Symbol regression method based on space-time decoupling genetic programming

Abstract

The invention provides a symbol regression method based on space-time decoupling genetic programming, which comprises the following steps: constructing a parallel island model environment based on a spark cluster, dividing a population into a plurality of sub-populations, partitioning all the sub-populations through a space partitioning mechanism, and creating a plurality of sub-populations; collecting production equipment operation data of the production groups, wherein the production equipment operation data of each production group is used as a sub-population to calculate a mathematical model for describing the production equipment operation data; self-adaptively adjusting a local topological structure in the sub-population by using a dynamic sensing strategy in the sub-population and carrying out local migration; and dynamically triggering global migration operation among the subgroups based on the change trend of the global gene entropy, and obtaining an optimal mathematical model for describing the operation data of the production equipment. According to the method, the complex relation between the production data is disclosed, the efficiency and accuracy of mathematical model symbol regression for describing the operation data of the production equipment are improved, and the method particularly plays an important role in solving the problem of complex industrial production data relation modeling.

Description

Technical Field

[0001] The present invention belongs to the technical field of artificial intelligence, and relates to a symbolic regression method based on spatio-temporal decoupled genetic programming, belonging to the cross technical field of data-driven modeling and intelligent optimization. Background Art

[0002] In the field of data-driven modeling, understanding and revealing the internal relationships between data is crucial for both scientific research and industrial applications. Symbolic Regression (SR) is a modeling method that reveals the relationships between variables through mathematical expressions. Its purpose is to discover mathematical expressions that can describe the relationships between independent variables and dependent variables in a dataset. These expressions are usually constructed through a series of mathematical manipulation operators, so that the constructed model can better complete prediction or classification tasks. It is a key technology in this field and has broad application prospects, such as industrial optimization, scientific law discovery, and financial forecasting.

[0003] Genetic Programming (GP), as the main implementation means of symbolic regression, generates mathematical expressions by simulating the evolutionary process of natural selection. Its core idea is to continuously evolve individuals through genetic operations such as mutation and crossover, and search within the possible solution space in order to find the optimal solution to the problem. However, traditional genetic programming has some limitations in symbolic regression tasks, such as:

[0004] High time complexity: When traditional GP performs fitness evaluation on large-scale datasets, the computational cost is huge, resulting in too long training time.

[0005] Low space efficiency: When the population size is large, the storage and operation of individuals will occupy a large amount of memory resources, limiting the scalability of the algorithm in practical applications.

[0006] Overfitting problem: Traditional GP is prone to generating complex expressions, resulting in insufficient generalization ability of the model on the test set.

[0007] Low global search efficiency: Traditional GP is prone to falling into local optima during the search process and is difficult to efficiently explore the entire search space.

[0008] In recent years, researchers have tried to improve the efficiency and effectiveness of genetic programming through methods such as distributed computing and heuristic search strategies. One of these methods is the genetic programming framework based on the parallel island model, which divides the population into multiple "islands", evolves independently within each island, and realizes information exchange between individuals through migration strategies. However, current research mainly focuses on the application of static topologies and simple dynamic migration strategies, lacking a system research on state-aware dynamic adjustment mechanisms and heterogeneous designs. Current research still has not fully resolved the contradiction between time complexity and space complexity, and lacks decoupled optimization of genetic programming in the time and space dimensions.

[0009] Especially in an industrial production environment, in the face of a large amount of real-time monitoring data, such as the energy consumption data of numerically controlled machine tools, more effective algorithms are needed to reduce the contradiction between time complexity and space complexity, and to decouple and optimize genetic programming in the time and space dimensions. By introducing a genetic programming method with spatio-temporal decoupling, it is possible to effectively balance local search and global exploration, reduce communication overhead, avoid interference from frequent global migrations, and improve the generalization ability and computational efficiency of the model. This improvement is of great significance for processing complex industrial production data, optimizing production processes, and reducing costs.

[0010] Therefore, how to provide an equipment fault recommendation and diagnosis method that can further improve the diagnosis accuracy is an urgent problem to be solved by those skilled in the art. Summary of the Invention

[0011] In view of this, the present invention proposes a symbolic regression method based on spatio-temporal decoupled genetic programming to reveal the complex relationships between production data, aiming to improve the efficiency and accuracy of symbolic regression of mathematical models describing the operating data of production equipment, especially playing an important role in solving the data relationship modeling problems of complex industrial production data and optimizing production processes.

