A 3D UAV Path Planning Method Based on an Improved Gray Wolf Optimization Algorithm

Abstract

This invention relates to a 3D UAV path planning method based on an improved gray wolf optimization algorithm, comprising: acquiring a 3D environment model; setting the start and end positions of the UAV based on the 3D environment model; employing the improved gray wolf optimization algorithm, using the objective function as the fitness function; updating the positions of all gray wolves synchronously during the iterative process; and outputting the optimal path. This invention introduces a circle chaotic mapping to the gray wolf optimization algorithm to increase population diversity; introduces an adaptive exploration factor to increase the balance between global and local search; combines the global and local development formulas of the dung beetle optimization algorithm to compensate for the slow convergence speed of the traditional gray wolf optimization algorithm; subsequently introduces a sine and cosine strategy to help the algorithm search for potential optimal solution regions, thus better exploring the global optimal solution; and finally introduces a pooling mechanism to randomly recombine stored historical poor solutions to generate new solutions, accelerating the convergence speed and improving the robustness of the algorithm.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) path planning technology, and in particular to a three-dimensional UAV path planning method based on an improved gray wolf optimization algorithm. Background Technology

[0002] In recent years, drone technology has been increasingly applied in military, civilian, and commercial fields, covering various scenarios such as disaster relief, agricultural monitoring, and logistics delivery. Path planning is one of the core issues of drone autonomous navigation, especially in complex three-dimensional environments. How to efficiently and safely plan an optimal path has become an extremely challenging task.

[0003] Traditional path planning methods (such as A* and Dijkstra's algorithms), while performing excellently in 2D scenes, suffer from high computational complexity in 3D environments and struggle to handle dynamic obstacles and complex terrain, often failing to meet real-time and accuracy requirements. Furthermore, traditional algorithms are prone to computational bottlenecks and low planning efficiency when facing large search spaces. To overcome these limitations, path planning methods based on intelligent optimization algorithms (such as genetic algorithms and particle swarm optimization) have gradually become a research hotspot in recent years. The Grey Wolf Optimization (GWO) algorithm is an emerging swarm intelligence optimization algorithm that has received widespread attention in recent years due to its fast convergence speed and simple parameter settings. However, despite its excellent performance in simple optimization problems, the GWO algorithm still has shortcomings when dealing with complex problems. Its convergence accuracy and stability need further improvement, and it suffers from local optima and insufficient convergence accuracy when handling complex 3D path planning problems. Summary of the Invention

[0004] To address the problems existing in the prior art, the purpose of this invention is to provide a 3D UAV path planning method based on an improved Grey Wolf optimization algorithm, thereby enhancing the search capability, convergence accuracy, and obstacle avoidance capability of 3D path planning. This invention uses fitness function planning based on factors such as path length, altitude change, and smoothness during UAV flight, combined with the Grey Wolf optimization algorithm for path optimization.

[0005] To achieve the above objectives, the present invention provides the following solution:

[0006] A 3D UAV path planning method based on an improved gray wolf optimization algorithm includes:

[0007] A 3D environment model is obtained. Based on the 3D environment model, the starting and ending positions of the UAV are set. An improved gray wolf optimization algorithm is adopted, with the objective function forming the fitness function. During the iteration process, the positions of all gray wolves are updated synchronously, and the optimal path is output. The objective function includes: path length, altitude change, smoothness, and violation term.

[0008] The optimal path output using the improved Grey Wolf optimization algorithm includes:

[0009] Step 1: Initialize the population using the circle chaotic mapping to generate initial paths;

[0010] Step 2: Calculate the fitness value of the initial path according to the fitness function;

[0011] Step 3: Replace the shrinkage coefficient of the gray wolf optimization algorithm with an adaptive exploration factor to update the position of the gray wolf population. In the process of updating the position of the gray wolf population, introduce the global and local search mechanism of the dung beetle optimization algorithm to dynamically adjust the mechanism to balance the global and local exploration. Introduce the sine and cosine optimization strategy to jump out of local extreme values ​​during the optimization process. Introduce the pooling mechanism to store poor solutions and reuse the poor solutions in subsequent iterations.

