Three-dimensional space robot path planning method based on fusion meta-heuristic algorithm

Abstract

The present invention discloses a three-dimensional space robot path planning method based on a fusion metaheuristic algorithm. This method drives a robot in three-dimensional space from a starting point to an end point and searches for the optimal movement direction during the movement. The core of this method is the fusion metaheuristic algorithm. The fusion metaheuristic algorithm is an improvement on the conventional gray wolf optimization algorithm, which suffers from the drawback of prematurely falling into local optimality. Therefore, a nonlinear convergence factor and adaptive weight coefficient are designed to balance global and local search, and then integrated into the balanced optimization algorithm. By designing an iterative competition mechanism, the algorithm convergence speed is increased, thereby improving the operational efficiency of the robot path planning.

Description

Technical Field

[0001] The invention discloses a three-dimensional space robot path planning method based on a fusion meta-heuristic algorithm, belonging to the technical field of autonomous robot path planning. Background Art

[0002] Robotic path planning technology specifically involves finding a safe and feasible path from a starting point to a destination based on optimization criteria (such as shortest path, minimum energy consumption, and fastest time). Three-dimensional path planning technology is widely used in modern applications such as automated aerial inspections, underwater target search, and seabed resource exploration. Conventional path planning techniques often utilize heuristic algorithms, biomimetic algorithms, and swarm intelligence to achieve robot path planning.

[0003] Currently, conventional path planning technologies have the following problems:

[0004] Heuristic algorithms and bionic algorithms have drawbacks such as falling into local optimality too early and converging too early. An optimization algorithm that can balance the algorithm's exploration and development capabilities is needed to enhance the practical feasibility of three-dimensional space robot path planning technology. Summary of the Invention

[0005] In order to make up for the problems existing in the background technology and improve the shortcomings of the existing solutions. The present invention proposes a three-dimensional space robot path planning method based on a fusion metaheuristic algorithm. The method is oriented to three-dimensional space search applications, and its core is a fusion metaheuristic algorithm. The fusion metaheuristic algorithm is an improvement on the conventional gray wolf optimization algorithm. The conventional gray wolf optimization algorithm has the disadvantage of falling into local optimality too early. Therefore, a nonlinear convergence factor and an adaptive weight coefficient are designed to balance the global search and the local search, and are integrated into the fusion metaheuristic algorithm. By designing an iterative competition mechanism, the algorithm convergence speed is improved, thereby improving the operational efficiency of the robot path planning.

[0006] The technical solutions of the present invention are as follows:

[0007] A 3D robot path planning method based on a fusion metaheuristic algorithm is designed for 3D space search applications. In a given 3D space, the robot moves according to the following steps:

[0008] (1-1), set the starting point and end point;

[0009] (1-2), parameterized spatial environment, including obstacle location, number of obstacles, obstacle status, and spatial resistance;

[0010] (1-3), taking the spatial environment parameters as input, running, the optimization goal of the fusion meta-heuristic algorithm is the quality of the path and the algorithm convergence speed, and the output is a path;

[0011] (1-4) Determine whether the path has reached the end point. If not, update the environment information and run the fusion metaheuristic algorithm again to continue superimposing the path. If it has reached the end point, set the current path to the robot.

[0012] (1-5), the robot moves along the set path.

[0013] The fusion metaheuristic algorithm used in steps (1-3) and (1-4) is an improvement on the conventional grey wolf optimization algorithm. It designs nonlinear convergence factors and adaptive weight coefficients, balances global search and local search, and integrates them into the balanced optimization algorithm. By designing an iterative competition mechanism, the convergence speed of the algorithm is improved.

[0014] The method to improve the conventional gray wolf optimization algorithm is as follows:

[0015] The following terminology is used in the Grey Wolf optimization algorithm:

[0016] (1) Population: The total number of search individuals participating in the optimization within a certain search area.

[0017] (2) Search agent: an individual location that can move within the search area.

[0018] (3) Wolves α, β, σ: the best three search agents in each iteration.

[0019] (4) Alpha Wolf α: The best search agent in each iteration.

[0020] (5) Convergence factor a: The parameter that balances the algorithm's exploration and development capabilities during the iteration process of the Grey Wolf optimization algorithm.