[0012] To achieve the above object, the present invention adopts the following technical solutions:

[0013] The present invention discloses a symbolic regression method based on spatio-temporal decoupled genetic programming, comprising the following steps:

[0014] S1: Build a parallel island model environment based on the spark cluster, divide the population into multiple sub-populations, and partition all sub-populations through a spatial partitioning mechanism to create several subgroups;

[0015] S2: Collect the production equipment operation data of n production groups to obtain a high-dimensional time series data set. The production equipment operation data of each production group is used as a sub-population and located in an independent computing unit of the spark cluster to calculate the mathematical model describing the production equipment operation data and execute step S3, where n > 2; every s sub-populations are used as a subgroup to execute step S4, where n > s ≥ 1;

[0016] S3: Calculate the fitness difference between the predicted value and the actual value of the production equipment operation data within the sub-population, and adaptively adjust the local topological structure within the sub-population using a dynamic perception strategy and perform local migration regularly;

[0017] S4: Based on the change trend of the global gene entropy, real-time sense the optimization state among subgroups, and dynamically trigger the global migration operation to obtain the optimal mathematical model describing the production equipment operation data.

[0018] Preferably, in S2, the factory is used as the population, a factory includes multiple production workshops, a production workshop is used as a production group, and the production equipment operation data corresponding to the production workshop is obtained. Each Worker node of the Spark cluster corresponds to a production workshop.

[0019] Preferably, the production equipment operation data includes any multiple parameters of equipment current, voltage, spindle speed, and processing load collected according to a preset period.

[0020] Preferably, S3 includes the following steps:

[0021] The sub-populations within the subgroup are initially connected through a ring topology to form an initial random topological structure;

[0022] Parallelly use a solver to search and perform fitness evaluation on the production equipment operation data of each production group within the subgroup;

[0023] When the change rate of the fitness variance within the subgroup exceeds the threshold, trigger the switching of the local topological rule until the local optimum is detected, determine the final local topological structure, and stop the switching of the local topological rule.

[0024] Preferably, after triggering the switching of the local topological rule, switch to a ring topology; when it is detected that the fitness variance continuously decreases within a continuous fixed number of evolutionary generations, switch to a grid topology; when the local optimum is detected, switch to a random topology.

[0025] Preferably, the fitness function calculation formula is as follows:

[0026]

[0027] where E predictedTo calculate the predicted value of the operation data of production equipment within a sub-population, E measured is the actual value of the operation data of production equipment calculated within a sub-population;

[0028] The fitness variance calculation formula is as follows:

[0029]

[0030] Among them, F i is the individual fitness of the sub-population, is the average fitness of the sub-population, and N is the population size.

[0031] Preferably, the step S3 further includes a step of performing a local migration operation based on the dynamically adjusted topological structure:

[0032] The mathematical models within each subgroup are migrated according to the topological structure, and the optimal S migrate mathematical models within each production group are selected and transmitted across nodes to other production groups within the subgroup through Spark Streaming; among them, the migration scale S migrate is calculated by the following formula:

[0033] S migrate = α·N local + β·N global

[0034] Among them, N local and N global are respectively the population sizes of the sub-population and the subgroup, and α and β are weight parameters.

[0035] Preferably, the global migration operation of the step S4 includes the following steps:

[0036] When it is monitored that the change trend of gene entropy is less than the threshold, trigger the migration of mathematical models between subgroups, and exchange the optimal specified number of mathematical models within each subgroup into the sub-population of other subgroups.

[0037] Preferably, the gene entropy calculation formula is as follows:

[0038]

[0039] Among them, p j is the occurrence probability of the j-th gene, and M is the number of gene types.

[0040] Preferably, the triggering frequency of the global migration is lower than the triggering frequency of the local migration.

