Multi-modal robot path planning method based on multi-strategy improved grey wolf algorithm
By combining large language models with traditional biological heuristic algorithms and introducing multi-strategy improvements to the gray wolf algorithm and Chaos Tent elite reverse learning strategy, the existing algorithms have solved the problem of poor population diversity and easy to fall into local optimality in robot path planning, and achieved more efficient and accurate path planning.
Patent Information
- Application Number
- CN202510245409.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-04
- Publication Date
- 2025-06-10
- Estimated Expiration
- 2045-03-04
AI Technical Summary
The existing biological heuristic algorithms have problems such as poor population diversity, slow later convergence and easy to fall into local optimality in robot path planning, making it difficult to find the optimal path in the environment.
Combining large language models and traditional biological heuristic algorithms, multiple strategies are introduced to improve the gray wolf algorithm, and the optimal gray wolf position is updated through Chaos Tent Elite reverse learning strategy to improve the algorithm's planning accuracy and efficiency.
The convergence speed of the algorithm is accelerated, the accuracy and efficiency of path planning are improved, and the situation of falling into local optimal solutions in the early stages is avoided.
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Figure CN120122651A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of robot path planning, and particularly to a multi-modal robot path planning method based on a multi-strategy improved grey wolf algorithm. Background Art
[0002] Path planning is one of the important components of a robot software system and is one of the hot research directions in the field of robotics. In terms of type, path planning methods can be divided into global path planning and local path planning. Robots usually first perform global path planning based on known environmental information with the goal of the shortest time, shortest distance, least energy consumption, or lowest threat. Essentially, it is a multi-dimensional optimization problem. However, in real-world scenarios, it is difficult for robots to fully master all environmental information. Therefore, it is necessary to rely on the feedback information of multiple sensors to dynamically adjust the local path to meet the planning task objectives. Currently, the global path planning methods for robots can be divided into graph search-based planning methods, sampling-based planning methods, and biologically inspired algorithm-based path planning methods. The first two require more computing resources and have a slow planning speed. While the biologically inspired algorithm-based path planning methods have attracted the attention of researchers at home and abroad due to their advantages such as simple structure, fast planning speed, and strong optimization ability. These algorithms draw inspiration from nature and solve optimization problems by simulating the behavior of organisms.
[0003] Grey wolf optimization algorithm, whale optimization algorithm, and hippopotamus optimization algorithm are all common biologically inspired algorithms, which have problems such as poor population diversity, slow convergence in the later stage, and being easily trapped in local optima to varying degrees. When using them for mobile robot path planning, it is difficult to find the optimal path in a given environment. While large language models have significant advantages in decision-making. Combining their excellent decision-making ability with traditional biologically inspired algorithms can improve the planning efficiency of the algorithms and show broad research prospects. Summary of the Invention
[0004] 1. Object of the Invention:
[0005] To solve the problems in the above background art, the object of the present invention is to provide a multi-modal robot path planning method based on a multi-strategy improved grey wolf algorithm, which combines a large language model with a traditional biologically inspired algorithm, uses the decision-making ability of the former to accelerate the convergence speed of the algorithm, and introduces a chaotic Tent elite opposition-based learning strategy to update the position of the optimal grey wolf to improve the planning accuracy of the algorithm.
[0006] 2. Technical Solution:
[0007] To achieve the above object, the present invention provides a multi-modal robot path planning method based on a multi-strategy improved grey wolf algorithm, and the steps include:
[0008] Step 1: Obtain the feature information of the map through the multi-modal robot sensor and perform discretization processing;
[0009] Step 2: Rotate the coordinate system around the origin so that the rotated horizontal axis coincides with the line connecting the starting point and the ending point, and draw D + 1 perpendicular lines to this line, where one passes through the ending point E. D is the total number of path points of the robot. Let D = 5;
[0010] Step 3: Comprehensively consider the energy cost and obstacle threat cost of the multi-modal robot and standardize them. The total cost of path planning is calculated using the formula:
[0011]
[0012] where, C total is the total cost of the path; C e is the energy cost; C t is the obstacle threat cost; k 1 is the energy cost coefficient, which can be set artificially according to the task objectives and requirements; k 2 is the obstacle threat cost coefficient, which can be set artificially according to the task objectives and requirements; Φ e is the maximum energy cost set based on experience, which can be set artificially according to the task objectives and requirements; Φ t is the maximum threat cost set based on experience, which can be set artificially according to the task objectives and requirements;
[0013] Step 4: Set the parameters of the multi-strategy improved grey wolf algorithm; the number of wolf packs is N + W, which consists of alpha wolf, beta wolf, delta wolf, omega wolf, and epsilon wolf. Among them, the alpha wolf is the continuous guiding wolf, responsible for gradually approaching the prey; the beta wolf is the sub-optimal solution that must be inferior to the alpha wolf; the delta wolf is the sub-optimal solution that must be inferior to the beta wolf; the ordinary grey wolf is the omega wolf; the total number of alpha wolf, beta wolf, delta wolf, and omega wolf is N; the epsilon wolf is the linguistic grey wolf, which can provide solutions from a global perspective under the guidance of the large language model and continuously guide the omega wolf, with the number of W; the number of iterations is EP, and the maximum number of iterations is MaxEP.
