Multi-unmanned aerial vehicle cooperative path planning method based on improved MPGWO algorithm

Abstract

The invention discloses a multi-unmanned-aerial-vehicle cooperative path planning method based on an improved MPGWO algorithm, and belongs to the technical field of path planning, and the method comprises the steps: initializing a multi-unmanned-aerial-vehicle path planning task which comprises the target function of path planning, the position of an unmanned aerial vehicle, parameters and other information; then, constructing a three-dimensional environment map which comprises complex terrains and static cylindrical obstacles; secondly, relevant algorithm parameters are initialized, a population is initialized based on an SPSO algorithm, and a high-quality initial solution is generated; layering according to the fitness values, dynamically adjusting the number and the distribution mode of the sub-populations, and evaluating the fitness values of the individuals; secondly, independently optimizing each sub-population by adopting an improved MPGWO algorithm, and updating all individual positions meeting constraint conditions; the sub-populations share the global optimum alpha wolf every certain iteration times, and the fitness value and the global optimum solution of each sub-population are updated; and when the algorithm reaches the maximum number of iterations, outputting an optimal path. According to the method, by improving the MPGWO algorithm, the optimization efficiency and the solution quality of multi-unmanned aerial vehicle cooperative path planning are improved, the feasibility of the path is ensured, and finally efficient path planning and obstacle avoidance are realized.

Description

Technical Field

[0001] The present invention belongs to the field of path planning, and in particular relates to a multi-UAV collaborative path planning method based on an improved MPGWO algorithm. Background Art

[0002] The core task of path planning is to find the optimal path for a mobile entity from its starting point to its destination. This path must not only meet basic feasibility requirements but also comprehensively consider multiple factors, such as time, distance, cost, and safety. By optimizing the path to meet specific performance metrics, efficient mission execution is achieved. Path planning has a wide range of applications, including logistics, transportation, robotics, game design, and drone path planning. Drone path planning, due to its complexity and widespread application, has become a particularly interesting and challenging subfield within the path planning field.

[0003] With the rapid development of drone technology, the application of drones in various fields, including military reconnaissance, logistics distribution, and disaster relief, continues to expand. Multi-UAV collaborative path planning, as one of the core tasks in drone path planning, has become a hot topic of research. The coordinated operation and mission execution of multiple drones require efficient path planning algorithms to optimize flight trajectories. This not only improves mission efficiency and reduces energy consumption, but also ensures flight safety and promotes collaboration among multiple drones. Achieving multi-UAV collaborative flight through intelligent path planning, particularly in dynamic environments, has become a key issue in the current development of drone technology. Existing path planning algorithms, such as the A* algorithm and the Dijkstra algorithm, perform well for single-UAV path planning, efficiently finding the shortest path. However, when faced with the simultaneous path planning of multiple drones, these traditional algorithms face challenges such as high computational complexity and difficulty in achieving a global optimal solution. Their performance can significantly degrade, especially in complex three-dimensional environments. To address these issues, researchers are exploring more efficient and stable multi-UAV path planning methods.

[0004] The Multi-Population Grey Wolf Optimizer (MPGWO) algorithm is an improved version of the classic Grey Wolf Optimizer (GWO) algorithm. It incorporates the concept of a multi-population mechanism by partitioning the entire population into multiple sub-populations and optimizing them accordingly, enhancing the algorithm's global search capabilities and solution diversity. GWO optimizes the objective function through a collaborative mechanism based on the hunting behavior and social hierarchy of gray wolves. However, its single pack structure can lead to local optima in complex multi-objective problems. The MPGWO algorithm incorporates multi-population partitioning, population collaboration, and enhanced diversity, improving its global search capabilities and making it suitable for multi-objective optimization problems in multi-UAV path planning, such as simultaneously optimizing multiple objectives such as path length, number of collisions, and flight time. The traditional MPGWO algorithm enhances global search capabilities through multiple population divisions. However, its fixed population division method, single position update mechanism, and randomness of the initial solution limit the algorithm's optimization performance in high-dimensional complex problems. Its application in multi-UAV path planning still faces the dilemma of local optimal solutions, especially in large-scale, multi-path tasks, which are prone to low search efficiency and poor solution quality.

