A multi-objective directed evolution method and system based on decision variable analysis

Abstract

The application relates to a multi-objective directed evolution method and system based on decision variable analysis, and the method comprises the following steps: performing quantitative analysis on each decision variable in a multi-objective evolution method, calculating the convergence trend and the diversity trend of the decision variable, and dividing the decision variable into a convergence variable and a diversity variable; analyzing the dependency relationship between the convergence variables, and dividing the convergence variables into variable groups which are independent of each other; initializing a first population and a second population; the first population performs an evolution operation based on a convergence strategy, and the second population performs an evolution operation based on a diversity strategy; the first population and the second population perform offspring sharing, and the step is repeated until an optimal solution is obtained. Compared with the prior art, the directed evolution operator adopted in the application can be flexibly adapted to different multi-objective evolution calculation frameworks, different multi-objective evolution optimization algorithms can be designed according to the characteristics of different optimization problems, and the generality is high.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of large-scale multi-objective evolutionary computation, and in particular to a multi-objective directed evolution method and system based on decision variable analysis. BACKGROUND

[0002] With the rapid development of cloud computing, big data and artificial intelligence technologies, large-scale multi-objective optimization problems (LaMOPs) containing large-scale decision variables have begun to appear in scientific research and engineering application fields, such as unmanned aerial vehicle path planning, cloud resource scheduling optimization, hybrid vehicle control, etc. These problems can be abstracted as LaMOPs. Therefore, it is of great theoretical value and practical significance to research and design efficient optimization algorithms for LaMOPs.

[0003] Traditional multi-objective evolutionary algorithms usually perform well when solving low-dimensional multi-objective optimization problems. However, as the scale of decision variables and the dimensionality of objective variables increase: on the one hand, the decision space grows exponentially, and the computational complexity of the algorithm increases dramatically; on the other hand, the optimization conflict between different objectives intensifies, making it difficult to balance convergence and diversity, and the optimization effect of the algorithm significantly decreases. How to quickly and efficiently solve LaMOPs is still a research difficulty in the field of multi-objective evolutionary algorithms. SUMMARY

[0004] The present application is to overcome the defects of the prior art and provide a multi-objective directed evolution method and system based on decision variable analysis.

[0005] The object of the present application can be achieved by the following technical solutions:

[0006] A multi-objective directed evolution method based on decision variable analysis, comprising:

[0007] For each decision variable in the multi-objective evolutionary method, perform quantitative analysis to calculate its convergence trend and diversity trend, and divide the decision variables into convergence variables and diversity variables;

[0008] Analyze the dependency relationship between the convergence variables, and divide the convergence variables into variable groups that are independent of each other;

[0009] Initialize the first population and the second population;

[0010] The first population performs evolution operation based on the convergence strategy, and the second population performs evolution operation based on the diversity strategy. The first population and the second population share offspring, and this step is repeated until the optimal solution is obtained.

[0011] Furthermore, the quantitative analysis of each decision variable in the multi-objective evolutionary method is specifically as follows:

[0012] Calculate the convergence tendency and diversity tendency for each decision variable:

[0013]

[0014] Wherein, C(x) i ) represents the decision variable x i The convergence trend, M represents the pre-set number of perturbations, m is used to identify the m-th perturbation, and X represents a solution, X m This indicates the decision variable x i The solution obtained from X after adding perturbation, where λ represents the weight vector, is a unit vector passing through the origin and having the same angle with each coordinate axis, and the coordinate axes represent the objective function in the multi-objective evolution method;

[0015]

[0016] Where D(x) i ) represents the decision variable x i The trend towards diversity.

[0017] Furthermore, the decision variables are further divided into convergent variables and diversity variables as follows:

[0018] Calculate the intrinsic properties of each decision variable:

[0019] R(x i )=C(x i )-D(x i )

[0020] Where R(x) i ) represents the decision variable x i The inherent properties of R(x) i If ) > 0, the decision variable x i It is determined to be a convergent variable; when R(x) i When ) < 0, the decision variable x i It was identified as a diversity variable.

[0021] Furthermore, the analysis of the dependencies between convergence variables is as follows:

[0022] Convergence variables are used as nodes to construct a binary search tree;

[0023] The variable to be detected is determined, and the binary search method is used to search for the dependency relationship between each node and the variable to be detected, starting from the root node of the binary search tree. This step is repeated until the dependency relationship of all convergent variables is detected. The dependency relationship between two variables is determined by the link learning method.

[0024] Furthermore, the convergence variables are divided into independent variable groups as follows:

[0025] Treat each convergent variable as a vertex, and connect convergent variables with dependencies with edges to obtain an undirected graph of variables;

[0026] A search algorithm is used to find all maximal connected subgraphs in the undirected graph of variables. The convergent variables in each maximal connected subgraph are grouped as variables to complete the grouping of convergent variables.