[0014] Step 5: Under the simultaneous guidance of an alpha wolf, a beta wolf, a delta wolf, and an epsilon wolf, the next position of an omega wolf is X(t + 1), and the guiding strength of the alpha wolf, beta wolf, delta wolf, and epsilon wolf is updated through a non-linear piecewise strategic adjustment factor;
[0015] Step 6: At the optimal position of the epsilon wolf, use chaotic Tent elite opposition-based learning mutation to improve the elite opposition-based learning process with chaotic Tent;
[0016] Step 7: With the goal of minimizing the total cost C total of the path, plan the cost-optimal path based on the multi-strategy improved grey wolf algorithm and the map feature information.
[0017] Further, in step 1, the feature information includes the starting position and ending position of the robot, as well as the position information and range of the circular obstacles after the obstacles are processed by dilation.
[0018] Further, in step 2, there is a path planning waypoint on each vertical line. The 6 vertical lines correspond to 5 process waypoints and 1 ending point, thus transforming the path planning problem into a 5-dimensional function optimization problem.
[0019] Further, in step 3, the coordinates of the robot and the obstacles can be expressed after the coordinate system is rotated as:
[0020]
[0021] where x and y are the original horizontal and vertical coordinates; x' and y' are the new horizontal and vertical coordinates after the coordinate system is rotated; x E and y E are the original horizontal and vertical coordinates of the ending point E; x S and y S are the original horizontal and vertical coordinates of the starting point S.
[0022] Further, in step 4, the energy cost is calculated using the formula:
[0023]
[0024] where D is the total number of path points of the robot; E is the energy consumption per unit distance of the robot at a constant speed; x i is the abscissa of the robot at the i-th path point; y i is the ordinate of the robot at the i-th path point.
[0025] Connect the adjacent path points in pairs, and take 5 points at equal intervals from each segment. Assuming that the i-th path connected by the i-th and (i + 1)-th path points is within the dilated circular obstacle range, the obstacle threat cost is calculated using the formula:
[0026]
[0027] where M is the number of circular obstacles; O i is the path length of the i-th path; d 4 0.1,i,m 、d 4 0.3,i,m 、d 4 0.5,i,m 、d 4 0.7,i,m 、d 4 0.9,i,mThe distances from the 10%, 30%, 50%, 70%, and 90% positions of the $i$-th sub-route segment to the center of the $m$-th obstacle; $R$ m is the threat level of the $m$-th obstacle, and its value is determined by the result of semantic segmentation: when the obstacle is an enemy radar, missile, anti-aircraft gun, or electronic jamming device, $R$ m = 6; in other cases, $R$ m = 4.
[0028] Furthermore, in step 5, the position of the $\varepsilon$-wolf at the beginning of each iteration is initialized to the position $X$ of the $\alpha$-wolf α , and a line $V$ is drawn through the current position and perpendicular to the line connecting the starting point $S$ and the ending point $E$ EP ; during the iteration, the $\varepsilon$-wolf provides the area information between $V$ EP and the perpendicular line where the ending point is located to a large language model pre-configured with a specific prompt Prompt. The expression for this process is:
[0029] $(x$ ω,i+1 , $y$ ω,i+1 ) = LLM(Prompt, Map_Information, $\theta$);
[0030] where $(x$ ω,i+1 , $y$ ω,i+1 ) is the next position of the $\varepsilon$-wolf planned by the large language model, LLM() represents the output of the large language model, Prompt is the preset prompt, Map_Information is the original information provided by the $\varepsilon$-wolf, that is, the feature information of the area, and $\theta$ is the key parameter of the large language model, including top_p, top_k, Temperature, Max_Tokens, etc.