[0012] Step 4: Calculate the fitness value of the current gray wolf population position based on the fitness function;

[0013] Step 5: Determine if the maximum iteration condition is met. If the maximum iteration condition is not met, repeat steps 1-4 until the maximum iteration condition is met. If the maximum iteration condition is met, output the optimal path.

[0014] Optionally, the fitness function comprises:

[0015] L=(ω1·J path +ω2·J hight +ω3·J smooth )+Violation·p f

[0016] Where ω1, ω2, and ω3 are weights, J path J is the path length. hight For height variation, J smooth For smoothness, p f The penalty factor is 'Violation', which is a default term.

[0017] Optionally, initializing the population using the circle chaotic map includes:

[0018]

[0019] Among them, Positions i+1 Positions are the mapped positions. i Let i be the original position, i represent the dimension, and a and b are both natural numbers.

[0020] Optionally, the expression for the adaptive exploration factor is:

[0021]

[0022] Where l is the number of iterations, and Max_iter is the maximum number of iterations.

[0023] Optionally, replacing the shrinkage coefficient of the gray wolf optimization algorithm with the adaptive exploration factor includes:

[0024] A = 2a·r1-a

[0025] C = 2r²

[0026] Where C and A are coefficient vectors, and r1 and r2 are random vectors in [0,1].

[0027] Optionally, updating the location of the gray wolf population includes:

[0028]

[0029] Among them, D α D β D δ Let α, β, and δ represent the distances between α, β, and δ and other individuals, respectively. Let l be the current iteration number, C1, C2, and C3 be the coefficient vectors, and Positions be the distances between α, β, and δ and other individuals. α Positions β Positions δ Let α, β, and δ be the position vectors of wolves in the current population, and Positions(l) be the individual position vectors of gray wolves in the l-th iteration.

[0030]

[0031] Positions(l+1)=(Positions1+Positions2+Positions3) / 3

[0032] Where Position1, Position2, and Position3 are position update vectors guided by α, β, and δ wolves.

[0033] Optionally, the dynamic adjustment mechanism of the global and local search mechanisms in the dung beetle optimization algorithm to balance global and local exploration includes:

[0034]

[0035] Where Alpha_pos is the current optimal solution, Worse_pos is the worse solution, Delta_pos is the suboptimal solution, a is the random coefficient, 0.3 and 0.1 are the weight coefficients, θ is the random angle, tan(θ) is the random step size generated, and r1 is the random factor.

[0036] Optionally, introducing the sine and cosine optimization strategy to escape local optima during the optimization process includes:

[0037]

[0038] Where ω is the dynamic inertia weight, r2 is the random angle factor, r3 is a random factor, and Alpha_pos is the position of the current optimal solution. Let be the position of the i-th gray wolf in the j-th dimension during the l-th iteration.

[0039] Optionally, introducing the pooling mechanism to store poor solutions includes:

[0040] P = B × X brnd +(1-B)×X worst

[0041] Where P is the matrix used to store poor solutions in the pooling mechanism, B is a randomly generated binary matrix, and X... brnd The position is randomly generated based on the current optimal solution; X worst This is the worst solution in the current iteration.

[0042] The beneficial effects of this invention are as follows:

[0043] This invention utilizes fitness function planning based on path length, altitude changes, and smoothness during UAV flight, combined with the Grey Wolf Optimization Algorithm for path optimization. The invention introduces a circle chaotic mapping to the Grey Wolf Optimization Algorithm to increase population diversity; it introduces an adaptive exploration factor to improve the balance between global and local search; it incorporates the global and local development formulas of the Dung Beetle Optimization Algorithm to compensate for the slow convergence speed of the traditional Grey Wolf Optimization Algorithm, balancing exploration and development; subsequently, it introduces a sine and cosine strategy to help the algorithm search for potential optimal solution regions, enabling better exploration of the global optimum; finally, it introduces a pooling mechanism to randomly reorganize stored historical poor solutions to generate new solutions, accelerating the convergence speed and improving the algorithm's robustness. Attached Figure Description

[0044] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0045] Figure 1 This is a flowchart of a 3D UAV path planning method based on an improved gray wolf optimization algorithm according to an embodiment of the present invention.

