure 1 Flowchart of the multi-strategy grey wolf algorithm of the present invention.

[0091] Figure 2 This is a map model simulation diagram in one embodiment of the present invention.

[0092] Figure 3 This is a height data analysis diagram for the experimental test of the present invention.

[0093] Figure 4 This is a data analysis diagram of the experimental test path length of the present invention.

[0094] Figure 5 This is a data analysis diagram of the fitness value of the experimental test of the present invention. DETAILED DESCRIPTION

[0095] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without creative work are within the scope of protection of the present invention.

[0096] A drone search method based on a multi-strategy gray wolf algorithm includes the following steps:

[0097] S1. Based on the battlefield map environment, establish a three-dimensional spatial terrain model within the mission area; construct a multi-objective evaluation function that includes path length, flight altitude, and turning angle.

[0098] A drone search mission in a battlefield environment requires the drone to take off from a designated location and fly across the center of the battlefield to reach the designated mission location. Within the mission area, there are no-fly zones consisting of threat areas and mountain peaks. A 3D terrain model is built based on the battlefield map environment. This 3D terrain model includes both digital terrain models and other terrain models.

[0099] The digital terrain model is as follows:

[0100]

[0101] Where (x, y) is the horizontal coordinate, z is the horizontal height corresponding to the horizontal coordinate; ψ1, ψ2, ψ3, ψ4, ψ5, ψ6, and ψ7 are all coefficients, and the terrain can be changed by adjusting the coefficients.

[0102] Other terrain models include threat area terrain models and mountain terrain models.

[0103] The terrain model of the threat area is as follows:

[0104] ((xx threat ) 2 +(yy threat ) 2 =r threat 2 )∩(z=[0,h]) (2)

[0105] In the formula, (x threat ,y threat ) represents the location coordinates of the threat area, r threat represents the radius of the threat area, and h represents the height of the threat area.

[0106] The mountain terrain model is as follows:

[0107]

[0108] Where h(x,y) is the peak height corresponding to the horizontal coordinate; h e represents the peak's altitude; B1 and B2 are the horizontal coordinates of the peak's highest point; b1 and b2 represent the slope of the peak along the x and y directions, respectively; smaller values ​​of b1 and b2 indicate steeper slopes. exp is an exponential function; E is the total number of peaks, and h0 is the lowest peak position. The subscript e is the peak's index.

[0109] Considering the actual flight scenario of UAV in three-dimensional space, under the condition that the UAV completes path planning and effectively avoids obstacles, a multi-objective evaluation function including path length, flight altitude and steering angle is constructed to effectively evaluate the quality of path planning results.

[0110] (1) Path length: The shorter the flight path length of the drone after path planning, the less fuel consumption and exposure time the drone will have, which can reduce flight costs and improve flight safety. Therefore, path length is one of the important evaluation indicators, and its expression is:

[0111]

[0112] Where dx, dy and dz are the incremental values ​​on the x, y and z axes respectively. Denotes the Euclidean distance. The path length P is obtained by summing the Euclidean distances between all adjacent points on the path.

[0113] (2) Flight altitude: When conducting combat missions, a lower flight altitude can make it easier for the UAV to blend into the terrain and environment, reduce the possibility of being detected by the enemy, and improve its concealment and stealth capabilities.

[0114]

[0115] Where Z represents the height vector, and mean(Z) represents the mean of the height vector Z. The flight height H is obtained by calculating the square root of the difference between each element and the mean, and then summing all the results.

[0116] (3) Flight turning angle: A smaller turning angle can provide a more stable and smoother flight turning process, reduce lateral force and attitude changes, thereby keeping the UAV in a more stable flight state and reducing the probability of loss of control or accidents.

[0117] D x =x(G+1)-x(G),D y =y(G+1)-y(G),D z =z(G+1)-z(G) (6)

[0118]

[0119] In the formula, x(G), y(G), z(G) are the x, y, and z vector coordinates of the G-th point, respectively; x(G+1), y(G+1), and z(G+1) are the x, y, and z vector coordinates of the G+1-th point, respectively; D x (G), D y (G), D z (G) are the x, y, and z direction vectors between two adjacent points G and G+1, respectively, and D x (G+1), D y (G+1), D z (G+1) are the x, y, and z direction vectors between two adjacent points G+1 and G+2 respectively.

[0120] D x 、D y and D z where x, y, and z represent the difference vectors of the sequences respectively. C(G) is the cosine of the angle between adjacent difference vectors, indicating the smoothness of the direction change. The flight turning angle C is obtained by calculating and summing the cosine values ​​of the angle between all adjacent difference vectors.

[0121] In summary, the expression of the multi-objective evaluation function of UAV path planning is:

[0122] f=f1*P+f2*H+f3*C (9)

[0123] Wherein, f1 is the weight coefficient of path length P, f2 is the weight coefficient of flight altitude H, and f3 is the weight coefficient of flight turning angle C. In this embodiment, weight coefficients f1 and f2 are both 0.4, and weight coefficient f3 is 0.2. The weight coefficients are used to adjust the contribution of each factor to fitness.