[0041] It can be seen from the above technical solutions that compared with the existing method of realizing diagnosis by simply searching and matching through a predefined inference path, the beneficial effects of the present invention include:

[0042] Improve the level of intelligence: The present invention uses the changing trends of fitness variance and gene entropy to sense the optimization state in real time and dynamically trigger local topology adjustment or global migration operations. Fitness variance is used to measure the population diversity within an island, while gene entropy is used to measure the diversity of the entire population. This mechanism can adaptively adjust the search strategy according to actual production data, thereby maintaining high-efficiency exploration ability in complex and changeable industrial environments.

[0043] Enhance diversity and global search ability: The subgroups where different islands of the present invention are located adopt heterogeneous topological structures to adapt to the optimization requirements at different stages. In addition, heterogeneous evolutionary strategies and migration scales are adopted within different subgroups, which not only enhance the population diversity but also improve the global search ability of the algorithm. For high-dimensional time-series data sets, this method can more effectively discover the patterns and rules hidden in big data, and then optimize production scheduling and reduce energy consumption.

[0044] Improve the efficiency of hierarchical management: The present invention realizes effective hierarchical management of local development and global exploration through time decoupling, reduces communication overhead, and avoids the frequent interference problems that may be caused by traditional global migration strategies. Specifically in industrial applications, each workshop acts as an independent "island" for local optimization, and at the same time, it can share the optimal solution through the global migration strategy, promoting the effective exchange of information between workshops and improving the overall production efficiency.

[0045] In summary, the symbolic regression method based on spatio-temporal decoupled genetic programming proposed by the present invention provides an efficient data-driven modeling solution for large-scale real-time monitoring data in industrial production. It can not only effectively solve the problems faced by traditional genetic programming, such as high time complexity and low space efficiency, but also enhance the generalization ability and computational efficiency of the model by dynamically adjusting the search strategy, and ultimately achieve the purpose of optimizing the production process and reducing costs. Description of the Drawings

[0046] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained according to the provided drawings;

[0047] Figure 1 It is the flowchart of the symbolic regression method based on spatio-temporal decoupled genetic programming provided by the embodiment of the present invention;

[0048] Figure 2 It is the schematic diagram of dynamic topology structure adjustment provided by the embodiment of the present invention. Detailed Embodiments

[0049] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0050] The embodiment of the present invention provides a symbolic regression method based on spatio-temporal decoupled genetic programming, and provides a spatio-temporal decoupled genetic programming framework. By constructing a two-level spatio-temporal decoupled architecture and a dynamic state perception mechanism, efficient modeling and optimization of symbolic regression tasks in a distributed environment are realized. As Figure 1 shown, the method includes the following steps:

[0051] S1: Build a parallel island model environment based on the spark cluster, divide the population into multiple sub-populations, partition all sub-populations through a spatial partitioning mechanism, create several subgroups, and group and store the subgroups.

[0052] S2: Collect the production equipment operation data of n production groups to obtain a high-dimensional time series data set. The production equipment operation data of each production group is used as a sub-population in an independent computing unit of the spark cluster to calculate the mathematical model describing the production equipment operation data and execute step S3, where n > 2; every s sub-populations are used as a subgroup to execute step S4, where n > s ≥ 1;

[0053] S3: Calculate the fitness difference between the predicted value and the actual value of the production equipment operation data within the sub-population, and adaptively adjust the local topological structure within the sub-population using a dynamic perception strategy and perform local migration regularly.

[0054] S4: Based on the change trend of the global gene entropy, the optimization state is sensed in real time between subgroups, and the global migration operation is dynamically triggered. It is judged whether the minimum fitness of each sub-population reaches the termination condition. If so, the optimal mathematical model describing the production equipment operation data is obtained; if not, continue to evolve.

[0055] It should be noted that the state perception mechanism monitors the change rate and change trend of the fitness variance and gene entropy, senses the optimization state in real time, and dynamically triggers local topological adjustment or global migration operations. The subgroups where different islands are located transform heterogeneous topological structures according to the state perception to meet the optimization requirements at different stages. Heterogeneous evolutionary strategies and migration scales are adopted within different subgroups to enhance the diversity and global search ability of the population.

[0056] The time decoupling includes:

[0057] Local migration: High-frequency triggering, based on the change trend of local fitness variance, dynamically adjusts the topological structure within the subgroup.

[0058] Global migration: Low-frequency triggering, based on the change trend of global gene entropy, exchanges elite individuals between subgroups to enhance the global search ability.