[0005] In order to overcome the above challenges, the present invention proposes a multi-UAV path planning method based on an improved MPGWO algorithm. The MPGWO algorithm is improved by proposing an improved MPGWO algorithm based on dynamic subpopulation division, a position update mechanism integrating historical optimality, a population initialization strategy using the spherical particle swarm optimization (SPSO) algorithm, and a constraint processing mechanism, so as to enhance the algorithm's global search capability, convergence efficiency, and solution diversity. Specifically, dynamic subpopulation division balances global exploration and local development by iteratively adjusting the population structure; the position update mechanism integrating historical optimality improves search efficiency; the SPSO population initialization strategy improves the quality of the initial solution through spherical projection to avoid premature convergence; the constraint processing mechanism ensures that multiple UAVs effectively avoid collisions during flight and collaboratively complete tasks, thereby improving overall efficiency.

[0006] Through these improvements, the method of the present invention can provide a more efficient, accurate and reliable solution in multi-UAV path planning tasks, significantly improve the optimization efficiency and solution quality of multi-UAV collaborative path planning, ensure the feasibility of the path, and provide a reliable solution for practical applications. Summary of the Invention

[0007] The technical problem to be solved by the present invention is to overcome the shortcomings of the existing technology and propose a multi-UAV collaborative path planning method with an improved MPGWO algorithm, so as to obtain better planning effect by improving the algorithm.

[0008] The technical solution adopted by the present invention is: a multi-UAV collaborative path planning method based on an improved MPGWO algorithm, comprising:

[0009] Step 1: Initialize the multi-UAV path planning task, including the objective function of path planning, UAV positions and parameters, and other information;

[0010] Step 2: Model the environment information, including the environment map, obstacle locations, and flightable areas;

[0011] Step 3: In the initialization phase, initialize the algorithm parameters, use SPSO to initialize the population, and generate high-quality initial solutions;

[0012] Step 4: Dynamic subpopulation division: calculate the fitness value of each individual according to the objective function, stratify according to the fitness value of the current population, dynamically adjust the number of subpopulations and the distribution method, and evenly distribute individuals to each subpopulation;

[0013] Step 5: Optimize within the subpopulation. Perform optimization on each subpopulation independently, update α, β, and δ wolves, update the positions of all individuals, check whether the path collides with static obstacles or collides with each other, adjust the path if collision occurs, and calculate the individual fitness value and subpopulation optimal solution after the path adjustment.

[0014] Step 6: Population collaboration, using the population collaboration mechanism of MPGWO, every G iterations, each sub-population shares the global optimal α wolf, and after collaboration, recalculates the fitness value of each sub-population and updates the global optimal solution;

[0015] Step 7, termination condition, determine whether the maximum number of iterations has been reached, if so, terminate the iteration, otherwise return to step 4;

[0016] Step 8: Output the results and the optimal path.

[0017] The issues regarding the drone's position and parameters mentioned in step 1 above include:

[0018] The objective function of drone i takes into account the path length cost f i , for the entire UAV cluster, the overall objective function is:

[0019] Initialize the starting and target positions of each drone, the safety distance of the drone, etc.

[0020] The environmental information modeling described in step 2 above includes:

[0021] Set up a 3D simulation environment, set the X, Y, and Z coordinate ranges for the environment map size, and use different colors to represent the flyable area and obstacle area in the environment map.

