CN112270398B - Cluster behavior learning method based on gene programming - Google Patents
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Abstract
The invention provides a cluster behavior learning method based on gene programming, which utilizes the gene programming method to search a solution space in a heuristic way under the condition of no priori knowledge, and finally provides a neighbor selection mechanism and a behavior decision function which can well reflect the real motion rules of clusters, and under the current trend of commonly adopting a forward modeling means, the invention adopts an inversion way to learn the individual motion rules of the clusters. The invention realizes the regular learning of the cluster behaviors under the condition of no priori knowledge, can fill the gap of the learning method in the field, and can be used for learning unmanned cluster behaviors and researching biological cluster behaviors.
Description
Technical Field
The invention relates to the field of inversion modeling, in particular to a cluster behavior inversion method, which is an inversion task of an individual behavior model facing cluster motion data.
Background
Cluster motion is a ubiquitous natural phenomenon, and is a typical representative of cluster motion, whether bird clusters fly, or fish clusters are subjected to stress swimming, or microbial community migration. An increasing number of artificial clusters, such as robot clusters or drone clusters, are also emerging in the current age. The movement of these clusters all exhibit a "flooding" phenomenon in clustered systems. With the development of computer technology, microelectronic technology and the like, the group cooperation in the future must become a new trend, and the group system has the advantages of low cost, substitution, easy expansion, high efficiency and the like.
On the premise that unmanned, intelligent and clustering becomes more and more the current mainstream trend, the learning of the cluster behavior model is an important subject in the future. In particular, learning of non-cooperative cluster behaviors is very challenging to a traditional forward modeling mode because communication and negotiation cannot be performed and learning can only be performed based on motion data acquired by simple observation, so that a data-driven reverse modeling mode is a necessary choice.
In recent years, good results have been achieved for forward modeling method research of the cluster motion model, but no breakthrough has yet occurred in the reverse evolution modeling method.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a cluster behavior learning method based on gene programming. Genetic programming is essentially an evolutionary algorithm that implements the optimal solution of the problem by mimicking the process of choosing the winner and the worse of a biological population in nature. The evolution algorithm maintains a generational evolving population during operation, and each individual in the population is a solution to the problem. The essential difference between genetic programming and traditional genetic algorithms is the way in which individuals in a genetic population are encoded. In the genetic algorithm, the chromosomes of population individuals are encoded linearly, and the genetic programming is encoded by a tree structure. According to the invention, on the premise of not relying on priori knowledge, the observation data is learned, and the cluster behavior model is obtained.
The technical scheme adopted by the invention for solving the technical problems comprises the following steps:
Step 1: acquiring cluster motion data;
Acquiring target cluster data by using a video processing and target tracking technology, or generating cluster motion data by using an existing cluster model based on simulation, wherein the cluster motion data comprises state information of the position and the speed of a cluster individual at any moment;
Step 2: coding the population;
Coding the behavior rules, wherein the adopted codes are double-layer real number codes (different from binary codes) of nested structures, and correspond to two dimensions of the cluster individual motion rules, wherein the two dimensions are respectively neighbor selection and response strategies; the neighbor information of the individual behaviors corresponding to the primary codes is generated by evolution of the behavior model of the clustered individual from none to none on two levels by utilizing and processing the model; the neighbor selection model is encoded into a neighbor selection radius r, an individual in the radius r is regarded as a neighbor, and the information of the neighbor forms the input of a secondary model; the secondary model is encoded according to a tree structure, and the encoded content is decoded to be a function for responding and deciding based on the perception information of the cluster individuals; fig. 1 is a schematic diagram of tree coding, after decoding, the following response function with two inputs x, y:
wherein x and y are determined according to the definition of a user, and the decoding mode only completes the construction of the relation between input and output. For example, x is the abscissa value of the relative distance between a certain neighbor and the self, and y is the ordinate value of the relative distance between a certain neighbor and the self;
Step 3: generating an initial population;
The population corresponds to the population formed by individuals in the evolutionary algorithm (genetic programming), and the behavior decision rule represented by the genetic code of the individuals is an optimized target; namely, the decision rule corresponds to the movement mode of a group of movement intelligent agents, and the set of the movement intelligent agents is called a cluster;
the individual codes of the first-class population correspond to the neighbor selection radius r of the represented cluster individuals, and are initialized according to the random probability of uniform distribution; each individual of the first population corresponds to a second population, individual codes in the second population are decision functions, and random sampling is adopted for initialization; wherein the genes of each node (node, a unit in the chromosomal dendrogram of the population of individuals, e.g., x, + in FIG. 1, etc.) are selected from a given set of functions and variables;
Step 4: evaluating population fitness;
firstly, according to the design of the evolution algorithm, individual fitness function description is given, the fitness function describes the expected evolution direction of a user on the cluster individuals, for example, the expected clusters are kept gathered, and the fitness is defined as the cluster density.