[0124] S2. Set the starting point and target point of the search task, complete the path search based on the three-dimensional spatial terrain model, use the multi-strategy gray wolf algorithm to generate candidate paths, evaluate the pros and cons of the candidate paths through a multi-objective evaluation function, and obtain the optimal path for completing the search task and meeting the evaluation indicators.

[0125] The Gray Wolf Algorithm (GWA), a decision-making algorithm for drone search tasks, can solve drone flight problems in complex battlefield environments and effectively meet the requirements of drone path planning. However, the search process suffers from poor population diversity and a tendency to fall into local optimality. To overcome these problems, this paper proposes a multi-strategy Gray Wolf Algorithm (AIGWO). First, the algorithm selects a search method based on adaptively adjusting the decay factor and the position changes of the leader and target, balancing the breadth and depth of search to accelerate the search. Second, it performs dimensional learning to increase candidate search update locations and ensure search diversity. Finally, it guides the multi-strategy Gray Wolf Algorithm toward the optimal solution, improving the algorithm's local optimization capabilities.

[0126] The Gray Wolf Algorithm simulates the social hierarchy of wolves. From highest to lowest, the social hierarchy is: α, β, δ, and ω. These correspond to the optimal, suboptimal, third-best, and worst solutions in the Gray Wolf Algorithm. In the GWO algorithm, the search is guided by α, β, and δ wolves, and the wolves follow them to siege and capture prey.

[0127] Gray wolves track their prey during hunting, and mathematically model their tracking behavior:

[0128]

[0129] Where, represents the position vector of the gray wolf, represents the updated position vector of the gray wolf, represents the position vector of the prey, iter is the current iteration number, and T is the maximum iteration number. The control parameter a decreases linearly from 2 to 0 during the iteration process. and is a random vector in [0,1]. is a random vector in the interval [-a,a]. When the wolf pack tries to disperse to different areas to search for prey, When , the wolf pack concentrates on searching for prey in a certain area. Search coefficient is a random vector in the interval [0,2]. Search coefficient Provides a random weight for prey, which is used to reduce or increase the weight ratio of prey distance calculation.

[0130] Gray wolves can identify and surround their prey. The search process is directed by α, β, and δ wolves. Each iteration retains the positions of α, β, and δ wolves, and updates the positions of the other wolves based on the positions of α, β, and δ wolves. A mathematical model of hunting behavior is constructed as follows:

[0131]

[0132]

[0133] Where, represents the position vector of the gray wolf, Represent the current position vectors of α gray wolf, β gray wolf, and δ gray wolf respectively. Represent the distances between the current candidate gray wolf and α gray wolf, β gray wolf, and δ gray wolf respectively. Respectively represent the updated positions of α gray wolf, β gray wolf, and δ gray wolf, They represent the search coefficients of α-gray wolf, β-gray wolf, and δ-gray wolf respectively.

[0134] Swarm intelligence algorithms often suffer from a loss of convergence accuracy and optimization performance due to the imbalance between global and local search capabilities. The gray wolf algorithm also suffers from poor population diversity and the tendency to fall into local optimality during the search process.

[0135] The GWO algorithm achieves a balance between global and deep search by controlling the parameter a. The control parameter a is linear, which is inconsistent with the actual situation. Therefore, the control parameter is defined as follows.

[0136]

[0137] Among them, D i,j Represents the distance matrix between the current individual i and the neighbor individual j, μ curret is the current average distance, μ initial is the average distance at the initial iteration. The diversity ratio γ can delay parameter decay and prevent the AIGWO algorithm from falling into a local optimum too early. n is the number of individuals.

[0138]

[0139] k=k base ×(0.5+0.5×γ) (21)

[0140] Basic decay k base The decay factor decreases linearly with the number of iterations, but a nonlinear adjustment is introduced through the diversity ratio γ. This eliminates the need to manually set a fixed decay rate, as it can be automatically adjusted based on the population state. Limiting the decay factor k∈[0.1,2] ensures the stability of the AIGWO algorithm and prevents extreme values ​​from affecting convergence.

[0141] When the population is dispersed (high diversity), the decay factor k is increased to enhance global exploration capabilities; when the population is concentrated (low diversity), the decay factor k is decreased to accelerate local exploration. By combining iteration progress and population diversity, the decay factor k is adaptively adjusted to balance global exploration and local exploration, improving the robustness and convergence efficiency of the AIGWO algorithm.

[0142] Select a search method:

[0143] Random behavior is often used in the process of exploring unknown environments or finding optimal solutions to avoid falling into local optimal solutions or converging to a specific behavior too early. If the agent always chooses the same optimal behavior, it may miss other potentially better options. By setting randomness, the agent has the opportunity to try different behaviors, thereby better exploring the environment and finding better solutions. It should be noted that random behavior is usually performed at a certain exploration rate, rather than completely randomly selecting behaviors. The exploration rate gradually decreases as learning progresses, so that the agent gradually transitions from random exploration to deterministic behavior during the learning process, thereby better utilizing the acquired knowledge. The specific position update process is as follows:

[0144] (1) Initial search: When updating the position, the first three wolves (α, β, and δ) are weighted according to the dominant position of the leading wolf (α), so that the wolf pack can move toward the target more accurately and the algorithm converges faster.