[0022] The initialization algorithm parameters and the SPSO initialization population content described in step 3 above include:

[0023] Initialize the relevant parameters of the SPSO algorithm, including particle swarm size, inertia weight w1, learning factors c1 and c2, and maximum number of iterations T SPSO Initialize MPGWO algorithm parameters, including wolf pack size, subpopulation number N, maximum number of iterations T MPGWO , inertia weight w2, learning factor C s , linear convergence factor a, etc., SPSO constrains the position update of the particle swarm to a high-dimensional sphere or sphere, calculates the fitness value for each particle (path), and records the individual optimal pbest i and the global optimal gbest.

[0024] Update the particle's velocity and position according to the following formula: v i (t+1)=w1·v i (t)+c1·r1(pbest i -x i (t))+c2·r2(gbest-x i (t))

[0025] where v i (t) is the velocity of particle i at time t, w1 is the inertia weight, c1 and c2 are learning factors, r1 and r2 are random numbers in [0, 1], x i (t) is the position of particle i at time t, C is the center of the sphere, and the radius is R. Ensure that all particles are within the spherical area and the algorithm reaches the maximum number of iterations T SPSO Or the fitness value converges, then stop.

[0026] The dynamic subpopulation division described in step 4 above includes:

[0027] Building on the multi-population partitioning of MPGWO, the algorithm dynamically adjusts the subpopulation size and the number of wolves in each subpopulation based on the iteration stage, and employs a fitness-based hierarchical partitioning strategy. Based on the total number of algorithm iterations, the algorithm's first 30%, middle 40%, and last 30% are categorized as the initial, mid, and late iteration stages, respectively. In the initial iteration, a larger subpopulation size (40% of the total population) is set, while the number of wolves in each subpopulation is smaller, to enhance global exploration. In the mid-iteration stage (25% of the total population), the subpopulation size and the number of wolves in each subpopulation are adjusted to a moderate level, balancing global exploration with local search. In the late iteration stage, a smaller subpopulation size (15% of the total population) is set, while the number of wolves in each subpopulation is larger, to enhance local search and accelerate algorithm convergence.

[0028] When dividing subpopulations, all individuals in the entire wolf pack are first sorted from low to high according to their fitness values ​​(lower fitness means better fitness), and then divided into three layers: excellent (top 30%), medium (middle 40%), and poor (bottom 30%). According to the number of subpopulations determined in the current iteration stage, the stratified individuals are evenly distributed to each subpopulation. Specifically, individuals are drawn from the excellent layer, medium layer, and poor layer respectively to ensure that each subpopulation contains the same proportion of excellent, medium, and poor individuals.

[0029] The specific operations of the subpopulation optimization described in step 5 above include:

[0030] The MPGWO algorithm inherits the social hierarchy and hunting mechanism of GWO and simulates the leadership hierarchy formed by gray wolves during hunting. It consists of α, β, δ, and ω wolves, with α, β, and δ representing the optimal, suboptimal, and third-optimal solutions, respectively. The remaining wolves are collectively referred to as ω wolves. They each assume different roles to achieve group cooperation and efficient goal achievement, independently optimizing each subpopulation. Specifically, α, β, and δ wolves guide ω wolves and assist them in searching for the optimal solution. ω wolves, being relatively weak, accept guidance and update their position: Among them, X(t+1) represents the updated position of ω wolf at the t+1th iteration, X1, X2, and X3 represent the intermediate positions calculated based on the positions of α wolf, β wolf, and δ wolf, respectively, which are used to guide the next movement of ω wolf. The calculation formula is as follows: Among them, X α 、X β 、X δDenote the positions of α, β, and δ wolves at the tth iteration, respectively, corresponding to the optimal, suboptimal, and third-optimal solutions in the current population; A is the coefficient controlling the distance, A = 2a·r1-a, r1 is a random number, r1∈[0,1], and a is a linearly decreasing parameter; D α 、D β and D δ Represents the distance between the current wolf (ω wolf) and the positions of α, β, and δ wolves. The calculation formula is:

[0031] Among them, x(t) represents the position of the current wolf (ωwolf) at the tth iteration; C is the random coefficient, C = 2.r2, r2 is a random number, r2∈[0,1].

