Multi-agent path planning algorithm based on adaptive memetic algorithm

Abstract

The invention discloses a multi-agent path planning algorithm based on an adaptive memetic algorithm, and aims to solve the problems that the multi-agent path planning algorithm is not mature enough and the convergence speed of the algorithm is low. According to the optimization method, through an algorithm structure in which a global optimization algorithm is matched with local search, chromosomes are used as generation paths in a two-dimensional grid map, strategies such as'selection 'and'crossing' are carried out on the generation paths to optimize fitness values of the generation paths, and a hill climbing algorithm is used as a sub-algorithm to carry out local optimization on the generation paths, so that a generated solution is prevented from falling into local optimum, and the generation efficiency of the two-dimensional grid map is improved. Therefore, the multi-agent motion control precision is improved, and the convergence speed and optimization efficiency of the algorithm are enhanced. The problems that the algorithm convergence speed is low and the path optimization precision is low in the current multi-agent-based path planning field are solved. Experimental results show that the method can accurately realize multi-target-point path optimization for multiple agents, each path is converged to the global optimal path length along with the population iteration average length, and the algorithm test achieves an expected effect.

Description

Technical Field

[0001] The present invention uses a path planning algorithm based on an adaptive meme algorithm to realize the path-based collaborative scheduling of multiple agents. The algorithm is a meta-heuristic optimization algorithm that combines a global heuristic algorithm with a local search. It has broad application prospects in solving multi-objective optimization models with complex constraints. Multi-agent collaborative scheduling, that is, by adding a constraint model, multiple agents can move along the planned path at the same time and avoid conflicts between agents. The study of this problem can improve the efficiency of the scheduling system and is a current research hotspot in the field of multi-agents. Background Art

[0002] With the development of intelligent manufacturing technology, many industrial workshops now use mobile robots to realize the dispatch and transportation of goods, which helps to promote unmanned operation and automated operation of workshops. With the continuous expansion of the market, single-agent systems are difficult to meet the needs of complex tasks, and multi-agent collaborative systems have emerged. They have stronger robustness and environmental adaptability, and promote the flexibility and fault tolerance of the system. Therefore, the research results of the present invention have broad application prospects.

[0003] The key challenge of path planning is that the optimization algorithm is not mature enough and the convergence speed of the algorithm is slow, which makes the robot unable to adapt to more complex work scenarios. Most scholars divide the optimization algorithm into two types: centralized planning algorithm and distributed planning algorithm for research, but the designed algorithm is generally of low quality and efficiency in solving the model, and needs to collect more complete map information and communication information of adjacent agents, thus consuming a lot of computing resources. When the algorithm processes a model with a large amount of map information or complex agent conflicts, it is common that the algorithm is prone to fall into local optimality during the iterative calculation process, which will cause the robot to be locked at the local optimal point during the process of path obstacle avoidance. Therefore, it is necessary to establish a path planning optimization algorithm with stronger search capabilities to improve the convergence speed and optimization efficiency of the algorithm in solving multi-agent path planning models.

[0004] The present invention designs a meme-based multi-agent path planning method, which solves the multi-agent path optimization model by constructing a path length optimization model. Summary of the invention

[0005] In order to solve the above practical problems, the present invention provides a multi-agent path planning algorithm based on an adaptive meme algorithm, which solves the multi-agent path optimization model by adding an optimization operator that combines global optimization with local optimization and improving its local optimization strategy. Compared with the traditional path planning algorithm, the algorithm improves the convergence speed and control accuracy of the algorithm, and improves the optimization efficiency of solving the multi-agent path planning problem.