[0145]

[0146] (2) Breadth search: Using a wider field of view to explore the location of prey and determine the approximate range of prey. This behavior can be expressed by a mathematical formula:

[0147]

[0148] in, Indicates the position after (iter+1) iterations, represents the position of wolf α after iteration iter. (1-iter / T) is explored by controlling the iteration. rand is a random number in the interval [0, 1]. represents the average position of the group in the ζ dimension; is the position of the mth gray wolf after the iterth iteration; Dim is the dimension.

[0149] (3) Deep search: After finding the prey, it tracks the prey at the same height as the ground. This behavior can be expressed mathematically as:

[0150]

[0151] Where Levy(D) is the Levy flight distribution function, D represents the dimension, and the calculation formula is as follows:

[0152]

[0153] u~N(0,σ u 2 ),v~N(0,1)

[0154] Where s is a fixed constant of 0.01, τ is a random number in [0, 2]. u is a random number with a mean of 0 and a standard deviation of σ. u The normal distribution of v is 0 and the standard deviation is 1. u The calculation formula is as follows:

[0155]

[0156] Wherein, Γ represents the traditional gamma function, which is The Levy process selects a random value in the interval [0, 2] at each iteration, which results in many short jumps. This random value can improve the development and exploration trends during the iteration process.

[0157] Different position update methods are used based on the position changes of the leader and the target. Initial search is used when the wolf pack is at the outermost edge, moving it toward a more optimal solution. Breadth search is used when the wolf pack is at the innermost edge, preventing it from falling into a local optimum. Deep search is used when the wolf pack is in the middle, using Levy jumps to redistribute the leader, preventing loss of population diversity and strengthening the global search trend.

[0158] In the gray wolf algorithm, other gray wolves follow the lead of the leader to generate new positions. This approach results in slow convergence, premature loss of population diversity, and trapping the algorithm in a local optimum. To address this, dimensional learning constructs a unique neighborhood space for each search agent, enabling effective sharing of neighborhood information and enabling the learning of individual gray wolf hunting behaviors by their neighbors.

[0159] ① Dynamic weight allocation:

[0160] By dynamically assigning normalized weights, we combine the guiding role of the leader with the individual's own performance to achieve adaptive adjustment of position updates. The core of this dynamic normalized weight allocation is to balance global search and local development through the tanh function and hierarchical coefficients, improving the algorithm's convergence speed and accuracy while maintaining robustness.

[0161]

[0162] Where, ω α ,ω β ,ω δ Represents the weights of α, β, and δ gray wolves respectively; S α , S β , S δ Represents the fitness values ​​of α, β, and δ gray wolves respectively. q Represents the fitness value of the current individual q. tanh(·) is the hyperbolic tangent function, which maps the input to the interval (-1, 1).

[0163] ω total =ω α +ω β +ω δ +∈1 (29)

[0164]

[0165] Among them, X α , X β , X δ are the positions of the gray wolves α, β, and δ respectively; ∈1 is the minimum value, which is used to prevent the denominator from being zero. ω total is the total weight, X GWO The updated position of the individual using the GWO algorithm.

[0166] By the total weight ω total Normalization ensures that the sum of weights is 1, avoiding unstable position updates caused by absolute weight values ​​that are too large or too small.

[0167] The weights are adaptively adjusted based on the fitness of the current individual and the gray wolves α, β, and δ. When the current individual's performance is poor, the input value of the tanh function is small, the weight is reduced, and the individual relies more on the leader's development. If the current individual's performance approaches that of the leader, the weight is increased, preserving its own exploration capabilities. The weights are dynamically adjusted based on individual performance to meet the search needs of different optimization stages and reduce reliance on manual parameter adjustment.

[0168] ②Adjust the dynamic radius:

[0169] The search range is controlled by parameterized decay, balancing the breadth and depth of the optimization algorithm while maintaining computational efficiency and robustness.

[0170] R initial =||u b -l b ||2 (31)

[0171] Among them, R initial is the initial search radius, u b and l b The upper and lower bound vectors of the variable are used to set the initial search radius based on the spatial range of the upper and lower bounds of the variable to ensure that the algorithm can fully explore the global range in the early stages.

[0172]

[0173] Where R current is the search radius, and λ is the decay rate coefficient. In this embodiment, the decay rate coefficient λ = 5. As the number of iterations increases, the search radius shrinks exponentially, shrinking rapidly in the early stage to focus on the potential optimal area, and then slowly decaying in the later stage to fine-tune the development.

[0174] Rmin =0.05·R initial (33)

[0175] R current =max(R current , R min ) (34)

[0176] R min The minimum radius is set to avoid stagnation of search due to too small search radius, and the local development capability is retained until the end of the algorithm.

[0177] r=R current ·l n×1 (35)

[0178] Among them, r is the dynamic radius, l n×1 It is a vector of all 1s. All agents use the same dynamic radius, which simplifies the calculation and ensures the fairness of the search behavior, avoiding the additional complexity introduced by radius differences between individuals.

[0179] D i，j =||X i -X j ||2=(ij=1,2,...,n) (36)

[0180] By dynamically reducing the search radius through exponential decay and combining it with the minimum radius constraint, an adaptive transition from global exploration to local development is achieved. i 、X j are the positions of the current individual i and the neighbor individual j respectively.