[0021] (6) Centrifugal distance: the spatial distance between each search agent in the population and the historical best position leader α.

[0022] (7) Balancing pool: The candidate solution set consisting of the four best search agents and their arithmetic mean in each iteration.

[0023] The working principle of the conventional gray wolf optimization algorithm is that the wolf position optimization update process (i.e., the robot's moving direction and distance) is guided by the three best solutions (i.e., wolves α, β, σ) in each generation of the population. The convergence factor in the conventional gray wolf optimization algorithm decreases linearly from 2 to 0. In the fusion metaheuristic algorithm, a nonlinear convergence factor strategy is used, in which the concept of centrifugal distance change rate is proposed. The change rate of the current centrifugal distance of each search agent can be calculated from the average centrifugal distance and the maximum centrifugal distance. Among them, the centrifugal distance is the spatial distance between the search agent in the population and the historical best position. The distribution of candidate solutions is judged by the change in the centrifugal distance, and the convergence factor is adjusted to dynamic change and nonlinear attenuation. The introduction of the centrifugal distance change rate enables the algorithm to better balance global search and local search. The centrifugal distance change rate λ is expressed as follows:

[0024]

[0025] where dist max It represents the maximum centrifugal distance of each search agent when the population n searches for the optimal solution in the D-dimensional space. dist ave It represents the average centrifugal distance of each search agent when the population n searches for the optimal solution in the D-dimensional space. is the best position vector in the iterative history (i.e., the position vector of the leader in the iterative process of the conventional gray wolf optimization algorithm), called the position vector of α; is the d-dimensional position vector of the gray wolf search agent i.

[0026] Adding λ to the update formula of the convergence factor a dynamically adjusts its convergence speed, effectively coordinating the global search and local search capabilities of the algorithm. The improved update formula of the convergence factor a is as follows:

[0027]

[0028] Iter represents the current number of iterations, max Indicates the maximum number of iterations of the algorithm.

[0029] In the conventional gray wolf optimization algorithm, the position update formula of the search agent is the algorithm average of the obtained positions under the guidance of α, β, and σ. In the fusion metaheuristic algorithm, an adaptive weight coefficient strategy is used to dynamically update the gray wolf position of the search agent according to the overall convergence degree of the population in the iterative process, thereby effectively improving the optimization performance of the algorithm. The rate of change of the centrifugal distance λ mainly reflects the degree of closeness between the search agent and the α wolf. However, the complexity of the actual environment means that the α wolf is not necessarily the global optimal solution, and it is also necessary to know the distance between each search agent and the β wolf and the σ wolf. Therefore, the rate of change λ of the current centrifugal distance of each search agent relative to α, β, σ j It is expressed as follows:

[0030]

[0031] Among them, j includes wolf α, β, σ, dist αmax Indicates the maximum centrifugal distance of the search agent relative to α at this time, dist βmax Indicates the maximum centrifugal distance of the search agent relative to β at this time, dist σmax Dist represents the maximum centrifugal distance of the search agent relative to σ at this time; αave It represents the average centrifugal distance of the search agent relative to the α wolf at this time, dist βave It represents the average centrifugal distance of the search agent relative to the β wolf at this time, dist σave It represents the average eccentric distance of the search agent relative to σwolf at this time.

[0032] Then, according to the change rate λ of the centrifugal distance of each search agent to wolves α, β, σ, j Design the following adaptive weight coefficients:

[0033]

[0034] Among them, ω1 is the weight coefficient corresponding to α, ω2 is the weight coefficient corresponding to β, and ω3 is the weight coefficient corresponding to σ.

[0035] Combined with the designed adaptive weight coefficient, the new search agent position update formula is as follows:

[0036]

[0037] where X i (Iter+1) represents the search agent position in the next iteration, X i,α represents the distance of search agent i relative to α, X i,β represents the distance of search agent i relative to β, X i,δ represents the distance of search agent i relative to σ.