Performing independent evolution calculation for a plurality of times on a secondary population corresponding to individuals in each primary population, and taking the minimum fitness in the history evolution as the final fitness of the individuals (the fitness is specific to the primary individuals, namely, the population individuals comprising the complete cluster individual decision rule); the individual fitness evaluation rules in the first population are as follows: firstly, decoding an individual according to an encoding mode to obtain a decision function Γ, further substituting a designated input into the decision function to calculate an estimated value, and comparing a calculated error with a true value in original data to serve as individual fitness:
Wherein θ i (t+Δt) =Γ (x (t)) is the motion direction of the next moment calculated from the generated decision function through the neighbor information of the previous moment; t at the current time, Δt is the time step;
step 5: selecting a good individual;
Selecting m excellent individuals from the generation population;
step 6: cross mutation is carried out on individuals to generate a next generation population;
The individuals in the first-class population only contain distance information, so that the cross mutation operation is integrated into one, namely, the original code (chromosome) is reinitialized by the preset mutation probability p cm; the individuals in the second-level population firstly cross-operate the selected individuals with a given probability p c, and then mutate all the individuals with a given probability p m;
Step7: the steps 4-6 are circulated until a trigger termination condition is triggered, and the minimum fitness individual appearing in the evolution process is the optimal individual;
Step 8: and decoding the optimal individual according to the coding rule to obtain an estimated solution of the individual motion rule in the cluster.
The selection method for selecting the excellent individuals comprises the following steps: extracting k individuals from the population at random each time, and taking the individuals with the smallest fitness, which is a complete preference process, and repeating the preference process until m individuals are selected;
In step 6, the crossover is that two parents A and B randomly select a crossover point respectively, then the part after the crossover point of the individual A is discarded and replaced by the part after the crossover point of the individual B, and fig. 2 is a schematic diagram of crossover operation.
The variation is randomly selected between the existing single-point variation and subtree variation methods with the same probability.
The single-point variation is as follows: randomly selecting a variation point in individual codes, and randomly varying the codes of the point, namely replacing the gene codes of the point with another symbol with the same type, specifically: if the point is a function, another function with the same number of self variables is replaced, and if the point is a variable, another randomly generated variable is replaced. The operation is similar to the bit flipping operation in genetic algorithms.
The subtree variation is: the variation points are randomly selected in the individual codes, subtrees after the points are replaced by the randomly generated subtrees, and fig. 3 is a subtree variation schematic diagram.
And the termination condition is that the circulation algebra reaches the maximum set value or the model error is smaller than the set threshold value.
The value of p cm is 0.5.
The p c takes a value of 0.5.
The p m takes a value of 0.1.
The invention has the advantages that the heuristic search is carried out on the solution space by using the genetic programming method without priori knowledge, and the neighbor selection mechanism and the behavior decision function which can well reflect the actual movement rules of the clusters are finally provided, so that under the current trend of commonly adopting the forward modeling means, the way of adopting inversion to learn the individual movement rules of the clusters is also developed.
The invention discloses a cluster behavior learning technology based on genetic programming for non-cooperative cluster motion data, which can be used for learning and inverting unknown cluster motion rules, realizing cluster behavior rule learning under the condition of no priori knowledge, filling the gap of the learning method in the field, and can be used for learning unmanned cluster behaviors and researching biological cluster behaviors.