[0006] A multi-agent path planning algorithm based on an adaptive meme algorithm is characterized by establishing a fitness function based on turning cost, designing a chromosome selection strategy based on an improved roulette operation, designing a chromosome optimization strategy based on crossover and mutation, establishing a continuous path function and a local optimization strategy, and realizing the optimization of the goal of "shortest path length", including the following steps:

[0007] (1) Establishing a fitness function based on turning cost

[0008] The chromosome in binary string format is used to represent the generated path in the two-dimensional grid map. The distance between the center points of the two-dimensional grid map is used to represent the adjacent distance of the grid. The turning cost is used to measure the robot's travel state in the adjacent grid, and the turning cost is encoded using the fitness function. The turning cost fitness function F is established. i k as follows:

[0009]

[0010] Among them, F i k Represents the fitness value of the kth chromosome in the population in the i-th grid, using Represents the rectangular coordinate of the kth chromosome in the population after decoding in the i-th grid, represents the rectangular ordinate of the kth chromosome in the population after decoding in the i-th grid. If the robot makes a straight turn, the value of the turning cost function is encoded as 1; if it makes an oblique turn, the value of the turning cost function is encoded as If other forms of turning are performed, i.e., jumping grids or crossing obstacles, the turning cost function value is encoded as 100;

[0011] (2) Design of a chromosome selection strategy based on an improved roulette wheel operation

[0012] ①First, a set of initial solutions is randomly generated in the form of chromosomes as the initial population, and the fitness F corresponding to the chromosome individuals contained in the initial population is i k Take the reciprocal as the roulette fitness, where the roulette fitness of the kth chromosome individual in the population is V k The calculation formula of ′ is as follows:

[0013]

[0014] ② The roulette fitness V corresponding to the chromosome k ′ linearly maps to the range of [0,1], and normalizes the value P k As the probability of being selected, the selection is made randomly, where the probability P of the kth individual in the population being selected isk The calculation formula is as follows:

[0015]

[0016] Among them, F i k represents the fitness value of the kth chromosome individual in the i-th grid, the number of chromosome individuals m in the population is set to 200, and the number of genes n of the individual chromosome is set to 20;

[0017] ③ Each chromosome in the population uses the roulette strategy to select individuals according to the roulette selection probability Gr and the individuals are retained;

[0018] ④In process ③, the chromosomes that are not selected are selected according to the random selection probability Rr to select a certain size of population individuals and be retained;

[0019] ⑤ The chromosome individuals selected in processes ③ and ④ are combined to form a new generation of population and retained;

[0020] Among them, Gr is the probability of achieving individual selection through the roulette strategy, and its value is set to 0.7, and Rr is the probability of achieving individual selection through the random search strategy, and its value is set to 0.3;

[0021] (3) Designing chromosome optimization strategies based on crossover and mutation

[0022] A single-point crossover strategy is constructed to achieve global optimization of chromosomes. cp is used to represent the probability of each chromosome in the population participating in the crossover, and its value is set to 0.4.

[0023] ①First, select a chromosome population of a certain size in the new generation population according to the crossover probability cp, and use P k and P k+1 represents the parent chromosome, which satisfies the sequence and in Represents the undecoded binary value of the k-th chromosome in the i-th grid;

[0024] ②Use the pointer index position to randomly find the parent chromosome P k and P k+1 Select two crossover points in the sequence, and the gene sequences of the chromosomes will be exchanged at the crossover points, so that the daughter chromosomes after the crossover all carry the gene sequences of their parent chromosomes. k and C k+1 The formula is as follows:

[0025] C k =P k ×a+P k+1×(1-a) (4)

[0026] C k+1 =P k ×(1-a)+P k+1 ×a (5)

[0027] Where a represents the cross random number that determines the pointer index position, and its value will be linearly assigned in the range of [0,1] according to the pointer index position;

[0028] ③ Use point mutation strategy to generate offspring chromosome C k and C k+1 To perform mutation optimization, first randomly select a progeny chromosome, and then randomly select a mutation point using the position of the pointer index. The gene at the mutation point of the chromosome will undergo allelic mutation. Each population individual mutates according to the mutation probability mp, which is set to 0.3. The mutation strategy calculation formula is as follows:

[0029]

[0030] in, represents the undecoded binary value of the kth chromosome in the i-th grid, and R is the direction of the binary mutation flip;

[0031] (4) Establishing a continuous path function

[0032] ① Select parameter list C[] to store the continuous path that meets the requirements, and use equations (7) and (8) to decode the chromosomes in the population into the rectangular coordinates of the center points of each grid, and judge whether there are obstacles around the inserted grid and whether the position jumps out of the area of ​​the grid map, and compare whether the inserted grid is in the path stored in list C[]. If there are no obstacles around the inserted grid and it is not on the existing path, the grid coordinates of the next state will be inserted. and The iterative calculation formula for inserting grid coordinates is as follows:

[0033]

[0034] in, represents the floor operation, and Indicates the grid coordinates of the previous state, F i k represents the fitness value of the kth chromosome individual in the i-th grid, Represents the undecoded binary value of the k-th chromosome in the i-th grid;

[0035] ② Use formulas (9) and (10) to determine whether the grid coordinates of the current point on this path are continuous with the coordinates of the inserted grid point, where Indicates rounding up operation;

[0036]

[0037] If the current grid center and the inserted grid center point coordinate value and is less than or equal to 1, then two adjacent grid points and If continuous, the next grid point will be inserted according to equations (9) and (10) If the current grid center and the inserted grid center point coordinate value and If greater than 1, then two adjacent grid points and If it is not continuous, use the filter function to filter out the path;

[0038] (5) Design a local search strategy based on the hill climbing algorithm

[0039] ① By constructing a local search operator to locally optimize the population, first randomly select a pointer i in the population and compare the chromosome fitness in its neighborhood; where q represents the value of the selected neighborhood individual, and its value is set to 2, then the algorithm will compare the fitness F corresponding to the i-1, i, i+1 chromosome individuals i-1 , F i , F i+1 ;

[0040] ② Use list P[] to store the better chromosomes after local optimization, that is, keep the individuals with smaller fitness values ​​compared in ① in this list, then the pointer traverses the entire population, repeats the fitness comparison process in ①, and updates list P[] as the pointer traverses;

[0041] ③ In the P[] list, randomly generate l chromosome paths with the minimum fitness according to the fitness function, and decode the chromosome corresponding to each path into grid rectangular coordinates for path conflict constraints, and the constraints satisfy and Make Make sure that each motion track does not collide with each other, and realize the generation of multiple optimal paths for robots in the grid map;

[0042] ④ Use the grid map method to model the path planning environment, set the grid simulation map size to 20×20, set the number of obstacles in the grid to 20, set the number of paths generated by the algorithm to l=3, and add the maximum number of iterations N=200 or less than the optimal solution error limit δ≤0.05 as the setting conditions for algorithm termination. If the algorithm termination conditions are met, the algorithm will stop iterating and generate a population with the best fitness to achieve the solution of multi-agent path planning. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 Design flow chart for the algorithm of the present invention

[0044] Figure 2 The grid simulation map of the present invention

[0045] Figure 3 The simulation effect diagram of the present invention is

[0046] Figure 4 This is the optimization effect diagram of the present invention DETAILED DESCRIPTION

[0047] The present invention designs a meme-based multi-agent path planning method, which solves the multi-agent path optimization model by constructing a path length optimization model. The proposed algorithm model can be deployed to multiple robot terminals to achieve the effect of collaborative scheduling.

[0048] A multi-agent path planning algorithm based on an adaptive meme algorithm is characterized by establishing a fitness function based on turning cost, designing a chromosome selection strategy based on an improved roulette operation, designing a chromosome optimization strategy based on crossover and mutation, establishing a continuous path function and a local optimization strategy, and realizing the optimization of the goal of "shortest path length", including the following steps:

[0049] (1) Establishing a fitness function based on turning cost

[0050] The chromosome in binary string format is used to represent the generated path in the two-dimensional grid map. The distance between the center points of the two-dimensional grid map is used to represent the adjacent distance of the grid. The turning cost is used to measure the robot's travel state in the adjacent grid, and the turning cost is encoded using the fitness function. The turning cost fitness function F is established. i k as follows:

[0051]

[0052] Among them, F i k Represents the fitness value of the kth chromosome in the population in the i-th grid, using Represents the rectangular coordinate of the kth chromosome in the population after decoding in the i-th grid, represents the rectangular ordinate of the kth chromosome in the population after decoding in the i-th grid. If the robot makes a straight turn, the value of the turning cost function is encoded as 1; if it makes an oblique turn, the value of the turning cost function is encoded as If other forms of turning are performed, i.e., jumping grids or crossing obstacles, the turning cost function value is encoded as 100;