[0038] The specific method of integrating the improved grey wolf optimization algorithm into the balance optimization algorithm is as follows:

[0039] The conventional balance optimization algorithm selects the four best particle solutions and their arithmetic mean as candidate solution sets in each iteration and puts them into the balance pool. Other particles are optimized and updated based on the excellent particles in the balance pool. In the fusion metaheuristic algorithm, first, it is initialized and the maximum number of iterations Iter is set. max and population size n, and the search agent in the initial path Generates the following:

[0040]

[0041] Among them, X up 、X low Represent the upper and lower boundaries of the variable X, that is, the search area of ​​the algorithm, rand [0,1] Represents a random number in [0,1].

[0042] Afterwards, determine the balancing pool C eq,cool (Iter), that is, determine the candidate solution pool, as follows:

[0043]

[0044] Among them, C ave (Iter) represents the optimal four search agents C eqi (Iter), the arithmetic mean of (i=1,2,3,4), C eqi (Iter), (i=1,2,3,4) represents the best four search agents in the current iteration.

[0045] Then, an adaptive grey wolf search phase is added, where the best search agents in the balancing pool guide other search agents to perform global updates, as follows:

[0046]

[0047] Among them, D α 、D β 、D σ Represent the position vector matrices based on α, β, and σ respectively, X1, X2, and X3 represent the positions of the corresponding search agents under the guidance of α, β, and σ respectively, and X eqα (Iter), X eqβ (Iter), X eqσ (Iter) represents the position of α, β, and σ in the current iteration, respectively, and X eqi (Iter) represents the position of the i-th search agent at the current iteration. In addition, the corresponding coefficient vector is set to:

[0048]

[0049] Among them, Iter is the current iteration number, A i and C i is the coefficient vector, a is the improved nonlinear convergence factor, and r1 and r2 are random vectors in [0,1].

[0050] Subsequently, in order to speed up the convergence of the algorithm, a competition mechanism is designed, as follows:

[0051]

[0052] in, represents the optimal search agent obtained in the current iteration, represents the search agent position obtained by adaptive grey wolf search, C eqi (Iter) represents the position of the i-th search agent, and the function f represents the fitness value of the corresponding search agent. The smaller the fitness value, the better the resulting search agent.

[0053] At this time, the new balance pool Updated to:

[0054]

[0055] in, Represents the new optimal four search agents after iteration The arithmetic mean of Represents the best four search agents obtained after the current iteration.

[0056] Finally, when the number of iterations Iter>1, the better solutions are retained by:

[0057] C eqi (Iter)=C eqi (Iter-1),if f(C eqi (Iter-1)) <f(C eqi (Iter)) (12)

[0058] C eqi (Iter) represents the i-th search agent in the current iteration, C eqi (Iter-1) represents the i-th search agent in the previous iteration. Similarly, function f represents the fitness value of the corresponding search agent.

[0059] During the iteration, each search agent C i The position of (Iter) is updated as follows:

[0060]

[0061] Among them, C i (Iter) represents the i-th search agent, From the balancing pool, γ is a random vector in the interval [0,1]. Other parameters are as follows:

[0062]

[0063] Where r, r1, r2 are random numbers in [0, 1], C eq (Iter) comes from the balance pool, C i (Iter) represents the i-th search agent. sign(r-0.5) controls the exploration direction, and positive and negative probabilities are equal.

[0064] The beneficial effects of the present invention are:

[0065] The core of the method is a fusion metaheuristic algorithm. This fusion metaheuristic algorithm is an improvement on the conventional gray wolf optimization algorithm, which suffers from the drawback of prematurely falling into local optima. Therefore, a nonlinear convergence factor and adaptive weight coefficient are designed to balance global and local search. These are then integrated into the balanced optimization algorithm. By designing an iterative competition mechanism, the algorithm convergence speed is increased, thereby improving the operational efficiency of robot path planning. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 It is a three-dimensional space robot path planning process based on the fusion meta-heuristic algorithm;

[0067] Figure 2 It is an example of a seabed detection application;

[0068] Figure 3 An example of a path map for an autonomous underwater glider. DETAILED DESCRIPTION

[0069] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention.

[0070] like Figure 1 As shown in the figure, a 3D space robot path planning method based on a fusion meta-heuristic algorithm is designed for 3D space search applications. In a given 3D space, the robot moves according to the following steps:

[0071] (1-1), set the starting point and end point;

[0072] (1-2), parameterized spatial environment, including obstacle location, number of obstacles, obstacle status, and spatial resistance;

[0073] (1-3), taking the spatial environment parameters as input, running, the optimization goal of the fusion meta-heuristic algorithm is the quality of the path and the algorithm convergence speed, and the output is a path;

[0074] (1-4) Determine whether the path has reached the end point. If not, update the environment information and run the fusion metaheuristic algorithm again to continue superimposing the path. If it has reached the end point, set the current path to the robot.