Drawings
FIG. 1 is a schematic diagram of the crossover operation of the present invention.
FIG. 2 is a single point variation schematic diagram of the present invention.
FIG. 3 is a schematic representation of subtree variation according to the present invention.
Fig. 4 shows the adaptability change curve of a certain evolution experiment of the present invention.
Fig. 5 is a graph showing neighbor identification distance change curves given by 10 monte carlo experiments according to the present invention.
Detailed Description
The invention will be further described with reference to the drawings and examples.
The invention will now be further described with reference to the examples, figures:
Step 1: to illustrate the effectiveness of the present invention, the present embodiment employs simulation means to generate cluster motion data and inverts the cluster motion rules based thereon. First, a simulation program is written, and cluster motion raw data for learning is generated. The adopted cluster motion model is a variant of Vicsek model, the motion speed of each individual in the population described by the model is constant as v, and the individual only changes the speed direction in the motion process. Any body, denoted as a i, updates its own motion direction to the average of the neighbor motion directions with random noise at each moment. The selection of the neighbor is based on the distance from the neighbor to the individual itself, and all individuals whose distance from the individual itself is within a radius r are defined as neighbors of a i, denoted as N i.
100 Individuals were simulated by a simulation program based on the above model, initially randomly distributed in a 500x500 virtual simulation environment. The individual neighbor judging range is 50, the speed is 3, the simulation step length is 1/30s, and the noise is random noise uniformly distributed within the range of [ -0.01, +0.01 ]. And (5) recording individual motion data for the model simulation time length of 1 s.
Step 2: coding the population;
The behavior rules are encoded, and the encoding adopted by the invention is double-layer real number encoding (different from binary encoding) of a nested structure, and corresponds to two dimensions of the individual motion rules of the cluster, neighbor selection and response strategies. The neighbor information of the individual behaviors corresponding to the primary codes is generated by evolution of the behavior models of the clustered individuals from none to none on two levels by utilizing and processing the neighbor information of the individual behaviors corresponding to the secondary codes. The neighbor selection model is encoded as a neighbor selection radius r, and other individuals within this radius are considered neighbors whose information constitutes the input to the secondary model. The secondary model is encoded according to a tree structure, and the encoded content is decoded to be a function of the cluster individuals for response decision based on the perception information.
Step 3: generating an initial population
The primary population size is 100, and the evolution algebra is 100. The individual codes are neighbor selection radius r, and are initialized through uniformly distributed random numbers r-U (0,500). Each individual of the first population corresponds to a second population, the population size is 100, and the evolution algebra is 100 generations. Individuals in the population are encoded as decision functions, where the genes for each node are selected from a set of functions and a set of variables. The specific function set is { +, -, ×, ++sin, cos, tan, count, sum, count, rand }, the variable set is { x, rand }, wherein x is a vector represented by [ θ 1,θ2,…θn]T ], n is the number of neighbors corresponding to the current individual according to the first-level rule, θ i is the speed direction of the ith neighbor, and the output of the coding decision function is the motion direction of the target individual at the next moment.
Wherein p cm is set to 0.5, and p c and p m are set to 0.5 and 0.1, respectively.
Step 4: assessing population fitness
Firstly, according to the design of the evolution algorithm, individual fitness function description is given, the fitness function describes the expected evolution direction of a user on the cluster individuals, for example, the expected clusters are kept gathered, and the fitness is defined as the cluster density.
And 5 independent evolution calculations are carried out on the secondary population corresponding to the individuals in each primary population, and the minimum fitness in the history evolution is taken as the final fitness of the individuals (the fitness is specific to the primary individuals, namely the population individuals comprising the complete cluster individual decision rule). The individual fitness evaluation rules in the first population are as follows: firstly, decoding an individual according to a coding mode to obtain a decision function gamma, substituting a designated input into an estimated value calculated by the decision function, and comparing a calculated error with a true value in original data to obtain individual fitness
Here, θ i (t+Δt) =Γ (x (t)) is the motion direction of the next moment calculated from the generated decision function by the neighbor information of the previous moment.