[0031] Furthermore, in step 6, the next position $X(t + 1)$ of the $\omega$-wolf is:
[0032]
[0033] where $X$ α,i , $X$ β,i , $X$ δ,i , $X$ ε,i are the guiding positions generated by the $\omega$-wolf under the guidance of the $\alpha$-wolf, $\beta$-wolf, $\delta$-wolf, and $\varepsilon$-wolf respectively; $\lambda$ is a non-linear piecewise strategic adjustment factor; in the early stage, the $\varepsilon$-wolf is in the leading position and quickly determines a better solution and a better encirclement area based on a global perspective; during the iteration, the $\varepsilon$-wolf based on the language model is always independently instructed and restricted by the large language model and cannot be continuously optimized in each iteration; the language model cannot provide fine decisions, so in the later stage, the leading position of the $\varepsilon$-wolf is far inferior to that of the $\alpha$-wolf, $\beta$-wolf, and $\delta$-wolf, and the algorithm is committed to concentrating on the local encirclement area to improve the convergence accuracy; the formula used is:
[0034]
[0035] Among them, MaxEP is the maximum number of iterations; is the optimization adjustment parameter, and it is set that f(t) is the fitness function, and the formula used is:
[0036]
[0037] Maxf(t) is the maximum fitness during the iteration process.
[0038] Furthermore, in step 7, the chaotic Tent elite backtracking learning mutation at the ε-wolf optimal position adopts the formula:
[0039] X * best = Y D (X l best + X h best ) - X best (9)
[0040] Among them, X * best is the optimal position of chaotic Tent elite backtracking learning; X h best and X l best are respectively the maximum and minimum values of the gray wolf optimal position X best ; Y d is the d-th chaotic sequence value from 0 to 1, and the mapping sequence model is:
[0041]
[0042] Among them, k is the chaos coefficient.
[0043] 3. The multi-modal robot path planning method based on the multi-strategy improved gray wolf algorithm of the present invention has the following improvements and advantages compared with the prior art:
[0044] (1) Introduce ε-wolves with a global perspective to participate in the position guidance of ω-wolves, improve the planning efficiency and mining efficiency of the algorithm, and accelerate the early convergence speed.
[0045] (2) Since ε-wolves only have a significant guiding role in macroscopic global planning, as the iteration progresses, the guiding effect of ε-wolves gradually weakens, thus effectively avoiding the situation that the algorithm falls into a local optimal solution in the early stage.
[0046] (3) ε-wolves mutate based on the chaotic Tent elite backtracking learning strategy at the optimal position to improve the planning accuracy.
[0047] In summary, this method is a robot planning method with high planning efficiency and high planning accuracy. Brief Description of the Drawings
[0048] Figure 1 is the step flow chart of the multi-modal robot path planning method based on the multi-strategy improved grey wolf algorithm provided by the present invention;
[0049] Figure 2 is the hierarchical system of the grey wolf group during the early iteration process of the multi-modal robot path planning method based on the multi-strategy improved grey wolf algorithm provided by the present invention;
[0050] Figure 3 is the hierarchical system of the grey wolf group during the later iteration process of the multi-modal robot path planning method based on the multi-strategy improved grey wolf algorithm provided by the present invention;
[0051] Figure 4 is the 6×6 grid map of the multi-modal robot path planning method based on the multi-strategy improved grey wolf algorithm provided by the present invention; Detailed Embodiment
[0052] The following further details the embodiments of the present invention in conjunction with the drawings and specific embodiments:
[0053] Figure 1 is the step flow chart of the multi-modal robot path planning method based on the multi-strategy improved grey wolf algorithm described in the present invention. The specific implementation steps of this method include:
[0054] S1. The multi-modal robot obtains the feature information of the 6×6 map, including the starting position, ending position of the robot, and the position information and range of the circular obstacles after the obstacles are processed by dilation, and performs discretization processing;
[0055] S2. Rotate the coordinate system around the origin so that the rotated horizontal axis coincides with the line connecting the starting point and the ending point. The formula is:
[0056]
[0057] and draw 6 perpendicular lines to this line, one of which passes through the ending point E;
[0058] S3. Comprehensively consider the energy cost and obstacle threat cost of the multi-modal robot and standardize them. The total cost of path planning is calculated by the formula:
[0059]