[0032] The present invention increases the randomness and diversity of the search by integrating the historically optimal position update mechanism. The position update formula of ω wolf is as follows:

[0033] Among them, v i (t+1) represents the next iteration speed of individual i, w2 is the inertia weight, C s is the learning factor, r s is a random number, r s ∈[0,1],X s are the positions of the leading wolves α, β, and δ, where s∈{α, β, δ}; γ∈[0, 1] is the fusion coefficient, balancing the contribution of GWO.

[0034] In each iteration of the algorithm, the path is checked to see if it satisfies the static environmental constraints and dynamic coordination constraints. The main contents are as follows:

[0035] Under the constraints of a static environment, the waypoints need to avoid obstacles and not cross the boundary, and must meet the following requirements: dist((x i ,y i , z i ), O abs )>d safety

[0036] Among them, dist is the shortest Euclidean distance from the point to the center of all obstacles, O abs is the obstacle area, d safety is the safety distance threshold, and the collision point P that does not meet the constraint d Adjust to P avoid :

[0037] Where Δd is the offset distance, To avoid the direction vector, that is, the center point of the collision obstacle to the collision point P d Vector direction to ensure that the new waypoint maintains a safe distance from obstacles.

[0038] Under the dynamic coordination constraint, the spatiotemporal conflict detection of UAVs is carried out: for any two UAVs i and j, the UAV trajectories are checked to see if they conflict at the same time t and the same spatial position (x, y, z). ik , t i(k+1) ], determine the path segments reached by the two drones are [P ik , P i(k+1) ] and [P jk , P j(k+1) ], then at time t∈[t ik , t i(k+1) ], the positions of drones i and j are:

[0039] The distance between the two drones is:

[0040] If d ij (t) <d safety , it is determined to be a spatiotemporal conflict, and the corresponding path point is marked as the conflict point P c , the conflict point P that does not satisfy the constraints c Adjust to P′ avoid , ensure a safe distance between drones:

[0041] Where Δd is the offset distance, To avoid the direction vector, that is, the opposite direction vector between the drone and the conflict point, ensure that a safe distance is maintained between the drones.

[0042] The content of population collaboration described in step 6 above includes:

[0043] After G iterations, the local optimal solutions of all subpopulations are collected, their fitness values ​​are compared, the global optimal α wolf is selected, and its position information is passed to each subpopulation. In each subpopulation, the individuals with the worst fitness are selected according to the fitness value sorting, and the positions of these individuals are replaced with the positions of the global optimal α wolf. After the replacement, the fitness values ​​of all individuals in each subpopulation are recalculated, and the local optimal solutions and global optimal solutions of the subpopulations are updated.

[0044] Repeat steps 4-6 until the maximum number of iterations is reached and the optimal path is output; BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1It is a flow chart of the present invention.

[0046] Figure 2 1 is a test function diagram and a fitness curve diagram of Example 1.

[0047] Figure 3 It is the environment diagram of the path planning task in Example 2.

[0048] Figure 4 It is the path planning graph of the SPSO algorithm in Example 2.

[0049] Figure 5 It is the path planning graph of the MPGWO algorithm in Example 2.

[0050] Figure 6 is the path planning diagram of the algorithm of the present invention in Example 2 DETAILED DESCRIPTION

[0051] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. The following embodiments are used to illustrate the present invention but are not intended to limit the scope of protection of the present invention.