[0075] (1-5), the robot moves along the set path.

[0076] The fusion metaheuristic algorithm used in steps (1-3) and (1-4) is an improvement on the conventional grey wolf optimization algorithm. It designs nonlinear convergence factors and adaptive weight coefficients, balances global search and local search, and integrates them into the balanced optimization algorithm. By designing an iterative competition mechanism, the convergence speed of the algorithm is improved.

[0077] The method to improve the conventional gray wolf optimization algorithm is as follows:

[0078] The following terminology is used in the Grey Wolf optimization algorithm:

[0079] (8) Population: The total number of search individuals participating in the optimization within a certain search area.

[0080] (9) Search agent: an individual location that can move within the search area.

[0081] (10) Wolves α, β, σ: the best three search agents in each iteration.

[0082] (11) Alpha Wolf α: The best search agent in each iteration.

[0083] (12) Convergence factor a: The parameter that balances the algorithm's exploration and development capabilities during the iteration process of the Grey Wolf Optimization Algorithm.

[0084] (13) Centrifugal distance: the spatial distance between each search agent in the population and the historical best position leader α.

[0085] (14) Balancing pool: The candidate solution set consisting of the four best search agents and their arithmetic mean in each iteration.

[0086] The working principle of the conventional gray wolf optimization algorithm is that the wolf position optimization update process (i.e., the robot's moving direction and distance) is guided by the three best solutions (i.e., wolves α, β, σ) in each generation of the population. The convergence factor in the conventional gray wolf optimization algorithm decreases linearly from 2 to 0. In the fusion metaheuristic algorithm, a nonlinear convergence factor strategy is used, in which the concept of centrifugal distance change rate is proposed. The change rate of the current centrifugal distance of each search agent can be calculated from the average centrifugal distance and the maximum centrifugal distance. Among them, the centrifugal distance is the spatial distance between the search agent in the population and the historical best position. The distribution of candidate solutions is judged by the change in the centrifugal distance, and the convergence factor is adjusted to dynamic change and nonlinear attenuation. The introduction of the centrifugal distance change rate enables the algorithm to better balance global search and local search. The centrifugal distance change rate λ is expressed as follows:

[0087]

[0088] where dist max It represents the maximum centrifugal distance of each search agent when the population n searches for the optimal solution in the D-dimensional space. dist ave It represents the average centrifugal distance of each search agent when the population n searches for the optimal solution in the D-dimensional space. is the best position vector in the iterative history (i.e., the position vector of the leader in the iterative process of the conventional gray wolf optimization algorithm), called the position vector of α; is the d-dimensional position vector of the gray wolf search agent i.

[0089] Adding λ to the update formula of the convergence factor a dynamically adjusts its convergence speed, effectively coordinating the global search and local search capabilities of the algorithm. The improved update formula of the convergence factor a is as follows:

[0090]

[0091] Iter represents the current number of iterations, max Indicates the maximum number of iterations of the algorithm.

[0092] In the conventional gray wolf optimization algorithm, the position update formula of the search agent is the algorithm average of the obtained positions under the guidance of α, β, and σ. In the fusion metaheuristic algorithm, an adaptive weight coefficient strategy is used to dynamically update the gray wolf position of the search agent according to the overall convergence degree of the population in the iterative process, thereby effectively improving the optimization performance of the algorithm. The rate of change of the centrifugal distance λ mainly reflects the degree of closeness between the search agent and the α wolf. However, the complexity of the actual environment means that the α wolf is not necessarily the global optimal solution, and it is also necessary to know the distance between each search agent and the β wolf and the σ wolf. Therefore, the rate of change λ of the current centrifugal distance of each search agent relative to α, β, σ j It is expressed as follows:

[0093]

[0094] Among them, j includes wolf α, β, σ, dist αmax Indicates the maximum centrifugal distance of the search agent relative to α at this time, dist βmax Indicates the maximum centrifugal distance of the search agent relative to β at this time, dist σmax Dist represents the maximum centrifugal distance of the search agent relative to σ at this time; αave It represents the average centrifugal distance of the search agent relative to the α wolf at this time, dist βave It represents the average centrifugal distance of the search agent relative to the β wolf at this time, dist σave It represents the average eccentric distance of the search agent relative to σwolf at this time.