[0059] In one embodiment, in S2, for the construction of the parallel island model environment, by deploying a spark distributed cluster, the islands are mapped to their respective corresponding worker nodes, and the driver node is responsible for controlling the migration between the islands. Taking a factory as the population, a factory includes multiple production workshops, taking a production workshop as a production group, obtaining the operation data of the production equipment corresponding to the production workshop, and each Worker node of the Spark cluster corresponds to a production workshop.

[0060] In one embodiment, the production equipment operation data includes any multiple parameters among the equipment current, voltage, spindle speed, and processing load collected according to a preset period.

[0061] In one embodiment, S3 includes the following steps:

[0062] The subpopulations within the subgroup are initially connected through a ring topology to form an initial random topological structure;

[0063] For the operation data of the production equipment of each production group within the subgroup, the solver is used for parallel search and fitness evaluation respectively;

[0064] When the change rate of fitness variance within the subgroup exceeds the threshold, trigger the local topology rule switch until the local optimum is detected, determine the final local topological structure, and stop the local topology rule switch.

[0065] In one embodiment, as Figure 2 shown, after triggering the local topology rule switch, switch to the ring topology; when it is detected that the fitness variance continuously decreases within a continuous fixed number of evolutionary generations, switch to the grid topology; when the local optimum is detected, switch to the random topology.

[0066] In one embodiment, the calculation formula of the fitness function is as follows:

[0067]

[0068] Among them, E predicted is the predicted value of the production equipment operation data calculated within the subpopulation, and E measured is the actual value of the production equipment operation data calculated within the subpopulation;

[0069] The calculation formula of the fitness variance is as follows:

[0070]

[0071] Among them, F i is the fitness of individuals in the sub-population, is the average fitness of the sub-population, N is the population size, and in this embodiment, the value of N is s.

[0072] In one embodiment, S3 further includes the step of performing local migration operations based on the dynamically adjusted topological structure:

[0073] The mathematical models within each subgroup are migrated according to the topological structure, and the optimal S migrate mathematical models in each production group are selected and transmitted across nodes to other production groups within the subgroup through Spark Streaming; among them, the migration scale S migrate is calculated by the following formula:

[0074] S migrate = α·N local + β·N global

[0075] Among them, N local and N global are the population sizes of the sub-population and the subgroup respectively, and α and β are weight parameters.

[0076] The heterogeneous migration rules adopt heterogeneous migration frequencies and scales in different subgroups to enhance the diversity and global search ability of the population.

[0077] In one embodiment, the global migration operation of S4 includes the following steps:

[0078] When it is monitored that the change trend of gene entropy is less than the threshold, trigger the migration of mathematical models between subgroups, and exchange the optimal specified number of mathematical models in each subgroup into the sub-population of other subgroups.

[0079] In one embodiment, the gene entropy calculation formula is as follows:

[0080]

[0081] Among them, p j is the occurrence probability of the j-th gene, and M is the number of gene types.

[0082] It can be understood that the fitness variance is used to measure the population diversity within the island, while the gene entropy is used to measure the global population diversity.

[0083] It should be noted that the time decoupling of the present invention mainly involves how to effectively manage local development and global exploration through different time scales during the evolution process of the algorithm. Specifically, it includes:

[0084] Local migration: This is a high-frequency triggering mechanism that dynamically adjusts the topological structure within a subgroup according to the changing trend of local fitness variance. This helps to quickly respond to changes in the local search environment and improve local search efficiency.

[0085] Global migration: A low-frequency triggering mechanism that exchanges elite individuals between subgroups based on the changing trend of global gene entropy. This method can enhance the global search ability of the algorithm and help the algorithm jump out of local optima.

[0086] In addition, time decoupling also realizes a more intelligent search process by combining a state perception mechanism to real-time perceive the optimization state and dynamically trigger local or global adjustments accordingly.

[0087] The spatial decoupling of the present invention refers to enhancing population diversity and global search ability through heterogeneous topological structures and heterogeneous migration strategies, which are specifically embodied in the following aspects:

[0088] Heterogeneous topological structures: Subgroups where different islands are located can adopt different topological structures (such as ring, grid, random connection) according to state perception conversion to adapt to the optimization requirements at different stages.