[0053] (2) Design of a chromosome selection strategy based on an improved roulette wheel operation

[0054] ①First, a set of initial solutions is randomly generated in the form of chromosomes as the initial population, and the fitness F corresponding to the chromosome individuals contained in the initial population is i k Take the reciprocal as the roulette fitness, where the roulette fitness of the kth chromosome individual in the population is V k The calculation formula of ′ is as follows:

[0055]

[0056] ② The roulette fitness V corresponding to the chromosome k ′ linearly maps to the range of [0,1], and normalizes the value P k As the probability of being selected, the selection is made randomly, where the probability P of the kth individual in the population being selected is k The calculation formula is as follows:

[0057]

[0058] Among them, F i k represents the fitness value of the kth chromosome individual in the i-th grid, the number of chromosome individuals m in the population is set to 200, and the number of genes n of the individual chromosome is set to 20;

[0059] ③ Each chromosome in the population uses the roulette strategy to select individuals according to the roulette selection probability Gr and the individuals are retained;

[0060] ④In process ③, the chromosomes that are not selected are selected according to the random selection probability Rr to select a certain size of population individuals and be retained;

[0061] ⑤ The chromosome individuals selected in processes ③ and ④ are combined to form a new generation of population and retained;

[0062] Among them, Gr is the probability of achieving individual selection through the roulette strategy, and its value is set to 0.7, and Rr is the probability of achieving individual selection through the random search strategy, and its value is set to 0.3;

[0063] (5) Design a chromosome optimization strategy based on crossover and mutation

[0064] A single-point crossover strategy is constructed to achieve global optimization of chromosomes. cp is used to represent the probability of each chromosome in the population participating in the crossover, and its value is set to 0.4.

[0065] ①First, select a chromosome population of a certain size in the new generation population according to the crossover probability cp, and use Pk and P k+1 represents the parent chromosome, which satisfies the sequence and in Represents the undecoded binary value of the k-th chromosome in the i-th grid;

[0066] ②Use the pointer index position to randomly find the parent chromosome P k and P k+1 Select two crossover points in the sequence, and the gene sequences of the chromosomes will be exchanged at the crossover points, so that the daughter chromosomes after the crossover all carry the gene sequences of their parent chromosomes. k and C k+1 The formula is as follows:

[0067] C k =P k ×a+P k+1 ×(1-a) (4)

[0068] C k+1 =P k ×(1-a)+P k+1 ×a (5)

[0069] Where a represents the cross random number that determines the pointer index position, and its value will be linearly assigned in the range of [0,1] according to the pointer index position;

[0070] ③ Use point mutation strategy to generate offspring chromosome C k and C k+1 To perform mutation optimization, first randomly select a progeny chromosome, and then randomly select a mutation point using the position of the pointer index. The gene at the mutation point of the chromosome will undergo allelic mutation. Each population individual mutates according to the mutation probability mp, which is set to 0.3. The mutation strategy calculation formula is as follows:

[0071]

[0072] in, represents the undecoded binary value of the kth chromosome in the i-th grid, and R is the direction of the binary mutation flip;

[0073] (6) Establishing a continuous path function

[0074] ① Select parameter list C[] to store the continuous path that meets the requirements, and use equations (7) and (8) to decode the chromosomes in the population into the rectangular coordinates of the center points of each grid, and judge whether there are obstacles around the inserted grid and whether the position jumps out of the area of ​​the grid map, and compare whether the inserted grid is in the path stored in list C[]. If there are no obstacles around the inserted grid and it is not on the existing path, the grid coordinates of the next state will be inserted. and The iterative calculation formula for inserting grid coordinates is as follows:

[0075]

[0076] in, represents the floor operation, and Indicates the grid coordinates of the previous state, F i k represents the fitness value of the kth chromosome individual in the i-th grid, Represents the undecoded binary value of the k-th chromosome in the i-th grid;

[0077] ② Use formulas (9) and (10) to determine whether the grid coordinates of the current point on this path are continuous with the coordinates of the inserted grid point, where Indicates rounding up operation;