[0095] Then, according to the change rate λ of the centrifugal distance of each search agent to wolves α, β, σ, j Design the following adaptive weight coefficients:

[0096]

[0097] Among them, ω1 is the weight coefficient corresponding to α, ω2 is the weight coefficient corresponding to β, and ω3 is the weight coefficient corresponding to σ.

[0098] Combined with the designed adaptive weight coefficient, the new search agent position update formula is as follows:

[0099]

[0100] where X i (Iter+1) represents the search agent position in the next iteration, X i,α represents the distance of search agent i relative to α, X i,β represents the distance of search agent i relative to β, X i,δ represents the distance of search agent i relative to σ.

[0101] The specific method of integrating the improved grey wolf optimization algorithm into the balance optimization algorithm is as follows:

[0102] The conventional balance optimization algorithm selects the four best particle solutions and their arithmetic mean as candidate solution sets in each iteration and puts them into the balance pool. Other particles are optimized and updated based on the excellent particles in the balance pool. In the fusion metaheuristic algorithm, first, it is initialized and the maximum number of iterations Iter is set. max and population size n, and the search agent in the initial path Generates the following:

[0103]

[0104] Among them, X up 、X low Represent the upper and lower boundaries of the variable X, that is, the search area of ​​the algorithm, rand [0,1] Represents a random number in [0,1].

[0105] Afterwards, determine the balancing pool C eq,cool (Iter), that is, determine the candidate solution pool, as follows:

[0106]

[0107] Among them, C ave (Iter) represents the optimal four search agents C eqi (Iter), the arithmetic mean of (i=1,2,3,4), C eqi (Iter), (i=1,2,3,4) represents the best four search agents in the current iteration.

[0108] Then, an adaptive grey wolf search phase is added, where the best search agents in the balancing pool guide other search agents to perform global updates, as follows:

[0109]

[0110] Among them, D α 、D β 、D σ Represent the position vector matrices based on α, β, and σ respectively, X1, X2, and X3 represent the positions of the corresponding search agents under the guidance of α, β, and σ respectively, and X eqα (Iter), X eqβ (Iter), X eqσ (Iter) represents the position of α, β, and σ in the current iteration, respectively, and X eqi (Iter) represents the position of the i-th search agent at the current iteration. In addition, the corresponding coefficient vector is set to:

[0111]

[0112] Among them, Iter is the current iteration number, A i and C i is the coefficient vector, a is the improved nonlinear convergence factor, and r1 and r2 are random vectors in [0,1].

[0113] Subsequently, in order to speed up the convergence of the algorithm, a competition mechanism is designed, as follows:

[0114]

[0115] in, represents the optimal search agent obtained in the current iteration, represents the search agent position obtained by adaptive grey wolf search, C eqi (Iter) represents the position of the i-th search agent, and the function f represents the fitness value of the corresponding search agent. The smaller the fitness value, the better the resulting search agent.

[0116] At this time, the new balance pool Updated to:

[0117]

[0118] in, Represents the new optimal four search agents after iteration The arithmetic mean of Represents the best four search agents obtained after the current iteration.

[0119] Finally, when the number of iterations Iter>1, the better solutions are retained by:

[0120] C eqi (Iter)=C eqi (Iter-1),if f(C eqi (Iter-1)) <f(C eqi (Iter)) (12)

[0121] C eqi (Iter) represents the i-th search agent in the current iteration, C eqi (Iter-1) represents the i-th search agent in the previous iteration. Similarly, function f represents the fitness value of the corresponding search agent.

[0122] During the iteration, each search agent C i The position of (Iter) is updated as follows:

[0123]

[0124] Among them, C i (Iter) represents the i-th search agent, From the balancing pool, γ is a random vector in the interval [0,1]. Other parameters are as follows:

[0125]

[0126] Where r, r1, r2 are random numbers in [0, 1], C eq (Iter) comes from the balance pool, C i (Iter) represents the i-th search agent. sign(r-0.5) controls the exploration direction, and positive and negative probabilities are equal.