[0181] ③ Empty neighborhood processing:

[0182] The efficiency and quality of neighborhood search are optimized by pre-calculating global sorting and dynamic neighborhood definition.

[0183] Q sorted =argsort(F) (37)

[0184]

[0185] Among them, the argsort function is used to return the index of the sorted array, F = [F1, F2, ..., F n ] is the fitness value vector of all individuals, Q sorted is a list of indices sorted in ascending order of fitness value. The quality of the neighborhood is ensured by fixing the top 10% elite individuals as backup neighbors.

[0186] N θ ={j|||X L -X j||2≤R(iter),j∈{1,2,...,n}} (39)

[0187] Among them, N θ is the dynamic radius neighborhood, R(iter) is the search radius of the current iteration, X L is the position of individual L, X j is the location of neighbor individual j.

[0188]

[0189] Where L is the current individual index, K is the number of individuals in the top 10% of the global population, and it automatically switches to the global optimal individual when the neighborhood is empty to avoid search stagnation due to local information loss.

[0190] The dynamic radius is combined with the empty neighborhood fallback mechanism, and global elite guidance is introduced when local information is insufficient. Combined with fitness value normalization, this ensures that the algorithm can balance exploration and exploitation stably and efficiently in different scenarios.

[0191] ④ Roulette wheel selection of neighbor individuals:

[0192] By probabilistically selecting excellent neighbor individuals, fitness information is converted into a guiding signal for the search direction. The objective function value is used to dynamically adjust the selected individuals, accelerating convergence to the optimal region while preserving diversity through randomness.

[0193]

[0194] Among them, F j is the original fitness value of neighbor individual j, ∈2 is a very small positive number, For individuals Avoid negative fitness values ​​that lead to abnormal probability calculations while maintaining the relative difference in fitness.

[0195]

[0196] p j is the selection probability of neighbor individual j, if or ∑p j ≤0, then force normalization to uniform distribution:

[0197]

[0198] Enforcing uniform distribution avoids selection collapse caused by extreme fitness distribution and enhances stability.

[0199]

[0200] Where V is the index of the selected neighbor individuals along dimension d, and d = Dim is the dimension. By adjusting d, the number of selected neighbors is controlled to balance centralized exploration and decentralized exploration. Multinomial represents probability-based multinomial sampling.

[0201] r1=Permute([1,2,...,n]) (45)

[0202] Permute indicates a random permutation operation, and r1 indicates a random permutation index.

[0203] X DLH =X (x，d) +η·(X (V，d) -X (ρ，d) ) (46)

[0204] X DLH is the position updated by the candidate update strategy, X (χ，d) is the original position of the current individual χ in dimension d, X (V，d) represents the position of the neighbor individual in dimension d, ρ = r1(iter) is the random individual index corresponding to individual χ in the random permutation index r1, and η~U(0,1) is a uniformly distributed random number.

[0205] By X (V，d) With X (ρ，d) The difference vector of is used to add perturbations to the current position, expanding the search range. Each dimension independently selects the neighboring individual index V, allowing different dimensions to explore in different directions and avoiding inefficient search caused by inter-dimensional coupling. A random number η dynamically adjusts the perturbation intensity: η → 0 favors local exploration, while η → 1 favors global exploration.

[0206]

[0207] Compare two candidates X GWO and X DLH The fitness value is used to select the optimal solution, which is the next updated position.

[0208] Through dimensionally independent random differential perturbations, controllable randomness and directional diversity are introduced into the search space. The core of this approach is to enhance global exploration capabilities while maintaining local development potential through dimensionally independent perturbations and random step sizes.

[0209] ⑤Boundary reflection processing:

[0210] Through mirror reflection, the out-of-bounds points are pulled back to the feasible region to maintain the symmetry of the population distribution. Position mutations are avoided, and secondary truncation ensures strict feasibility.

[0211]

[0212] vi Represents the individual position vector to be processed, u b and l b are the upper and lower bound vectors of the variable, respectively.

[0213] In summary, the multi-strategy Grey Wolf algorithm proposed in this paper addresses the global optimization problem in UAV search missions in complex battlefield environments. It consists of three main parts: algorithm initialization, search method selection, and candidate position update. The specific process is as follows:

[0214] Step 1. Parameter initialization: Set the maximum number of iterations of the AIGWO algorithm, the attenuation factor k, and the random vector and search coefficient and other parameters;

[0215] Step 2: Based on the current position of the UAV and the three-dimensional terrain model, randomly generate the initial population in the search space, calculate the fitness value of each individual and sort them in ascending order of fitness value, and record the top three best gray wolf positions X in the sorting results. α 、X β 、X δ and fitness values;

[0216] Step 3: Adaptively adjust and update the attenuation factor k and random vector through formulas (21), (13), and (14). and search coefficient Calculate the original position based on dynamic weight distribution;

[0217] Step 4: According to Figure 1 The random number size is selected to update the position using formulas (22), (23), and (25);

[0218] Step 5: Select the optimal location update by adjusting the dynamic radius, handling empty neighborhoods, and selecting neighbor individuals using roulette wheel;

[0219] Step 6: If the preset end condition is met, stop the calculation, output the target position of the gray wolf, and obtain the candidate path; otherwise, return to step 2 to step 6.