[0089] Heterogeneous migration rules: Different migration frequencies and scales are adopted within different subgroups. For example, in local migration, the migration strategy is adaptively adjusted according to the state of the subgroup; while in global migration, elite migration across subgroups is dynamically triggered based on the global state, thereby enhancing population diversity and accelerating convergence.

[0090] Through the above designs of time decoupling and spatial decoupling, the invention aims to effectively balance local search and global exploration, reduce communication overhead, avoid the frequent interference problems that may be caused by traditional global migration strategies, and thus improve the efficiency and accuracy of the algorithm in large-scale data relationship modeling.

[0091] Next, the energy consumption of multiple CNC machine tools in a production line is modeled. Taking the optimization of production scheduling as an example, the present invention is further described:

[0092] The monitoring system collects parameters such as device current, voltage, spindle speed, and processing load every 5 minutes to form a high-dimensional time-series dataset (with a daily data volume of about 5 million records). The efficient modeling of the energy consumption equation is completed using the symbolic regression method based on spatio-temporal decoupled genetic programming mentioned in the present invention to optimize the production scheduling of the production line workshop and reduce energy consumption.

[0093] S1. Build a Spark parallel computing environment. Deploy the system on a 16-node Spark cluster (1 Driver + 15 Workers), where each Worker node corresponds to a factory workshop. And configure genetic parameters in the system: population size = 5000, crossover rate = 0.8, mutation rate = 0.05, maximum tree depth = 8.

[0094] S2. Population division and grouped storage. Execute the sparkContext.parallelize method on the Driver node, map each factory to a worker node and assign a sub-population to each factory, and complete the initialization of the population on the node according to the genetic parameters configured in S1. Divide all factory workshops into several subgroups, and the division rule is: according to the factory workshop number, every four consecutive factory workshops are assigned to the same subgroup. The islands within the subgroup are initially connected through a ring topology to form an initial random topology.

[0095] S3. Workshop-level parallel modeling. Each workshop subgroup (5000 individuals) evolves independently, respectively and parallelly uses a solver for search, and conducts fitness evaluation. The fitness function is defined as:

[0096]

[0097] where, E predicted is the predicted energy consumption value of an individual

[0098] S4. Dynamic topology adjustment. When the change rate of the fitness variance of a certain workshop subgroup satisfies exceeds the threshold θ local (θ local = 0.15), trigger the local topology rule to switch to a ring topology; when it is detected that the variance continuously decreases within 10 consecutive generations, it will automatically switch to a grid topology; when a local optimum is detected, switch to a random topology. Realize the parameter sharing of different processing modes within the factory workshop in different states during the evolution process.

[0099] S5. Shift-level local migration. Within a fixed number of evolution generations, perform local migration operations based on the dynamically adjusted topology structure. The individuals within each subgroup migrate according to the topology structure, select the optimal S migrate expressions within each workshop, and transmit them across nodes to other factory workshops within the subgroup through Spark Streaming. Among them, the migration scale S migrate is calculated by the following formula:

[0100] S migrate = α·N local + β·N global

[0101] where, Nlocal and N global are the local and global population sizes respectively, and α and β are weight parameters

[0102] S6. Dynamic global migration. When the changing trend of gene entropy is monitored it triggers the elite migration between sub - groups, and exchanges the 25 optimal expressions in each workshop within each sub - group to each workshop in other sub - groups to enhance the global search ability and accelerate convergence. The calculation formula of gene entropy is as follows:

[0103]

[0104] where p j is the occurrence probability of the j - th gene, and M is the number of gene types.

[0105] S7. Model output and application. After 200 generations of evolution, the global optimal expression is output as the decision basis for workshop production scheduling to reduce the energy consumption error.

[0106] The above has introduced in detail the symbolic regression method based on spatio - temporal decoupled genetic programming provided by the present invention. In this embodiment, specific examples are used to elaborate the principle and implementation manner of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention; at the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation manner and application scope. In summary, the content of this specification should not be construed as a limitation to the present invention.

[0107] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be obvious to those skilled in the art. The general principles defined in this embodiment can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to these embodiments shown in this embodiment, but will conform to the widest scope consistent with the principles and novel features disclosed in this embodiment.