[0046] Figure 2 This is a three-dimensional environment simulation diagram of an embodiment of the present invention;

[0047] Figure 3 The above are contour path diagrams of the original and improved Grey Wolf algorithms according to embodiments of the present invention.

[0048] Figure 4 The original and improved gray wolf algorithms of this invention are shown in three-dimensional path diagrams.

[0049] Figure 5 The fitness function curves of the original gray wolf algorithm and the improved gray wolf algorithm in this embodiment of the invention are shown. Detailed Implementation

[0050] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0051] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0052] This embodiment discloses a 3D UAV path planning method based on an improved gray wolf optimization algorithm, including:

[0053] A 3D environment model is obtained. Based on the 3D environment model, the starting and ending positions of the UAV are set. An improved gray wolf optimization algorithm is adopted, with the objective function forming the fitness function. During the iteration process, the positions of all gray wolves are updated synchronously, and the optimal path is output. The objective function includes: path length, altitude change, smoothness, and violation term.

[0054] The improved Grey Wolf optimization algorithm outputs the following optimal paths:

[0055] Step 1: Initialize the population using the circle chaotic mapping to generate initial paths;

[0056] Step 2: Calculate the fitness value of the initial path based on the fitness function;

[0057] Step 3: Replace the shrinkage coefficient of the gray wolf optimization algorithm with an adaptive exploration factor to update the position of the gray wolf population. In the process of updating the position of the gray wolf population, introduce the global and local search mechanism of the dung beetle optimization algorithm to dynamically adjust the mechanism to balance global and local exploration. Introduce the sine and cosine optimization strategy to escape local extrema in the optimization process. Introduce the pooling mechanism to store poor solutions and reuse the poor solutions in subsequent iterations.

[0058] Step 4: Calculate the fitness value of the current gray wolf population position based on the fitness function;

[0059] Step 5: Determine if the maximum iteration condition is met. If the maximum iteration condition is not met, repeat steps 1-4 until the maximum iteration condition is met. If the maximum iteration condition is met, output the optimal path.

[0060] Specifically:

[0061] This embodiment discloses a 3D UAV path planning method based on an improved gray wolf optimization algorithm, such as... Figure 1 As shown, the simplified steps of this method are as follows: (1) Establish a three-dimensional environment model. (2) Initialize the gray wolf population using circle chaotic mapping to generate the initial path of the UAV. (3) Calculate the fitness value of the initial path according to the fitness function. (4) Update and record the optimal path. (5) Introduce an adaptive exploration factor to update the position of the gray wolf population. (6) Introduce the global search and local search mechanism of the dung beetle optimization algorithm to update the position of the gray wolf population. (7) Introduce a sine and cosine strategy to update the position of the gray wolf population. (8) Use a pooling mechanism to process poor solutions. (9) Record the current optimal solution. (10) Determine whether the maximum number of iterations has been reached. If not, return to update and record the optimal solution. (11) If satisfied, output the optimal path.

[0062] Furthermore, the fitness function comprises:

[0063] L=(ω1·J path +ω2·J hight +ω3·J smooth )+Violation·p f

[0064] Where ω1, ω2, and ω3 are weights, J path J is the path length. hight For height variation, J smooth For smoothness, p f The penalty factor is 'Violation', which is a default term.

[0065] Specifically:

[0066] This invention utilizes a 150*100*3 three-dimensional environment model of a natural mountain scene with five obstacles of varying sizes and positions. The start and end points of the drone are set at diagonal positions in the coordinate system. This invention plans the fitness function based on factors such as path length, altitude variation, and smoothness.

[0067] To minimize energy consumption and time during flight, the specific formula for path length is as follows:

[0068]

[0069] In the formula, x i y i z i These represent the x-coordinate, y-coordinate, and altitude values ​​of the UAV at the i-th step during its flight; i+1 y i+1 z i+1 These represent the x-coordinate, y-coordinate, and altitude values ​​of the UAV at the (i+1)th step during its flight.

[0070] To avoid unnecessary vertical fluctuations in the control path during flight, the specific formula for altitude change is as follows:

[0071]

[0072] In the formula, n is the number of data points, and μ is the average altitude during the UAV path optimization process.