[0220] S3. Random noise and dynamic obstacles are introduced to verify the robustness of the AIGWO algorithm in different environments.

[0221] In order to reasonably simplify the problem and focus on the research objectives, the UAV is equivalent to a point mass in the three-dimensional terrain model to achieve efficient path planning.

[0222] Noise injection is used to simulate real-world uncertainties and verify the robustness of the UAV search method in complex environments.

[0223]

[0224] Where M(I, J) is the basic terrain function, f(I, J) is the basic terrain function, ∈3=0.2 is the noise intensity coefficient, is a standard Gaussian distributed random variable, N x is the horizontal dimension, N y is the size of the vertical dimension, I is the horizontal coordinate, and J is the vertical coordinate.

[0225] Superimposing Gaussian noise on the base terrain function simulates real-world terrain uncertainty caused by measurement errors, natural undulations, or sensor noise. This generates non-uniform, non-idealized, and complex terrain, providing a more realistic test scenario.

[0226] Dynamic obstacles: Simulate moving obstacles with different motion patterns (linear, circular, random) to provide a complex test environment.

[0227] (1) Linear motion: P1(t+Δt)=P1(t)+V1·Δt (50)

[0228] The boundary reflection conditions are as follows:

[0229]

[0230] represents the initial position, is the velocity vector, Δt = 0.1s is the time step. P1(t) is the coordinate position of obstacle 1 at movement time t, P1(t+Δt) is the updated position of obstacle 1, t is the movement time, is the updated position in the x direction, is the updated position in the y direction, is the velocity vector in the x direction, is the velocity vector in the y direction.

[0231] (2) Circular motion:

[0232] θ(t+Δt)=θ(t)+ω·Δt (52)

[0233]

[0234] Wherein, ω is the angular velocity, θ(t) is the arc angle of the obstacle relative to the center of the circle at the time t, θ(t+Δt) is the updated angle, P2(t+Δt) is the updated position of obstacle 2, c is the center point of the circular motion, and R is the radius of the circular motion. In this embodiment, the angular velocity ω = 0.1 rad / s, c = [100, 150], and R = 50.

[0235] (3) Random motion:

[0236]

[0237] P3(t+Δt)=P3(t)+V3·Δt (55)

[0238] Among them, V3 is the velocity vector of obstacle 3, is a two-dimensional random vector, P3(t) is the coordinate position of obstacle 3 at time t, and P3(t+Δt) is the updated position of obstacle 3.

[0239] The cylinder model is as follows:

[0240] X I =r I cosφ, Y I =r I sinφ, Z I =h I κ (56)

[0241]

[0242] Among them, φ∈[0, 2π], κ∈[0, 1], r I Indicates the obstacle radius, h I Indicates the height of the obstacle. X I 、Y I , Z I is the coordinate matrix of the basic cylinder, φ is is the two-dimensional position coordinate of the center of the bottom surface of the obstacle, X w 、Y w , Z w is the coordinate matrix of the obstacle after transformation.

[0243] This dynamic obstacle simulation framework defines multi-mode motion rules through mathematical formulas, supports mixed scenarios of multiple motion modes, and provides a high-fidelity testing environment for drone search methods.

[0244] To verify the effectiveness of the present invention, further explanation is given below in conjunction with experimental data:

[0245] The simulation environment is run in MATLAB R2022b. The size of the simulation environment is 200×200×60. Figure 2 As shown in the map model, the map includes a starting point, an end point, peaks, and a threat zone. Each peak has varying heights and slopes, simulating a realistic battlefield terrain environment to the greatest extent possible. The threat zone is a closed cylindrical space. As the drone flies from the starting point to the end point, it must avoid the peaks and threat zone. Collisions or entry into the threat zone are considered mission failures. Experiments evaluate the path planning results using criteria such as run time, path length, flight altitude, convergence speed, and optimal fitness.

[0246] In order to verify the performance of the AIGWO algorithm, a three-dimensional path planning simulation comparison experiment was carried out using the GWO algorithm, Aquila exploration Grey wolf Optimizer (AGWO), Improved Grey Wolf Optimizer (IGWO), Levy-embedded GWO (LGWO) and the AIGWO algorithm proposed in this paper under the same map.

[0247] In order to ensure the comparability of the experiments and the credibility of the results and eliminate the influence of external factors on the experimental results, as shown in Table 1, the basic parameters such as the number of iterations, population size and number of trials are uniformly set in the experiment.

[0248] Table 1 - Initial experimental parameter settings

[0249]

[0250]

[0251] After the experimental parameters are set, the algorithm comparison experiment test is carried out in the experimental model.

[0252] Robustness analysis:

[0253] The robustness of the AIGWO algorithm in complex and uncertain environments was verified by introducing random noise and dynamic obstacles in MATLAB. By superimposing Gaussian noise on the basic terrain function, we simulated the terrain uncertainty caused by measurement errors, natural undulations, or sensor noise in real environments, balancing the controllability of the terrain structure with the randomness of the environment. The dynamic obstacle simulation framework uses mathematical formulas to define multi-modal motion rules, combined with interactive visualization, to provide a high-fidelity, customizable dynamic testing environment for algorithm testing.