Claims

1. A symbolic regression method based on spatio-temporal decoupled genetic programming, characterized in that, It includes the following steps: S1: Build a parallel island model environment based on the spark cluster, divide the population into multiple sub-populations, and partition all sub-populations through a spatial partitioning mechanism to create several subgroups; S2: Collect the production equipment operation data of n production groups to obtain a high-dimensional time series data set. The production equipment operation data of each production group is used as a sub-population and located in an independent computing unit of the spark cluster to calculate the mathematical model describing the production equipment operation data and execute step S3, where n > 2; every s sub-populations are used as a subgroup to execute step S4, where n > s ≥ 1; S3: Calculate the fitness difference between the predicted value and the actual value of the production equipment operation data within the sub-population, and adaptively adjust the local topological structure within the sub-population using a dynamic perception strategy and perform local migration regularly; S4: Based on the change trend of the global gene entropy, real-time perceive the optimization state among subgroups and dynamically trigger the global migration operation to obtain the optimal mathematical model describing the production equipment operation data.

2. The symbolic regression method based on spatio-temporal decoupled genetic programming according to claim 1, characterized in that In S2, the factory is used as the population, and a factory includes multiple production workshops. Each production workshop is used as a production group to obtain the production equipment operation data corresponding to the production workshop. Each Worker node of the Spark cluster corresponds to a production workshop.

3. A symbolic regression method based on spatio-temporal decoupled genetic programming according to claim 1, characterized in that The production equipment operation data includes any multiple parameters among equipment current, voltage, spindle speed, and processing load collected according to a preset cycle.

4. A symbolic regression method based on spatio-temporal decoupled genetic programming according to claim 1, characterized in that, S3 includes the following steps: The sub-populations within the subgroup are initially connected through a ring topology to form an initial random topology; Parallelly search and perform fitness evaluation on the production equipment operation data of each production group within the subgroup using a solver; When the change rate of the fitness variance within the subgroup exceeds the threshold, trigger the local topology rule switch until the local optimum is detected, determine the final local topological structure, and stop the local topology rule switch.

5. A symbolic regression method based on spatio-temporal decoupled genetic programming according to claim 4, characterized in that, After triggering the local topology rule switch, switch to the ring topology; when it is detected that the fitness variance continuously decreases within a continuous fixed number of evolutionary generations, switch to the grid topology; when the local optimum is detected, switch to the random topology.

6. The symbolic regression method based on spatio-temporal decoupled genetic programming according to claim 1, characterized in that, The fitness function calculation formula is as follows: Among them, E predicted is the predicted value of the operating data of the production equipment calculated within the sub-population, and E measured is the actual value of the operating data of the production equipment calculated within the sub-population; The fitness variance calculation formula is as follows: Among them, F i is the fitness of individuals in the sub-population, is the average fitness of the sub-population, and N is the population size.

7. A symbolic regression method based on spatio-temporal decoupled genetic programming according to claim 4, characterized in that, S3 also includes the step of performing local migration operations based on the dynamically adjusted topological structure: The mathematical models within each subgroup are migrated according to the topological structure, and the optimal S migrate mathematical models within each production group are selected and transmitted across nodes to other production groups within the subgroup through Spark Streaming; among them, the migration scale S migrate is calculated by the following formula: S migrate = α·N local + β·N global where N local and N global are the population sizes of the sub-population and the sub-group respectively, and α and β are weight parameters.

8. A symbolic regression method based on spatio-temporal decoupled genetic programming according to claim 1, characterized in that, The global migration operation of S4 includes the following steps: When it is monitored that the change trend of the gene entropy is less than the threshold, trigger the migration of the mathematical model between subgroups, and exchange the specified number of optimal mathematical models within each subgroup into the sub-populations of other subgroups.

9. A symbolic regression method based on spatio-temporal decoupled genetic programming according to claim 8, characterized in that, The gene entropy calculation formula is as follows: where p j is the occurrence probability of the j-th gene, and M is the number of gene types.

10. A symbolic regression method based on spatio-temporal decoupled genetic programming according to claim 1, wherein The triggering frequency of the global migration is lower than the triggering frequency of the local migration.

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