[0052] Example 1: Algorithm flow as follows Figure 1 As shown in the figure, a comparative experiment is carried out on the standard test function to comprehensively evaluate the convergence speed, global search ability and stability of the optimization algorithm. In this experiment, four algorithms, MPGWO, PSO, SPSO and the improved MPGWO of the present invention are selected for comparison. The test function dimension is set to 30, the population size is 50, and the maximum number of iterations is 30. Three representative functions are selected for the experiment:

[0053] F3 (Shifted Rotated High Conditioned Elliptic Function, single-peak function, evaluates convergence speed), F13 (Shifted Rotated Expanded Scaffer's F6 Function, multi-peak function, evaluates global search capability), F20 (Rotated Hybrid Composition Function with a Narrow Basin for the Global Optimum, hybrid combination function, evaluates comprehensive performance);

[0054] Each algorithm was run independently 30 times on each test function, and the average fitness value was taken to draw the convergence curve as shown in Figure 2 The worst value, best value, average value and standard deviation are statistically analyzed to evaluate the stability and optimization accuracy of the algorithm. The experimental results are shown in Table 1. Table 1 Function test results

[0055] Test results show that the improved MPGWO algorithm outperforms PSO, SPSO, and MPGWO on all test functions, demonstrating superior optimization accuracy, convergence consistency, and stability. The algorithm's global search capabilities are particularly prominent on complex, multi-modal, and mixed combination functions, effectively avoiding local optima and providing a superior solution to complex optimization problems.

[0056] Example 2: To systematically verify the performance of the improved MPGWO algorithm in multi-UAV collaborative path planning, the present invention designed a comparative experiment to evaluate the key indicators of path planning and analyze and compare the performance differences between the improved MPGWO algorithm and other algorithms. The experimental comparison includes the SPSO algorithm, the MPGWO algorithm, and the algorithm of the present invention (the improved MPGWO algorithm). The experiment was conducted in the following steps:

[0057] Implementation step 1: First, initialize the multi-UAV path planning task, with the path length minimization as the experimental goal, set the starting points of the four UAVs to [50, 100, 150; 100, 55, 150; 30, 20, 150; 105, 120, 150], and the target points to [875, 875, 160; 800, 875, 180; 875, 800, 150; 800, 800, 200];

[0058] Set the drone safety distance d safety = 25m, ensuring that there is no collision between drones and meeting safety requirements;

[0059] Implement step 2, and then build the 3D map environment information such as Figure 3 As shown, a three-dimensional simulation environment map is set up, where the green area represents the complex and uneven terrain that can be flown (altitude variation 0-400m), and the red cylinders represent static obstacles, with obstacle diameters ranging from 20-70m and heights ranging from 100-300m, distributed in the map;

[0060] In step 3, set the algorithm parameters. For example, SPSO parameters include the number of particles 60, inertia weight w1 = 0.9, and learning factor c1 = c2 = 2; MPGWO algorithm parameters include the wolf pack size 60, the number of subpopulations N = 10, inertia weight w2 = 0.8, the random coefficient a linearly decreases from 2 to 0, and the learning factor C s =2, fusion coefficient γ = 0.5, and the maximum number of iterations is uniformly set to 300;

[0061] The SPSO algorithm is used to perform fast global search to initialize the population, and the particle swarm is guided to explore the potential high-quality solution space through individual optimal and global optimal, generating high-quality initial solutions.

[0062] Implement step 4. Based on the SPSO initialized population, dynamically adjust the number of subpopulations and the number of wolves in each subpopulation during the iteration phase. Sort the individuals by fitness value from low to high (lower fitness means better), and divide them into three layers: good, medium, and poor. According to the stratification results, evenly distribute the individuals in the good, medium, and poor layers to each subpopulation.

[0063] Implement step 5, optimize each subpopulation independently, update α, β and δ wolves, update the positions of all individuals, check whether the paths meet the constraints, adjust the paths that do not meet the constraints, calculate the fitness value of the updated individuals and the optimal solution within the subpopulation;

[0064] Every 50 iterations, each subpopulation shares the global optimal α wolf, and after collaboration, recalculates the fitness value of each subpopulation and updates the global optimal solution;

[0065] Repeat the above operation until the maximum number of iterations is reached, and finally output the optimal path;