[0254] Based on the comparison of the average data from 10 experimental tests, we can observe that after the introduction of random noise and dynamic obstacles to the map, the various data of the AIGWO algorithm have slight fluctuations, as shown in Table 2, but they are all within the fluctuation range, verifying the robustness of the AIGWO algorithm in complex environments.

[0255] Table 2 - Random noise and dynamic obstacles introduced into the map

[0256]

[0257] Simulation results analysis:

[0258] Because obstacles obstruct the full path in the simulation results, the results are displayed from different angles. The starting angle view shows the entire flight process, while the front view view shows the ups and downs of the drone during flight.

[0259] The experimental results show that the AIGWO algorithm converges faster and more smoothly, while also achieving a significantly lower flight altitude than the other algorithms, better meeting the experimental requirements. It is also clear that the AIGWO algorithm's optimal fitness value is significantly lower than that of the other four algorithms. Because the GWO, AGWO, IGWO, LGWO, and AIGWO algorithms inherently utilize random numbers, the experimental results exhibit a certain degree of randomness. However, despite this randomness, the AIGWO algorithm exhibits greater stability, demonstrating that AIGWO is more suitable for battlefield drone search missions than the other four algorithms.

[0260] Five sets of data were selected for analysis. As shown in Table 3, it can be observed that the running time of the GWO algorithm is the shortest, the running time of the LGWO algorithm is the longest, and the running time of the AIGWO algorithm is medium. Figure 3 As shown, it can be seen intuitively that AIGWO's flight altitude is always at the lowest, which is more suitable for solving search problems and better meets experimental requirements.

[0261] Table 3 - Comparison of running time of GWO, AGWO, IGWO, LGWO and AIGWO algorithms

[0262]

[0263]

[0264] Five representative samples were randomly selected from 40 independent experimental data sets for analysis. As shown in Table 4, the AIGWO algorithm showed a significant convergence speed advantage. The objective function value of the AIGWO algorithm quickly approached the global optimal solution at the beginning of the iteration, and the average number of convergence iterations was reduced by about 58.8%, verifying the high solution efficiency of the AIGWO algorithm. Figure 4 As shown in the figure, the average flight path length obtained by the AIGWO algorithm is 8.9% shorter than that of the GWO algorithm, and is 5.1%, 7.6% and 9.2% shorter than that of the AGWO, IGWO and LGWO algorithms, respectively. This fully verifies that the AIGWO algorithm can effectively reduce path redundancy and improve path planning quality in complex scenarios after the improvement of the neighborhood search mechanism.

[0265] Table 4-Comparison of convergence speed of GWO, AGWO, IGWO, LGWO and AIGWO algorithms

[0266]

[0267] like Figure 5 As shown in the figure, analysis of the 40 sets of experimental data from the test reveals that the AIGWO algorithm achieves an average improvement of 11.34% to 26.65% in optimal fitness compared to the other four algorithms. Furthermore, the AIGWO algorithm achieves smaller standard deviations and ranges, indicating lower data dispersion and improved algorithm stability. This demonstrates that the adaptive weighting strategy introduced effectively mitigates parameter sensitivity. By dynamically adjusting candidate positions, the AIGWO algorithm achieves a better balance between exploration and exploitation, significantly improving the robustness of the optimization process.

[0268] In order to improve the search efficiency of drones in battlefield environments, the present invention establishes a three-dimensional space model based on the actual battlefield background, and proposes a multi-objective evaluation function including path length, flight altitude and flight turning angle to effectively evaluate the quality of path planning results. In response to the global optimization problem existing in drone search tasks in complex battlefield environments, a multi-strategy grey wolf algorithm (AIGWO) is proposed. First, the search speed is accelerated by adaptively adjusting parameters; secondly, different position update methods are selected according to the position changes of the leader wolf and the target to balance the breadth and depth of search; then, neighbor individuals are selected according to the dynamic adjustment radius and roulette wheel to increase the candidate search update position, ensure the diversity of the search, and guide the algorithm to search for the optimal solution. A large number of experimental simulations were carried out according to the set parameter weight ratio. The results show that after random noise and dynamic obstacles are introduced into the map, the data fluctuate slightly within the fluctuation range, verifying that the AIGWO algorithm has strong robustness. A comparison was also made with four other advanced algorithms, and the result showed that the running time of the AIGWO algorithm was medium, the flight altitude was the lowest in the test results, and the average number of convergence iterations was reduced by about 58.8%; the average flight path length was shortened by 8.9% compared with the GWO algorithm, and by 5.1%, 7.6% and 9.2% compared with the AGWO, IGWO and LGWO algorithms respectively; the average optimal fitness value was increased by 26.65% compared with the GWO, and by 24.4%, 11.34% and 16.56% compared with the AGWO, IGWO and LGWO algorithms respectively, verifying the effectiveness of the AIGWO algorithm in drone search.