[0073] To avoid sharp turns during flight and promote stable drone movement, the specific formula for smoothness is:

[0074]

[0075] In the formula, θ represents the deflection angle of the i-th point.

[0076] To ensure safety and avoid obstacles during flight, the specific formula for the breach of contract is as follows:

[0077]

[0078] In the formula, M represents the number of obstacles, and d i r is the distance from the path point to the center of the i-th obstacle. i It is the radius of influence of the i-th obstacle.

[0079] The final fitness function is derived from the above four evaluation indicators:

[0080] L=(ω1·J path +ω2·J hight +ω3·Jsmooth )+Violation·p f

[0081] In the formula, ω1, ω2, and ω3 are weights, defined as ω1 = 0.5; ω2 = 0.3; ω3 = 0.2, p f The penalty factor is defined as 10. 5 .

[0082] Furthermore, initializing the population using the circle chaotic map includes:

[0083]

[0084] Among them, Positions i+1 Positions are the mapped positions. i Let i be the original position, i represent the dimension, and a and b are both natural numbers.

[0085] Furthermore, the expression for the adaptive exploration factor is:

[0086]

[0087] Where l is the number of iterations, and Max_iter is the maximum number of iterations.

[0088] Furthermore, replacing the shrinkage coefficient of the gray wolf optimization algorithm with an adaptive exploration factor includes:

[0089] A = 2a·r1-a

[0090] C = 2r²

[0091] Where C and A are coefficient vectors, and r1 and r2 are random vectors in [0,1].

[0092] Furthermore, updating the location of the gray wolf population includes:

[0093]

[0094] Among them, D α D β D δ Let α, β, and δ represent the distances between α, β, and δ and other individuals, respectively. Let l be the current iteration number, C1, C2, and C3 be the coefficient vectors, and Positions be the distances between α, β, and δ and other individuals. α Positions β Positions δ Let α, β, and δ be the position vectors of wolves in the current population, and Positions(l) be the individual position vectors of gray wolves in the l-th iteration.

[0095]

[0096] Positions(l+1)=(Positions1+Positions2+Positions3) / 3

[0097] Where Position1, Position2, and Position3 are position update vectors guided by α, β, and δ wolves.

[0098] Specifically:

[0099] This invention relates to an improved gray wolf optimization algorithm, which introduces a circle chaotic mapping initialization to improve the quality of the initial population; introduces an adaptive exploration factor to balance exploration and development; combines the global and local development formulas of the dung beetle optimization algorithm to enhance the algorithm's convergence accuracy; introduces a sine and cosine strategy to help the algorithm expand the search range; and introduces a pooling mechanism to accelerate the algorithm's convergence speed by storing poor solutions. The specific operation steps are as follows:

[0100] The initial position of the gray wolf is generated using a circle chaotic mapping:

[0101]

[0102] In the formula, a = 0.5; b = 0.2, Positions i+1 Positions are the mapped positions. i The original position is represented by 'i', where 'i' represents the dimension.

[0103] An adaptive exploration factor is used instead of the shrinkage coefficient in the gray wolf optimization algorithm to maintain high exploration capability in the early stages; a quadratic exponential descent smoothly transitions in the mid-stages; and local exploration is promoted in the late stage. This balances the algorithm's global and local search capabilities, improving both convergence accuracy and speed. The specific operation is as follows:

[0104]

[0105] In the formula, l is the number of iterations, and Max_iter is the maximum number of iterations.

[0106] The Grey Wolf's position is updated using the following formula:

[0107] A = 2a·r1-a

[0108] C = 2r²

[0109] In the formula, C and A are coefficient vectors.

[0110]

[0111] In the formula, D α D β Dδ Let α, β, and δ represent the distances between α, β, and δ and other individuals, respectively, and l be the current iteration number.

[0112]

[0113] Positions(l+1)=(Positions1+Positions2+Positions3) / 3

[0114] Positions in the formula α Positions β Positions δ These represent the current positions of α, β, and δ wolves, respectively.