[0066] Different algorithms were run independently 30 times, and the average value was taken as the data output, as shown in Table 2. Figure 4 、 5 ,6 respectively show the path planning results of different algorithms, where the dark blue rectangle represents the starting position, and the light blue circle represents the end position. Table 2 Algorithm experimental results

[0067] Experimental data analysis shows that the improved MPGWO algorithm performs best across all metrics, achieving the shortest total path length, complete collision avoidance, the lowest objective function value, a short runtime, and excellent distribution uniformity. The MPGWO algorithm outperforms the SPSO algorithm, with the improved version significantly improving path planning quality while maintaining a low runtime. The improved MPGWO algorithm significantly enhances both global search and local exploitation capabilities, demonstrating excellent performance in multi-UAV collaborative path planning, providing reliable theoretical support and practical reference for practical applications.

[0068] In summary, the method of the present invention demonstrates efficient and safe performance in the collaborative path planning process of multiple UAVs in a three-dimensional complex environment, has higher applicability and robustness, further improves the balance between global search and local optimization, and is applicable to a variety of complex path planning problems.

Claims

1. A multi-UAV collaborative path planning method based on the improved MPGWO algorithm is characterized by: The steps include: Step 1: Initialize the multi-UAV path planning task, including the objective function of path planning, UAV positions and parameters, and other information; Step 2: Model the environment information, including the environment map, obstacle locations, and flightable areas; Step 3: In the initialization phase, initialize the algorithm parameters, use SPSO to initialize the population, and generate high-quality initial solutions; Step 4: Dynamic subpopulation division: calculate the fitness value of each individual according to the objective function, stratify according to the fitness value of the current population, dynamically adjust the number of subpopulations and the distribution method, and evenly distribute individuals to each subpopulation; Step 5: Optimize within the subpopulation. Perform optimization on each subpopulation independently, update α, β, and δ wolves, update all individual positions, check and adjust constraints, and calculate the fitness value of the updated individuals and the optimal solution within the subpopulation. Step 6: Population collaboration, using the population collaboration mechanism of MPGWO, every G iterations, each sub-population shares the global optimal α wolf, and after collaboration, recalculates the fitness value of each sub-population and updates the global optimal solution; Step 7, termination condition, determine whether the maximum number of iterations has been reached, if so, terminate the iteration, otherwise return to step 4; Step 8: Output the results and the optimal path.

2. The multi-UAV collaborative path planning method based on the improved MPGWO algorithm described in claim 1 is characterized in that: The step 3 of initializing the population using SPSO includes: Initialize the relevant parameters of the SPSO algorithm, including particle swarm size, inertia weight w1, learning factors c1 and c2, and maximum number of iterations T SPSO Initialize MPGWO algorithm parameters, including wolf pack size, subpopulation number N, maximum number of iterations T MPGWO , inertia weight w2, learning factor C s , linear convergence factor a, etc.; SPSO constrains the position update of the particle swarm to a high-dimensional sphere or within a sphere, calculates the fitness value for each particle (path), and records the individual optimal pbest i and global optimal gbest; SPSO constrains the position update of the particle swarm to a high-dimensional sphere or within a sphere, calculates the fitness value for each particle (path), and records the individual optimal pbest i And the global optimal gbest, the speed update formula of SPSO is: v i (t+1)=w1·v i (t)+c1·r1(pbest i -x i (t))+c2·r2(gbest-x i (t)) where v i (t) is the velocity of particle i at time t, w1 is the inertia weight, c1 and c2 are learning factors, r1 and r2 are random numbers in [0, 1], pbest i is the historical optimal position of particle i, gbest is the global optimal position, x i (t) is the position of particle i at time t, and the position update formula is: Where C is the center of the sphere and the radius is R. It is necessary to ensure that all particles are located within the spherical area and the algorithm reaches the maximum number of iterations T. SPSO Or the fitness value converges, it stops. The SPSO algorithm generates high-quality solutions by iteratively optimizing the distribution of the initial population.