[0269] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A drone search method based on a multi-strategy grey wolf algorithm, characterized in that: The following steps are involved: S1. Based on the battlefield map environment, establish a three-dimensional spatial terrain model within the mission area; construct a multi-objective evaluation function including path length, flight altitude and turning angle; S2. Set the starting point and target point of the search task, use the multi-strategy gray wolf algorithm to complete the path search based on the three-dimensional spatial terrain model, generate candidate paths, evaluate the quality of the candidate paths using a multi-objective evaluation function, and obtain the optimal path that completes the search task and meets the evaluation criteria; S3. Random noise and dynamic obstacles are introduced to verify the robustness of the multi-strategy gray wolf algorithm in different environments.

2. The drone search method based on the multi-strategy gray wolf algorithm according to claim 1 is characterized in that: The method for completing path search using a multi-strategy gray wolf algorithm comprises: iteratively solving and outputting candidate paths within a task area through the gray wolf algorithm; selecting a search method from initial search, breadth search, and depth search based on adaptively adjusting a decay factor and position changes between a leader wolf and a target during the gray wolf algorithm solution; performing dimensional learning to construct a neighborhood space for each search agent, achieving effective sharing of neighborhood information, enabling individual hunting behaviors of gray wolves to be learned by their neighbors, and increasing candidate search update locations.

3. The drone search method based on the multi-strategy gray wolf algorithm according to claim 2 is characterized in that: The method of iteratively solving and outputting candidate paths within the task area through the gray wolf algorithm is: Step 1: Initialize the parameters of the AIGWO algorithm: including the maximum number of iterations, the decay factor k, and the random vector and search coefficient Step 2: Based on the current position of the UAV and the three-dimensional terrain model, randomly generate the initial population in the search space, calculate the fitness value of each individual and sort them in ascending order of fitness value, and record the top three best gray wolf positions X in the sorting results. α 、X β 、X δ and fitness values; Step 3: Adaptively adjust and update the attenuation factor k and random vector and search coefficient Calculate the original position based on dynamic weight distribution; Step 4: Select a search method and perform location update based on the selected search method. Step 5: Select the optimal location update by adjusting the dynamic radius, handling empty neighborhoods, and selecting neighbor individuals using roulette wheel; Step 6: If the preset end condition is reached, the calculation is stopped, the target position of the gray wolf is output, and the candidate path is obtained; Otherwise, return to step 2 to step 6.

4. The drone search method based on the multi-strategy gray wolf algorithm according to claim 3 is characterized in that: The expression of the attenuation factor k is: k=k base ×(0.5+0.5×γ); Where, the basic attenuation iter is the current number of iterations, T is the maximum number of iterations; Diversity ratio Among them, the current average distance D i,j Represents the distance matrix between the current individual i and the neighbor individual j, μ initial is the average distance at the initial iteration, n is the number of individuals; Basic decay k bae It decreases linearly with the number of iterations, but nonlinear adjustment is introduced through the diversity ratio γ. There is no need to manually set a fixed attenuation rate, and it can be automatically adjusted according to the population status. When the population diversity is high, the attenuation factor k is increased to enhance the global exploration capability. When the population diversity is low, the attenuation factor k is reduced to accelerate local development. By combining the iteration progress and population diversity, the attenuation factor k is adaptively adjusted to balance global exploration and local development.

5. The drone search method based on the multi-strategy gray wolf algorithm according to claim 3 is characterized in that: If the selected search method is initial search, the weights of α, β, and δ wolves are assigned according to the dominant position of α wolf during position update. The expression for position update is: If the selected search method is breadth search, a wider field of view is used to explore the location of the prey and determine the approximate range of the prey. The expression for position update is: If the selected search method is depth search, after finding the prey, track the prey at the same height as the ground, and the expression for position update is: Where Levy(D) is the Levy flight distribution function, D represents the dimension, and the calculation formula is as follows: in, Indicates the position after (iter+1) iterations, Respectively represent the updated positions of α gray wolf, β gray wolf, and δ gray wolf; Indicates the position of wolf α after the iter iteration; represents the average position of the population in the ζ dimension; rand is a random number in the interval [0, 1]; s is a fixed constant, τ is a random number in [0, 2]; u is a random number with a mean of 0 and a standard deviation of σ u The normal distribution of v is 0 and the standard deviation is 1; N(μ,σ 2 ) is the normal distribution function, is the position of the mth gray wolf after the iterth iteration, Dim is the dimension; When the wolf pack is at the outermost edge, an initial search is used to move the wolf pack toward a better solution; when the wolf pack is at the innermost edge, a breadth search is used to prevent the wolf pack from falling into a local optimum; when the wolf pack is in the middle, a depth search is used, and the α gray wolves can be redistributed based on Levy jumps to prevent the loss of population diversity.

6. The drone search method based on the multi-strategy gray wolf algorithm according to claim 3 is characterized in that: The method for adjusting the dynamic radius is: The search range is controlled by parameterized decay, and the initial search radius is set according to the spatial range of the upper and lower bounds of the variable: R initial =‖u b -l b ‖2; Among them, R initial is the initial search radius, u b and l b are the upper and lower bound vectors of the variable respectively; As the number of iterations increases, the search radius shrinks exponentially: Where R current is the search radius, λ is the decay rate coefficient, exp is the exponential function, iter is the current number of iterations, and T is the maximum number of iterations; Define a minimum radius constraint: R min =0.05·R initial ; R current =max(R current ,R min ); R min is the minimum radius; All agents use the same dynamic radius r. The expression for adjusting the dynamic radius r is: r＝R current ·l n×1 ； Among them, l n×1 is a vector of all 1s.