[0060] where, C total is the total cost of the path; C eis the energy cost; C t is the obstacle threat cost; k 1 is the energy cost coefficient; k 2 is the obstacle threat cost coefficient; Φ e is the maximum energy cost set based on experience, let Φ e = 30; Φ t is the maximum threat cost set based on experience, let Φ t = 20;
[0061] Furthermore, the energy cost is calculated by the formula:
[0062]
[0063] where D is the total number of path points of the robot, let D = 5; E is the energy consumption per unit distance of the robot at a constant speed, let E = 5 (UEC / UL), that is, the robot consumes 5 units of energy per unit length of movement; x i is the abscissa of the robot at the i-th path point; y i is the ordinate of the robot at the i-th path point;
[0064] Connect adjacent path points in pairs and take 5 points at equal intervals from each segment. Assume that the i-th sub-path connected by the i-th and i+1-th path points is within the inflated circular obstacle range. The obstacle threat cost is calculated by the formula:
[0065]
[0066] where M is the number of circular obstacles, let M = 9; O i is the path length of the i-th sub-path; d 4 0.1,i,m and d 4 0.3,i,m and d 4 0.5,i,m and d 4 0.7,i,m and d 4 0.9,i,m are the distances from the 10%, 30%, 50%, 70%, and 90% points of the i-th sub-path segment to the center of the m-th obstacle respectively; R m is the threat level of the m-th obstacle, and its value is determined by the result of semantic segmentation: when the obstacle is an enemy radar, missile, anti-aircraft gun or electronic jamming device, R m = 6; in other cases R m = 4.
[0067] S4. Set the parameters of the multi-strategy improved Grey Wolf Algorithm; the number of wolf packs N is N + W, which consists of alpha wolf, beta wolf, delta wolf, omega wolf and epsilon wolf. Among them, the alpha wolf is the continuous guiding wolf, responsible for gradually approaching the prey; the beta wolf is the sub-optimal solution that must be inferior to the alpha wolf; the delta wolf is the sub-optimal solution that must be inferior to the beta wolf; the ordinary grey wolf is the omega wolf; the total number of alpha wolf, beta wolf, delta wolf and omega wolf is N, and let N = 40; the epsilon wolf is the linguistic grey wolf, which can provide solutions from a global perspective under the guidance of the large language model and continuously guide the omega wolf, and the number is W, and let W = 1; the number of iterations is EP, which affects the search ability of the algorithm, and the maximum number of iterations is MaxEP, and let MaxEP = 500.
[0068] Further, the position of the epsilon wolf at the beginning of each iteration is initialized to the position X of the alpha wolf α And make a line V that passes through the current position and is perpendicular to the line connecting the starting point S and the ending point E EP ; During the iteration, the epsilon wolf will use V EP Provide the regional information between it and the perpendicular line where the end point is located to the large language model pre-configured with specific prompt words Prompt. The expression of this process is:
[0069] (x ω,i+1 , y ω,i+1 ) = LLM(Prompt, Map_Information, θ);
[0070] Among them, (x ω,i+1 , y ω,i+1 ) is the next position of the epsilon wolf planned by the large language model, LLM() represents the output of the large language model, Prompt is the preset prompt word, Map_Information is the original information provided by the epsilon wolf, that is, the characteristic information of the region, and θ is the key parameter of the large language model.
[0071] S5. Under the simultaneous guidance of the alpha wolf, beta wolf, delta wolf and epsilon wolf, the next position of an omega wolf is X(t + 1), and the guiding strength of the alpha wolf, beta wolf, delta wolf and epsilon wolf is updated through a non-linear piecewise strategic adjustment factor;
[0072] Further, the next position X(t + 1) of the omega wolf is:
[0073]
[0074] Among them, X α,i , X β,i , X δ,i , X ε,iThe guiding positions generated by ω wolves respectively under the guidance of α wolf, β wolf, δ wolf and ε wolf; λ is a non-linear piecewise strategic adjustment factor; in the early stage, ε wolf is in the leading position, and quickly determines the optimal solution and the optimal encirclement area based on the global perspective; during the iteration process, ε wolf based on the language model is always independently instructed and restricted by the large language model and cannot be continuously optimized in each iteration; the language model cannot provide fine decisions, so in the later stage, the leadership of ε wolf is far inferior to that of α wolf, β wolf, and δ wolf, and the algorithm is committed to concentrating on the local encirclement area to improve the convergence accuracy; the formula used is:
[0075]
[0076] Among them, MaxEP is the maximum number of iterations; is the optimization adjustment parameter, f(t) is the fitness function, and the formula used is:
[0077] f(t) = ||X(t) - X(t - 1)||;
[0078] Maxf(t) is the maximum fitness during the iteration process.