3. The multi-UAV collaborative path planning method based on the improved MPGWO algorithm as described in claim 1 is characterized in that: The step 4 of dynamic subpopulation division includes: Based on the multi-population division of MPGWO, the number of subpopulations and the number of wolves in each subpopulation are dynamically adjusted based on the iteration stage, and the subpopulations are divided using a fitness stratification strategy. Based on the total number of algorithm iterations, the first 30% iterations, the middle 40% iterations, and the last 30% iterations of the algorithm are represented as the initial iteration, the middle iteration, and the late iteration stages, respectively. In the early iteration, a larger number of subpopulations (40% of the total population) is set, while the number of wolves in each subpopulation is smaller, to enhance global exploration capabilities. In the middle iteration (25% of the total population), the number of subpopulations and the number of wolves in each subpopulation are adjusted to a moderate level to balance global exploration and local search. In the late iteration, a smaller number of subpopulations (15% of the total population) is set, while the number of wolves in each subpopulation is larger, to enhance local search capabilities and accelerate algorithm convergence. When dividing subpopulations, all individuals in the entire wolf pack are first sorted from low to high according to their fitness values ​​(lower fitness means better fitness), and then divided into three layers: excellent (top 30%), medium (middle 40%), and poor (bottom 30%). According to the number of subpopulations determined in the current iteration stage, the stratified individuals are evenly distributed to each subpopulation. Specifically, individuals are drawn from the excellent layer, medium layer, and poor layer respectively to ensure that each subpopulation contains the same proportion of excellent, medium, and poor individuals.

4. The multi-UAV collaborative path planning method based on the improved MPGWO algorithm described in claim 1 is characterized in that: The optimization within the subpopulation in step 5 includes: The MPGWO algorithm inherits the social hierarchy and hunting mechanism of GWO and simulates the leadership hierarchy formed by gray wolves during the hunting process. It includes α, β, δ, and ω wolves, among which α, β, and δ represent the optimal solution, the second-best solution, and the third-best solution, respectively. The remaining wolves are collectively referred to as ω wolves. They each assume different task roles to achieve group cooperation and efficient goal achievement, and independently optimize each sub-population. Specifically, α, β, and δ wolves are responsible for guiding ω wolves and assisting in searching for the optimal solution. ω wolves are relatively weak and accept guidance and update ω wolves' position: Among them, X(t+1) represents the updated position of ω wolf at the t+1th iteration, X1, X2, and X3 represent the intermediate positions calculated based on the positions of α wolf, β wolf, and δ wolf, respectively, which are used to guide the next movement of ω wolf. The calculation formula is as follows: Among them, X α 、X β 、X δ They represent the positions of α, β and δ wolves at the tth iteration, corresponding to the optimal, suboptimal and third-optimal solutions in the current population; A is the coefficient of the control distance, A = 2a·r1-a, r1 is a random number, r i ∈[0, 1], a is a linearly decreasing parameter; D α 、D β and D δ Represents the distance between the current wolf (ω wolf) and the positions of α, β, and δ wolves. The calculation formula is: Where X(t) represents the position of the current wolf (ωwolf) at the tth iteration; C is the random coefficient, C = 2·r2, r2 is a random number, r2∈[0,1]; The present invention increases the randomness and diversity of the search by integrating the historically optimal position update mechanism. The position update formula of ω wolf is as follows: Among them, v i (t+1) represents the next iteration speed of individual i, w2 is the inertia weight, C s is the learning factor, r s is a random number, r s ∈[0, 1], X s is the position of the leader wolf α, β, δ, where s∈{α, β, δ}, X i (t) represents the current position of individual i (ω wolf), X1, X2, and X3 represent the intermediate positions calculated based on the positions of α wolf, β wolf, and δ wolf, respectively, which are used to guide the next movement of ω wolf, and γ∈[0, 1] is the fusion coefficient to balance the contribution of GWO.

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