[0127] Example:

[0128] Seabed collaborative survey applications based on autonomous underwater gliders (AUG: Autonomous Underwater Glider) and autonomous surface vehicles (ASV: Autonomous Surface Vehicle), such as Figure 2 Initially, multiple AUGs and ASVs float on the sea surface, waiting for instructions from a base station, which can be a land station or a ship. When the AUG receives a seabed exploration command, it sinks underwater and conducts seabed exploration using a three-dimensional space robot path planning method based on a fusion metaheuristic algorithm.

[0129] Given the known seabed geographic information, the AUG can detect nearby obstacles and ocean currents to determine the movement path. The ASV on the surface knows the situation of the interaction points of the AUG in each cycle in real time. The AUG needs to float to the interaction plane and exchange information with the ASV, thereby sending the information collected on the seabed to the base station. During this period, the AUG runs a fusion metaheuristic algorithm based on the surrounding underwater environment information to perform underwater path planning, determine the AUG's global path, and determine the interaction points of the AUG in all cycles, such as Figure 3 .

[0130] The following algorithm explains the overall operation process of the three-dimensional space robot path planning method based on the fusion meta-heuristic algorithm in underwater glider path planning.

[0131]

[0132]

[0133] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A 3D space robot path planning method based on a fusion meta-heuristic algorithm, oriented to 3D space search applications, characterized by In a given three-dimensional space, the robot moves as follows: (1-1), set the starting point and end point; (1-2), parameterized spatial environment, including obstacle location, number of obstacles, obstacle status, and spatial resistance; (1-3) Taking spatial environment parameters as input, running, integrating meta-heuristic algorithm, the optimization goal is to achieve the quality of the path and the algorithm convergence speed, the output is a path; (1-4) Determine whether the path has reached the end point. If not, update the environment information and run the fusion meta-startup again. The algorithm continues to add paths; if the end point is reached, the current path is set to the robot; (1-5), the robot moves along the set path; The fusion meta-heuristic algorithm used in steps (1-3) and (1-4) is an improvement on the conventional grey wolf optimization algorithm, which designs a nonlinear convergence factor and an adaptive weight coefficient, balances global search and local search, and is integrated into the balanced optimization algorithm. By designing an iterative competition mechanism, the convergence speed of the algorithm is improved; The specific steps to improve the conventional gray wolf optimization algorithm are as follows: The following terminology is used in the Grey Wolf optimization algorithm: Population: the total number of search individuals participating in optimization within a specified search area; Search agents, i.e. wolves: individual locations that can move within the search area; Wolf α, β, σ: the best 3 search agents in each iteration; Alpha Wolf: The best search agent in each iteration; Convergence factor a: a parameter that balances the algorithm's exploration and development capabilities during the iteration process of the Grey Wolf Optimization Algorithm; Centrifugal distance: the spatial distance between each search agent in the population and the historical best position alpha wolf; Balance pool: The candidate solution set consisting of the best four search agents and their arithmetic mean in each iteration; A nonlinear convergence factor strategy is used to calculate the rate of change of each search agent's current eccentric distance from the average eccentric distance and the maximum eccentric distance. The eccentric distance is the spatial distance between the search agent in the population and the historical best position. The distribution of candidate solutions is judged by the change in eccentric distance, and the convergence factor is adjusted to dynamic change and nonlinear decay. The introduction of the eccentric distance change rate allows the algorithm to better balance global and local search. The eccentric distance change rate λ is expressed as follows: where dist max It represents the maximum centrifugal distance of each search agent when the population n searches for the optimal solution in the D-dimensional space. dist ave It represents the average centrifugal distance of each search agent when the population n searches for the optimal solution in the D-dimensional space. It is the best position vector in the iterative history process, that is, the position vector of the leader wolf in the iterative process of the conventional gray wolf optimization algorithm, called the position vector of α; is the d-dimensional position vector of the gray wolf search agent i; Adding λ to the update formula of the convergence factor a dynamically adjusts its convergence speed and effectively