[0079] S6. Perform chaotic Tent elite opposition-based learning mutation at the optimal position of ε wolf;
[0080] Further, the chaotic Tent elite opposition-based learning mutation at the optimal position of ε wolf adopts the formula:
[0081] X * best = Y d (X l best + X h best ) - X best
[0082] Where X * best is the optimal position of chaotic Tent elite opposition-based learning; X h best and X l best are respectively the maximum and minimum values of the optimal position X best of the grey wolf; Y d is the d-th chaotic sequence value from 0 to 1, and the mapping sequence model is:
[0083]
[0084] Among them, k is the chaos coefficient, and k is set to 0.6.
[0085] S7. Minimize the total cost C of the path totalPlan for the goal of path planning.
[0086] The present invention has been described according to an exemplary implementation, but is not limited to the above embodiments. Equivalent variations or substitutions made by those skilled in the technical field to which the present invention pertains without departing from the scope protected by the claims of the present invention shall fall within the scope of protection of the present invention. The scope of protection claimed for the present invention shall be subject to the appended claims.
Claims
1. A multimodal robot path planning method based on a multi-strategy improved grey wolf algorithm, characterized in that: The following steps are involved: Step 1: Obtain the feature information of the map through multimodal robot sensors and discretize it; Step 2: Rotate the coordinate system around the origin so that the horizontal axis after rotation coincides with the line connecting the starting point and the end point, and draw D+1 perpendicular lines perpendicular to the line, one of which passes through the end point E. D is the total number of path points of the robot. Step 3: Comprehensively consider the energy cost and obstacle threat cost of the multimodal robot and standardize them. The total cost of path planning is: Among them, C total is the total cost of the path; C e is the energy cost; C t is the obstacle threat cost; k1 is the energy cost coefficient; k2 is the obstacle threat cost coefficient; Φ e is the maximum energy cost set based on experience; Φ t is the maximum threat cost set based on experience; Step 4: Set the parameters of the multi-strategy improved gray wolf algorithm; the number of wolves is N+W, consisting of α wolf, β wolf, δ wolf, ω wolf and ε wolf, among which α wolf is the continuous guiding wolf, responsible for gradually approaching the prey; β wolf is the suboptimal solution that is definitely inferior to α wolf; δ wolf is the suboptimal solution that is definitely inferior to β wolf; the ordinary gray wolf is ω wolf; the total number of α wolf, β wolf, δ wolf and ω wolf is N; ε wolf is the language gray wolf, which can provide solutions from a global perspective under the guidance of the large language model and continuously guide ω wolf, the number is W; the number of iterations is EP, and the maximum number of iterations is MaxEP. Step 5: A wolf ω is guided by wolves α, β, δ and ε at the same time. Its next position is X(t+1). The guiding strength of wolves α, β, δ and ε is updated through the nonlinear piecewise strategic adjustment factor. Step 6: Use the Chaos Tent elite reverse learning mutation at the optimal position of the ε wolf; Step 7: Minimize the total cost C of the path total For the goal of path planning, the cost-optimal path is planned based on the multi-strategy improved grey wolf algorithm and map feature information.
2. The multimodal robot path planning method based on the multi-strategy improved grey wolf algorithm according to claim 1 is characterized in that: In step 1, the feature information includes the starting position and the ending position of the robot, and the position information and range of the obstacle after the obstacle is converted into a circular obstacle through expansion processing.
3. The multimodal robot path planning method based on the multi-strategy improved grey wolf algorithm according to claim 1 is characterized in that: In step 2, there is a path planning point on each vertical line, and the D+1 vertical lines correspond to D process path points and 1 end point, thereby converting the path planning problem into a D-dimensional function optimization problem.