[0078]

[0079] If the current grid center and the inserted grid center point coordinate value and is less than or equal to 1, then two adjacent grid points and If continuous, the next grid point will be inserted according to equations (9) and (10) If the current grid center and the inserted grid center point coordinate value and If greater than 1, then two adjacent grid points and If it is not continuous, use the filter function to filter out the path;

[0080] (5) Design a local search strategy based on the hill climbing algorithm

[0081] ① By constructing a local search operator to locally optimize the population, first randomly select a pointer i in the population and compare the chromosome fitness in its neighborhood; where q represents the value of the selected neighborhood individual, and its value is set to 2, then the algorithm will compare the fitness F corresponding to the i-1, i, i+1 chromosome individuals i-1 , F i , Fi+1 ;

[0082] ② Use list P[] to store the better chromosomes after local optimization, that is, keep the individuals with smaller fitness values ​​compared in ① in this list, then the pointer traverses the entire population, repeats the fitness comparison process in ①, and updates list P[] as the pointer traverses;

[0083] ③ In the P[] list, randomly generate l chromosome paths with the minimum fitness according to the fitness function, and decode the chromosome corresponding to each path into grid rectangular coordinates for path conflict constraints, and the constraints satisfy and Make Make sure that each motion track does not collide with each other, and realize the generation of multiple optimal paths for robots in the grid map;

[0084] ④ Use the grid map method to model the path planning environment, set the grid simulation map size to 20×20, set the number of obstacles in the grid to 20, set the number of paths generated by the algorithm to l=3, and add the maximum number of iterations N=200 or less than the optimal solution error limit δ≤0.05 as the setting conditions for algorithm termination. If the algorithm termination conditions are met, the algorithm will stop iterating and generate a population with the best fitness to achieve the solution of multi-agent path planning.

[0085] Table 1 is the parameter values ​​of the present invention

[0086]

Claims

1. A multi-agent path planning algorithm based on an adaptive memetic algorithm, characterized in that: The following steps are involved: (1) Establishing a fitness function based on turning cost The chromosome in binary string format is used to represent the generated path in the two-dimensional grid map. The distance between the center points of the two-dimensional grid map is used to represent the adjacent distance of the grid. The turning cost is used to measure the robot's travel state in the adjacent grid, and the turning cost is encoded using the fitness function. The turning cost fitness function F is established. i k as follows: Among them, F i k Represents the fitness value of the kth chromosome in the population in the i-th grid, using Represents the rectangular coordinate of the kth chromosome in the population after decoding in the i-th grid, represents the rectangular ordinate of the kth chromosome in the population after decoding in the i-th grid; if the robot makes a straight turn, the value of the turning cost function is encoded as 1; if it makes an oblique turn, the value of the turning cost function is encoded as If other forms of turning are performed, i.e., jumping grids or crossing obstacles, the turning cost function value is encoded as 100; (2) Design of a chromosome selection strategy based on an improved roulette wheel operation ①First, a set of initial solutions is randomly generated in the form of chromosomes as the initial population, and the fitness F corresponding to the chromosome individuals contained in the initial population is i k Take the reciprocal as the roulette fitness, where the roulette fitness of the kth chromosome individual in the population is V k The calculation formula of ′ is as follows: ② The roulette fitness V corresponding to the chromosome k ′ linearly maps to the range of [0,1], and normalizes the value P k As the probability of being selected, the selection is made randomly, where the probability P of the kth individual in the population being selected is k The calculation formula is as follows: Among them, F i k represents the fitness value of the kth chromosome individual in the i-th grid, the number of chromosome individuals m in the population is set to 200, and the number of genes n of the individual chromosome is set to 20; ③ Each chromosome in the population uses the roulette strategy to select individuals according to the roulette selection probability Gr and the individuals are retained; ④In process ③, the chromosomes that are not selected are selected according to the random selection probability Rr to select a certain size of population individuals and be retained; ⑤ The chromosome individuals selected in processes ③ and ④ are combined to form a new generation of population and retained; Among them, Gr is the probability of achieving individual selection through the roulette strategy, and its value is set to 0.7, and Rr is the probability of achieving individual selection through the random search strategy, and its value is set to 0.3; (3) Designing chromosome optimization strategies based on crossover and mutation A single-point crossover strategy is constructed to achieve global optimization of chromosomes. cp is used to represent the probability of each chromosome in the population participating in the crossover, and its value is set to 0.