Step 5: selection of good individuals
30 Good individuals were selected from the current generation population. The specific method is that 5 individuals are randomly extracted from the population each time, the individuals with the minimum fitness are selected, the whole optimization process is adopted once, and the optimization process is repeated until 30 individuals are selected.
Step 6: cross-variation of individuals to generate next generation population
The individuals in the first-class population only contain distance information, so that the cross mutation operation is integrated into one, namely, the original code (chromosome) is reinitialized by the preset mutation probability p cm; the individuals in the second-class population are subjected to cross operation on the selected individuals at a given probability p c, and then subjected to mutation operation on all the individuals at a given probability p m.
Crossing: for a, B two parents randomly select a crossing point respectively, then discard the part after the crossing point of a individual to replace the part after the crossing point of B individual, fig. 2 is a schematic diagram of crossing operation.
Variation: the existing single-point mutation and subtree mutation methods are randomly selected with the same probability.
Single point variation: randomly selecting a variation point in individual codes, and randomly varying the codes of the point, namely replacing the gene codes of the point with another symbol with the same type, specifically: if the point is a function, another function with the same number of self variables is replaced, and if the point is a variable, another randomly generated variable is replaced. The operation is similar to the bit flipping operation in genetic algorithms.
Subtree variation: the variation points are randomly selected in the individual codes, subtrees after the points are replaced by the randomly generated subtrees, and fig. 3 is a subtree variation schematic diagram.
Step 7: and (4) circulating the steps 4-6 until the algorithm triggers a termination condition, wherein the minimum fitness individual appearing in the evolution process is the optimal individual. Termination condition: the circulation algebra reaches the maximum set value or the model error is smaller than the set threshold.
Step 8: and decoding the optimal individual according to the coding rule to obtain an estimated solution of the individual motion rule in the cluster.
And programming by using an evolution calculation tool library DEAP in a Python environment, and realizing the inversion method and simulation. 10 independent Monte Carlo experiments were performed on an Intel (R) Core (TM) i7-7500U CPU@2.70GHz 2.90GHz,8G memory computer to obtain the optimal individual corresponding solutions as follows: the primary model neighbor selection radius gives a decision function alternative for the 48.9 secondary model:
divide(sum(X),count(X))
sum(divide(X,sum(count(cos(X)))))
divide(mul(X,X),add(X,count(sin(X))))
Through reduction calculation, all three alternative solutions can be classified as target expressions
Fig. 4 shows a fitness change curve of a certain evolution experiment, and fig. 5 shows a change curve of a first-order model optimal solution (neighbor selection range) given by 10 experiments.
As can be seen from fig. 4 and fig. 5, the method provided by the invention has good learning accuracy on the original model contained in the input experimental data based on the common evolution of the two models of the original cluster motion data. Under the background that a forward modeling method is commonly adopted in current research on clusters and the reverse modeling work mostly depends on priori knowledge, the gene programming model inversion method provided by the invention. The method can effectively invert the neighbor selection mechanism of the clustered individuals and the mapping relation from the neighbor information to the self decision variable through a genetic programming approach under the condition that the original model is not provided with prior information.