[0115] Furthermore, the dung beetle optimization algorithm introduces a global and local search mechanism and a dynamic adjustment mechanism to balance global and local exploration, including:

[0116]

[0117] Where Alpha_pos is the current optimal solution, Worse_pos is the worse solution, Delta_pos is the suboptimal solution, a is the random coefficient, 0.3 and 0.1 are the weight coefficients, θ is the random angle, tan(θ) is the random step size generated, and r1 is the random factor.

[0118] Furthermore, introducing sine and cosine optimization strategies to escape local maxima during the optimization process includes:

[0119]

[0120] Where ω is the dynamic inertia weight, r2 is the random angle factor, r3 is a random factor, and Alpha_pos is the position of the current optimal solution. for.

[0121] Furthermore, a pooling mechanism is introduced to store poor solutions, including:

[0122] P = B × X brnd +(1-B)×X worst

[0123] Where P is the matrix used to store poor solutions in the pooling mechanism, B is a randomly generated binary matrix, and X... brnd The position is randomly generated based on the current optimal solution; X worst This is the worst solution in the current iteration.

[0124] Specifically:

[0125] The dung beetle optimization algorithm is introduced: Since the gray wolf optimization algorithm is prone to getting trapped in local optima and may converge prematurely, the dung beetle optimization algorithm's search mechanism is introduced. This mechanism dynamically adjusts the balance between global and local exploration, enhancing the search capability of the gray wolf optimization algorithm. The specific expression is shown below.

[0126]

[0127] In the formula, Alpha_pos is the current optimal solution (the position of Alpha wolf); Worse_pos is the worse solution (here, the position of Beta wolf, Beta_pos, is used as the worse solution); Delta_pos is the suboptimal solution (the position of Delta wolf); a is a random coefficient, taking a value of 1 or -1, used to control the search direction; 0.3 and 0.1 are weight coefficients, used to adjust the search step size; θ is a random angle, taking a value in the range [0,π]; tan(θ) is used to generate a random step size, enhancing the diversity of the search.

[0128] A sine and cosine optimization strategy is introduced to improve the optimization ability of the gray wolf search algorithm. The specific expression is as follows:

[0129]

[0130] In the formula, ω is the dynamic inertia weight, which controls the search range and gradually decreases as the number of iterations increases; r1 is a random factor that controls the search step size; r2 is a random angle factor that controls the search direction; r3 is a random factor that controls the distance between the individual and the current optimal solution; and Alpha_pos is the position of the current optimal solution.

[0131] A pooling mechanism is introduced to store historically poor solutions in a pool and reuse these solutions in subsequent iterations, effectively improving the algorithm's convergence performance. The specific operation is as follows:

[0132] P = B × X brnd +(1-B)×X worst

[0133] In the formula, P is the matrix used in the pooling mechanism to store worse solutions, B is a randomly generated binary matrix that determines whether to use the randomly generated solution or the worse solution; X brnd The position is randomly generated based on the current optimal solution; X worst It is the worst solution in the current iteration.

[0134] By establishing a three-dimensional environment model, the experimental scenario is obtained, such as... Figure 2 As shown.

[0135] By comparing the UAV path optimization based on the Gray Wolf Optimization Algorithm and the improved Gray Wolf Optimization Algorithm under the initial conditions, such as Figure 3-4As shown, the 3D UAV path planning method based on the improved gray wolf optimization algorithm of this invention has the best performance.

[0136] By calculating the fitness function and comparing the current fitness values, such as... Figure 5 As shown.

[0137] in, Figure 2-4 The 3D environment model is set as a natural mountain scene of 150*100*3, defining five obstacles of different sizes and positions, as well as the start and end points.