4. ①First, select a chromosome population of a certain size in the new generation population according to the crossover probability cp, and use P k and P l+1 represents the parent chromosome, which satisfies the sequence and in Represents the undecoded binary value of the k-th chromosome in the i-th grid; ②Use the pointer index position to randomly find the parent chromosome P k and P k+1 Select two crossover points in the sequence, and the gene sequences of the chromosomes will be exchanged at the crossover points, so that the daughter chromosomes after the crossover all carry the gene sequences of their parent chromosomes. k and C k+1 The formula is as follows: C k =P k ×a+P k+1 ×(1-a) (4) C k+1 =P k ×(1-a)+P k+1 ×a (5) Where a represents the cross random number that determines the pointer index position, and its value will be linearly assigned in the range of [0,1] according to the pointer index position; ③ Use point mutation strategy to generate offspring chromosome C k and C k+1 To perform mutation optimization, first randomly select a progeny chromosome, and then randomly select a mutation point using the position of the pointer index. The gene at the mutation point of the chromosome will undergo allelic mutation. Each population individual mutates according to the mutation probability mp, which is set to 0.

3. The mutation strategy calculation formula is as follows: in, represents the undecoded binary value of the k-th chromosome in the i-th grid, and R is the direction of the binary mutation flip; (4) Establishing a continuous path function ① Select parameter list C[] to store the continuous path that meets the requirements, and use equations (7) and (8) to decode the chromosomes in the population into the rectangular coordinates of the center points of each grid, and judge whether there are obstacles around the inserted grid and whether the position jumps out of the area of ​​the grid map, and compare whether the inserted grid is in the path stored in list C[]. If there are no obstacles around the inserted grid and it is not on the existing path, the grid coordinates of the next state will be inserted. and The iterative calculation formula for inserting grid coordinates is as follows: in, represents the floor operation, and Indicates the grid coordinates of the previous state, F i k represents the fitness value of the kth chromosome individual in the i-th grid, Represents the undecoded binary value of the k-th chromosome in the i-th grid; ② Use formulas (9) and (10) to determine whether the grid coordinates of the current point on this path are continuous with the coordinates of the inserted grid point, where Indicates rounding up operation; If the current grid center and the inserted grid center point coordinate value and is less than or equal to 1, then two adjacent grid points and If continuous, the next grid point will be inserted according to equations (9) and (10) If the current grid center and the inserted grid center point coordinate value and If greater than 1, then two adjacent grid points and If it is not continuous, use the filter function to filter out the path; (5) Design a local search strategy based on the hill climbing algorithm ① By constructing a local search operator to locally optimize the population, first randomly select a pointer i in the population and compare the chromosome fitness in its neighborhood; where q represents the value of the selected neighborhood individual, and its value is set to 2, then the algorithm will compare the fitness F corresponding to the i-1, i, i+1 chromosome individuals i-1 , F i , F i+1 ; ② Use list P[] to store the better chromosomes after local optimization, that is, keep the individuals with smaller fitness values ​​compared in ① in this list, then the pointer traverses the entire population, repeats the fitness comparison process in ①, and updates list P[] as the pointer traverses; ③ In the P[] list, randomly generate l chromosome paths with the minimum fitness according to the fitness function, and decode the chromosome corresponding to each path into grid rectangular coordinates for path conflict constraints, and the constraints satisfy and Make Make sure that each motion track does not collide with each other, and realize the generation of multiple optimal paths for robots in the grid map; ④ Use the grid map method to model the path planning environment, set the grid simulation map size to 20×20, set the number of obstacles in the grid to 20, set the number of paths generated by the algorithm to l=3, and add the maximum number of iterations N=200 or less than the optimal solution error limit δ≤0.05 as the setting conditions for algorithm termination. If the algorithm termination conditions are met, the algorithm will stop iterating and generate a population with the best fitness.

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