7. The drone search method based on the multi-strategy gray wolf algorithm according to claim 3 is characterized in that: The method for processing the empty neighborhood is: Precompute the global ordering and define dynamic neighborhoods: Q sorted =argsort(F); Among them, the argsort function is used to return the index of the sorted array, F=[F1,F2,...,F n ] is the fitness value vector of all individuals, Q sorted is an index list sorted in ascending order by fitness value, and n is the number of individuals; Fix the top 10% elite individuals as backup neighbors: N θ ={j|||X L -X j ||2≤R(iter),j∈{1,2,...,n}}; Among them, N θ is the dynamic radius neighborhood, R(iter) is the search radius of the current iteration, X L is the position of individual L, X j is the location of neighbor individual j; Where K is the number of individuals in the top 10% globally, and L is the index of the current individual. When the neighborhood is empty, it automatically switches to the globally optimal individual.

8. The drone search method based on the multi-strategy gray wolf algorithm according to any one of claims 3 to 7, characterized in that: The roulette wheel method for selecting neighbor individuals is: By probabilistically selecting excellent neighbor individuals, the fitness information is converted into a guiding signal for the search direction, and the objective function value is used to dynamically adjust the selected individuals: Among them, N θ is the dynamic radius neighborhood, F j is the original fitness value of neighbor individual j, ∈2 is a very small positive number; The selection probability of neighbor individual j is: like or ∑p j ≤0, then force normalization to uniform distribution: Where V is the index of the selected neighbor individuals in dimension d, d = Dim is the dimension, and the number of selected neighbors is controlled by adjusting d to balance centralized development and decentralized exploration; Multinomial represents probability-based multinomial sampling; r1=Permute([1,2,...,n]); Permute indicates random permutation operation, r1 indicates random permutation index; X DLD =X (χ，d) +η·(X (V，d) -X (ρ，d) ); X (χ,d) is the original position of the current individual χ in the dth dimension, X (V，d) represents the position of the neighbor individual in the dth dimension, ρ = r1(iter) is the random individual index corresponding to individual χ in the random permutation index r1, and η~U(0,1) is a uniformly distributed random number; By X (V，d) With X (ρ，d) The difference vector of adds perturbations to the current position to expand the search range; each dimension selects the neighbor individual index V separately, allowing different dimensions to explore in different directions and avoiding inefficient searches caused by coupling between dimensions; the random number η dynamically adjusts the perturbation intensity, η→0 tends to local development, and η→1 tends to global exploration; X DLH is the position updated by the candidate update strategy, X GWO The updated position of the individual using the GWO algorithm; Compare two candidates X GWO and X DLH The fitness value is used to select the optimal solution, which is the next updated position.

9. The drone search method based on the multi-strategy gray wolf algorithm according to claim 1 or 3, characterized in that: The three-dimensional terrain model includes a digital terrain model and other terrain models; The expression of the digital terrain model is: z=sin(y+Ψ1)+Ψ2·sin(x)+Ψ3·cos(Ψ4(y 2 +x 2 ))+Ψ5·cos(Ψ6(y 2 +x 2 ))+Ψ7·cos(y) Where (x, y) is the horizontal coordinate, z is the horizontal height corresponding to the horizontal coordinate; ψ1, ψ2, ψ3, ψ4, ψ5, ψ6, ψ7 are all coefficients; The other terrain models include a threat area terrain model and a mountain terrain model. The expression of the threat area terrain model is: ((x-x threat ) 2 +(y-y threat ) 2 =r threat 2 )∩(z=[0,h]); In the formula, (x threat ,y threat ) represents the location coordinates of the threat area, r threat represents the radius of the threat area, and h represents the height of the threat area; The expression of the mountain terrain model is: Where h(x,y) is the peak height corresponding to the horizontal coordinate; h e represents the altitude of the peak; B1 and B2 are the horizontal coordinates corresponding to the highest point of the peak; b1 and b2 represent the variables of the slope of the peak along the x and y directions, and exp is the exponential function; E is the total number of peaks, h0 is the lowest position of the peak, and the subscript e is the sequence number of the peak.

10. The drone search method based on the multi-strategy gray wolf algorithm according to claim 9 is characterized in that: The expression of the multi-objective evaluation function is: f=f1*P+f2*H+f3*C; Among them, f1 is the weight coefficient of the path length P, f2 is the weight coefficient of the flight height H, and f3 is the weight coefficient of the flight turning angle C; the value of the flight height H is obtained by calculating the square root of the difference between each element and the mean, and then summing all the results; the value of the flight height H is obtained by calculating the square root of the difference between each element and the mean, and then summing all the results; the flight turning angle C is obtained by calculating and summing the cosine values ​​of the angles between all adjacent differential vectors.

Images