Claims (9)
1. The cluster behavior learning method based on gene programming is characterized by comprising the following steps:
Step 1: acquiring cluster motion data;
Acquiring target cluster data by using a video processing and target tracking technology, or generating cluster motion data by using an existing cluster model based on simulation, wherein the cluster motion data comprises state information of the position and the speed of a cluster individual at any moment;
Step 2: coding the population;
Coding the behavior rules, wherein the adopted codes are double-layer real number codes of nested structures, and correspond to two dimensions of the cluster individual motion rules, wherein the two dimensions are respectively neighbor selection and response strategies; the neighbor information of the individual behaviors corresponding to the primary codes is generated by evolution of the behavior model of the clustered individual from none to none on two levels by utilizing and processing the model; the neighbor selection model is encoded into a neighbor selection radius r, an individual in the radius r is regarded as a neighbor, and the information of the neighbor forms the input of a secondary model; the secondary model is encoded according to a tree structure, and the encoded content is decoded to be a function for responding and deciding based on the perception information of the cluster individuals; the decoded response function is the following with two inputs x, y:
wherein x and y are determined according to the definition of a user, the decoding mode only completes the construction of the relation between input and output, x is determined to be the abscissa value of the relative distance between a certain neighbor and the user, and y is determined to be the ordinate value of the relative distance between the certain neighbor and the user;
Step 3: generating an initial population;
The population corresponds to the population formed by individuals in the evolutionary algorithm, and the behavior decision rule represented by the genetic code of the individuals is an optimized target; namely, the decision rule corresponds to the movement mode of a group of movement intelligent agents, and the set of the movement intelligent agents is called a cluster;
the individual codes of the first-class population correspond to the neighbor selection radius r of the represented cluster individuals, and are initialized according to the random probability of uniform distribution; each individual of the first population corresponds to a second population, individual codes in the second population are decision functions, and random sampling is adopted for initialization; wherein the genes for each node are selected from a given set of functions and variables;
Step 4: evaluating population fitness;
Firstly, according to the design of an evolution algorithm, individual fitness function description is given, and the fitness function describes the expected evolution direction of a user on a cluster individual;
Performing independent evolution calculation for a plurality of times on a secondary population corresponding to the individuals in each primary population, and taking the minimum fitness in the history evolution as the final fitness of the individuals; the individual fitness evaluation rules in the first population are as follows: firstly, decoding an individual according to an encoding mode to obtain a decision function Γ, further substituting a designated input into the decision function to calculate an estimated value, and comparing a calculated error with a true value in original data to serve as individual fitness:
Wherein θ i (t+Δt) =Γ (x (t)) is the motion direction of the next moment calculated from the generated decision function through the neighbor information of the previous moment; t at the current time, Δt is the time step;
step 5: selecting a good individual;
Selecting m excellent individuals from the generation population;
step 6: cross mutation is carried out on individuals to generate a next generation population;
The individuals in the first-class population only contain distance information, so that the cross mutation operation is integrated into one, namely, the original code is reinitialized by the preset mutation probability p cm; the individuals in the second-level population firstly cross-operate the selected individuals with a given probability p c, and then mutate all the individuals with a given probability p m;
Step7: the steps 4-6 are circulated until a trigger termination condition is triggered, and the minimum fitness individual appearing in the evolution process is the optimal individual;
Step 8: and decoding the optimal individual according to the coding rule to obtain an estimated solution of the individual motion rule in the cluster.
2. The cluster behavior learning method based on genetic programming according to claim 1, wherein:
The selection method for selecting the excellent individuals comprises the following steps: k individuals are randomly extracted from the population each time, and the individual with the smallest fitness is selected, which is a complete optimization process, and the optimization process is repeated until m individuals are selected.
3. The cluster behavior learning method based on genetic programming according to claim 1, wherein:
in the step 6, the crossover is that for A, B two father individuals randomly select a crossover point respectively, then the part after the crossover point of A individual is discarded and replaced with the part after the crossover point of B individual;
The variation is randomly selected between the existing single-point variation and subtree variation methods with the same probability.
4. A cluster behavior learning method based on genetic programming as claimed in claim 3, wherein:
the single-point mutation is to randomly select a mutation point in individual codes, randomly mutate the codes of the point, namely, replace the gene codes of the point with another symbol with the same type, and replace the gene codes of the point with another function with the same self-variable number if the point is a function, and replace the gene codes of the point with another randomly generated variable if the point is a variable.
5.A cluster behavior learning method based on genetic programming as claimed in claim 3, wherein: the subtree mutation is to randomly select a mutation point in the individual codes and replace the subtree after the point with a randomly generated subtree.
6. The cluster behavior learning method based on genetic programming according to claim 1, wherein:
and the termination condition is that the circulation algebra reaches the maximum set value or the model error is smaller than the set threshold value.
7. The cluster behavior learning method based on genetic programming according to claim 1, wherein:
The value of p cm is 0.5.
8. The cluster behavior learning method based on genetic programming according to claim 1, wherein:
The p c takes a value of 0.5.
9. The cluster behavior learning method based on genetic programming according to claim 1, wherein:
the p m takes a value of 0.1.
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