4. The multimodal robot path planning method based on the multi-strategy improved grey wolf algorithm according to claim 1 is characterized in that: In step 2, the coordinates of the robot and the obstacle can be expressed as follows after the coordinate system is rotated: Among them, x and y are the original horizontal and vertical coordinates; x' and y' are the new horizontal and vertical coordinates after the coordinate system is rotated; E and E is the original horizontal and vertical coordinates of the end point E; S and S are the original horizontal and vertical coordinates of the starting point S.
5. The multimodal robot path planning method based on the multi-strategy improved grey wolf algorithm according to claim 1 is characterized in that: In step 3, the energy cost is calculated using the formula: Where D is the total number of path points of the robot; E is the energy consumption per unit distance of the robot at a constant speed; x i is the horizontal coordinate of the robot at the i-th path point; y i is the ordinate of the robot at the i-th path point; Connect adjacent path points in pairs, and select D points at equal intervals from each segment. Assume that the i sub-path connected by the i and i+1 path points is within the expanded circular obstacle range. The obstacle threat cost is calculated using the formula: Where M is the number of circular obstacles; O i is the path length of the ith subpath; d 4 0.1,i,m ,d 4 0.3,i,m ,d 4 0.5,i,m ,d 4 0.7,i,m ,d 4 0.9,i,m are the distances from the 10%, 30%, 50%, 70%, and 90% of the ith sub-route segment to the center of the mth obstacle circle; R m is the threat level of the mth obstacle, and its value is determined by the result of semantic segmentation: when the obstacle is an enemy radar, missile, anti-aircraft gun or electronic jamming equipment, R m =6; in other cases R m =4.
6. The multimodal robot path planning method based on the multi-strategy improved grey wolf algorithm according to claim 1 is characterized in that: In step 4, the position of the ε wolf at the beginning of each iteration is initialized to the position X of the α wolf α , and draw a line V that passes through the current position and is perpendicular to the starting point S and the end point E EP ; In the iteration, ε wolf will V EP The area information between the vertical line where the end point is located is provided to the large language model pre-configured with a specific prompt word Prompt. The expression of this process is: (x ω,i+1 ,y ω,i+1 )=LLM(Prompt,Map_Information,θ); Among them, (x ω,i+1 ,y ω,i+1 ) is the next position of the ε wolf planned by the large language model, LLM() represents the output of the large language model, Prompt is the preset prompt word, Map_Information is the original information provided by the ε wolf, that is, the feature information of the region, and θ is the key parameters of the large language model, including top_p, top_k, Temperature, Max_Tokens, etc.
7. The multimodal robot path planning method based on the multi-strategy improved grey wolf algorithm according to claim 1 is characterized in that: In step 5, the next position X(t+1) of the ω wolf is: Among them, X α,i , X β,i , X δ,i , X ε,i The guidance positions generated by ω wolf under the guidance of α wolf, β wolf, δ wolf and ε wolf respectively; λ is the nonlinear segmented strategic adjustment factor; ε wolf is in the main leadership position in the early stage, and quickly determines the better solution and better capture area based on the global perspective; the ε wolf based on the language model in the iterative process is always independently instructed and restricted by the large language model, and cannot be continuously optimized in each iteration; the language model cannot provide precise decision-making, so the leadership position of ε wolf in the later stage is far inferior to α wolf, β wolf and δ wolf, and the algorithm is committed to focusing on the local capture area to improve the convergence accuracy; the formula used is: Among them, MaxEP is the maximum number of iterations; To optimize the adjustment parameters; f(t) is the fitness function, and the formula used is: f(t) = ||X(t) - X(t-1)||; Maxf(t) is the maximum fitness during the iteration process.
8. The multimodal robot path planning method based on the multi-strategy improved grey wolf algorithm according to claim 1 is characterized in that: In step 6, the chaotic tent elite reverse learning mutation is performed at the optimal position of the ε wolf, and the formula used is: X * best =Y D (X l best +X h best )-X best Where X * best The optimal position for reverse learning of Chaos Tent Elite; X h best and X l best are the optimal positions X for the gray wolf respectively. best The maximum and minimum values of Y d is the dth chaotic sequence value from 0 to 1, and the mapping sequence model is: Among them, k is the chaos coefficient.
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