[0138] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A three-dimensional UAV path planning method based on an improved gray wolf optimization algorithm, characterized in that, include: A three-dimensional environment model is obtained. Based on the three-dimensional environment model, the starting position and ending position of the UAV are set. An improved gray wolf optimization algorithm is adopted, with the objective function forming the fitness function. During the iteration process, the position of all gray wolves is updated synchronously, and the optimal path is output. The objective function includes: path length, height variation, smoothness, and violation term; The optimal path output using the improved Grey Wolf optimization algorithm includes: Step 1: Initialize the population using the circle chaotic mapping to generate initial paths; Step 2: Calculate the fitness value of the initial path according to the fitness function; Step 3: Replace the shrinkage coefficient of the gray wolf optimization algorithm with an adaptive exploration factor to update the position of the gray wolf population. In the process of updating the position of the gray wolf population, introduce the global and local search mechanism of the dung beetle optimization algorithm to dynamically adjust the mechanism to balance the global and local exploration. Introduce the sine and cosine optimization strategy to jump out of local extreme values ​​during the optimization process. Introduce the pooling mechanism to store poor solutions and reuse the poor solutions in subsequent iterations. Step 4: Calculate the fitness value of the current gray wolf population position based on the fitness function; Step 5: Determine if the maximum iteration condition is met. If the maximum iteration condition is not met, repeat steps 1-4 until the maximum iteration condition is met. If the maximum iteration condition is met, output the optimal path.

2. The 3D UAV path planning method based on the improved gray wolf optimization algorithm according to claim 1, characterized in that, The fitness function comprises: L=(ω1·J path +ω2·J hight +ω3·J smooth )+Violation·p f Where ω1, ω2, and ω3 are weights, J path J is the path length. hight For height variation, J smooth For smoothness, p f The penalty factor is 'Violation', which is a default term.

3. The 3D UAV path planning method based on the improved gray wolf optimization algorithm according to claim 1, characterized in that, Initializing the population using the circle chaotic map includes: Among them, Positions i+1 Positions are the mapped positions. i Let i be the original position, i represent the dimension, and a and b are both natural numbers.

4. The 3D UAV path planning method based on the improved gray wolf optimization algorithm according to claim 1, characterized in that, The expression for the adaptive exploration factor is: Where l is the number of iterations, and Max_iter is the maximum number of iterations.

5. The 3D UAV path planning method based on the improved gray wolf optimization algorithm according to claim 4, characterized in that, Replacing the shrinkage coefficient of the gray wolf optimization algorithm with the adaptive exploration factor includes: A = 2a·r1-a C＝2r2 Where C and A are coefficient vectors, and r1 and r2 are random vectors in [0,1].

6. The three-dimensional UAV path planning method based on the improved gray wolf optimization algorithm according to claim 5, characterized in that, Updating the location of the gray wolf population includes: Among them, D α D β D δ Let α, β, and δ represent the distances between α, β, and δ and other individuals, respectively. Let l be the current iteration number, C1, C2, and C3 be the coefficient vectors, and Positions be the distances between α, β, and δ and other individuals. α Positions β Positions δ Let α, β, and δ be the position vectors of wolves in the current population, and Positions(l) be the individual position vectors of gray wolves in the l-th iteration. Positions(l+1)=(Positions1+Positions2+Positions3) / 3 Where Position1, Position2, and Position3 are position update vectors guided by α, β, and δ wolves.

7. The three-dimensional UAV path planning method based on the improved gray wolf optimization algorithm according to claim 1, characterized in that, The dung beetle optimization algorithm introduces a global and local search mechanism and a dynamic adjustment mechanism to balance global and local exploration, including: Where Alpha_pos is the current optimal solution, Worse_pos is the worse solution, Delta_pos is the suboptimal solution, a is the random coefficient, 0.3 and 0.1 are the weight coefficients, θ is the random angle, tan(θ) is the random step size generated, and r1 is the random factor.

8. The three-dimensional UAV path planning method based on the improved gray wolf optimization algorithm according to claim 1, characterized in that, The sine and cosine optimization strategy introduced to escape local maxima during the optimization process includes: Where ω is the dynamic inertia weight, r2 is the random angle factor, r3 is a random factor, and Alpha_pos is the position of the current optimal solution. Let be the position of the i-th gray wolf in the j-th dimension during the l-th iteration.

9. The three-dimensional UAV path planning method based on the improved gray wolf optimization algorithm according to claim 1, characterized in that, The pooling mechanism introduced to store poor solutions includes: P=B×X brnd +(1-B)×X worst Where P is the matrix used to store poor solutions in the pooling mechanism, B is a randomly generated binary matrix, and X... brnd The position is randomly generated based on the current optimal solution; X worst This is the worst solution in the current iteration.

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