coordinates the global search and local search capabilities of the algorithm. The improved update formula of the convergence factor a is as follows: Iter represents the current number of iterations, max Indicates the maximum number of iterations of the algorithm; The position update formula of the search agent uses an adaptive weight coefficient strategy to dynamically update the gray wolf position of the search agent according to the overall convergence degree of the population during the iteration process; the change rate λ of the current eccentric distance of each search agent relative to α, β, σ j It is expressed as follows: Among them, j includes wolf α, β, σ, dist αmax Indicates the maximum centrifugal distance of the search agent relative to α at this time, dist βmax Indicates the maximum centrifugal distance of the search agent relative to β at this time, dist σmax Dist represents the maximum centrifugal distance of the search agent relative to σ at this time; αave It represents the average centrifugal distance of the search agent relative to the α wolf at this time, dist βave It represents the average centrifugal distance of the search agent relative to the β wolf at this time, dist σave represents the average eccentric distance of the search agent relative to σ wolf at this time; According to the change rate λ of the eccentric distance of each search agent to wolves α, β, σ j Design the following adaptive weight coefficients: Among them, ω1 is the weight coefficient corresponding to α, ω2 is the weight coefficient corresponding to β, and ω3 is the weight coefficient corresponding to σ. Combined with the designed adaptive weight coefficient, the new search agent position update formula is as follows: where X i (Iter+1) represents the search agent position in the next iteration, X i,α represents the distance of search agent i relative to α, X i,β represents the distance of search agent i relative to β, X i,δ represents the distance of search agent i relative to σ; The specific method of integrating the improved grey wolf optimization algorithm into the balance optimization algorithm is as follows: First, initialize and set the maximum number of iterations Iter max and population size n, and the search agent in the initial path Generates the following: Among them, X up 、X low Represent the upper and lower boundaries of the variable X, that is, the search area of ​​the algorithm, rand [0,1] Represents a random number in [0,1]; Afterwards, determine the balancing pool C eq,cool (Iter), that is, determine the candidate solution pool, as follows: Among them, C ave (Iter) represents the optimal four search agents C eqi (Iter), the arithmetic mean of (i=1,2,3,4), C eqi (Iter), (i=1,2,3,4) represents the best four search agents in the current iteration; Then, an adaptive grey wolf search phase is added, where the best search agents in the balancing pool guide other search agents to perform global updates, as follows: Among them, D α 、D β 、D σ Represent the position vector matrices based on α, β, and σ respectively, X1, X2, and X3 represent the positions of the corresponding search agents under the guidance of α, β, and σ respectively, and X eqα (Iter), X eqβ (Iter), X eqσ (Iter) represents the position of α, β, and σ in the current iteration, respectively, and X eqi (Iter) represents the position of the i-th search agent at the current iteration number; the corresponding coefficient vector is set to: Among them, Iter is the current iteration number, A i and C i is the coefficient vector, a is the improved nonlinear convergence factor, r1 and r2 are random vectors in [0,1]; Subsequently, in order to speed up the convergence of the algorithm, a competition mechanism is designed, as follows: in, represents the optimal search agent obtained in the current iteration, represents the search agent position obtained by adaptive grey wolf search, C eqi (Iter) represents the position of the i-th search agent, and the function f represents the fitness value of the corresponding search agent. The smaller the fitness value, the better the search agent. At this time, the new balance pool Updated to: in, Represents the new optimal four search agents after iteration The arithmetic mean of represents the best four search agents obtained after the current iteration; Finally, when the number of iterations Iter>1, good solutions are retained by: C eqi (Iter)=C eqi (Iter-1),if f(C eqi (Iter-1))<f(C eqi (Iter))(12) C eqi (Iter) represents the i-th search agent in the current iteration, C eqi (Iter-1) represents the i-th search agent in the previous iteration. Similarly, function f represents the fitness value of the corresponding search agent. During the iteration, each search agent C i The position of (Iter) is updated as follows: Among them, C i (Iter) represents the i-th search agent, From the balancing pool, γ is a random vector in the interval [0,1]. Other parameters are as follows: Where r, r1, r2 are random numbers in [0, 1], C eq (Iter) comes from the balance pool, C i (Iter) represents the i-th search agent, sign(r-0.5) controls the exploration direction, and positive and negative probabilities are equal.

Images