[0027] Furthermore, the evolutionary operation includes a crossover operation. In the crossover operator design of the convergence strategy, the process of parent generation crossover generating offspring is as follows:

[0028] Obtain the convergence variables and their groups, and perform crossover operations on each group of convergence variables separately;

[0029] In the crossover operator design of the aforementioned diversity strategy, the process of parent generation crossover generating offspring is as follows:

[0030] Obtain all diversity variables and perform cross operations on all diversity variables as a whole.

[0031] Furthermore, the evolutionary operation includes a mutation operation, and in the design of the mutation operator in the convergence strategy, the mutation probability is set to:

[0032]

[0033] Wherein, P(x i ) represents the variable x i The mutation probability, R(x) i ) represents the variable x i The inherent characteristics of the decision variables; n represents the number of convergent variables among the decision variables; CV and DV represent the set of convergent variables and the set of diversity variables, respectively;

[0034] In the design of the mutation operator in the diversity strategy, the mutation probability is set to:

[0035]

[0036] Where h represents the number of diversity variables in the decision variables.

[0037] Furthermore, the evolutionary operation includes an individual selection operation; in the design of the individual selection operation in the convergent strategy, a convergent individual selection strategy is used; and in the design of the individual selection operation in the diversity strategy, a diverse individual selection strategy is used.

[0038] Furthermore, the evolutionary operation includes an environment selection operation. In the design of the environment selection operation in the convergent strategy, a convergent environment selection strategy is used. In the design of the environment selection operation in the diversity strategy, a diverse environment selection strategy is used.

[0039] A multi-objective directed evolution system based on decision variable analysis, based on the aforementioned multi-objective directed evolution method based on decision variable analysis, includes a decision variable quantitative analysis module and a population directed optimization module:

[0040] The decision variable quantitative analysis module performs the following steps:

[0041] For each decision variable in the multi-objective evolutionary method, a quantitative analysis is performed to calculate its convergence trend and diversity trend, and the decision variables are divided into convergence variables and diversity variables.

[0042] Analyze the dependencies between convergent variables and divide them into groups of independent variables;

[0043] The population-oriented optimization module performs the following steps:

[0044] Initialize the first and second populations;

[0045] The first population performs evolutionary operations based on a convergence strategy, while the second population performs evolutionary operations based on a diversity strategy. The first and second populations share offspring, and this process is repeated until the optimal solution is obtained.

[0046] Compared with the prior art, the present invention has the following beneficial effects:

[0047] (1) This invention divides the large-scale multi-objective evolutionary optimization process into two stages: quantitative analysis of decision variables and directed evolution of the population. In the quantitative analysis stage, the projection length of the solution set on the weight vector after variable perturbation is used as the convergence index, and the deviation of the solution set from the weight vector is used as the diversity index. Based on the binary tree search algorithm and link learning technology, the dimensionality reduction of large-scale decision variables is achieved by grouping. In the directed evolution stage, the inherent characteristics of the decision variables are utilized to design directed mating selection, directed crossover operators, and directed mutation operators respectively. Combined with the multi-objective evolutionary computation framework, the decision space is searched quickly and efficiently. The directed evolution operators used in this invention can be flexibly adapted to different multi-objective evolutionary computation frameworks, and different multi-objective evolutionary optimization algorithms can be designed for different optimization problem characteristics, with strong generalization.

[0048] (2) Unlike existing decision variable grouping methods that only perform qualitative analysis of variable characteristics, this invention proposes a quantitative analysis mechanism of variable characteristics based on the division of the target space. By analyzing the changing trends of decision variables in different weight vector directions in the target space, prior knowledge of specific optimization problems can be obtained, thereby helping and guiding subsequent evolutionary search.

[0049] (3) Unlike existing multi-objective evolutionary algorithms that distribute computational resources evenly to each gene of a chromosome, the directed evolution mechanism proposed in this invention guides the population to evolve in the expected direction by performing purposeful mating, crossover and mutation operations on convergent or diversity variables, effectively alleviating the problem of insufficient algorithm search capability in high-dimensional decision space.

[0050] (4) This invention can be applied to the task offloading optimization problem in the edge computing environment, and has a significant optimization effect on multiple conflicting objectives such as energy consumption, resource loss, communication traffic, and task completion delay in the edge computing environment. Attached Figure Description

[0051] Figure 1 This is a flowchart illustrating a multi-objective directed evolution method based on decision variable analysis.

[0052] Figure 2 A schematic diagram illustrating the quantitative analysis of the characteristics of decision variables. Detailed Implementation

[0053] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0054] In the accompanying drawings, components with the same structure are indicated by the same numerical designation, and components with similar structures or functions are indicated by similar numerical designations. The dimensions and thicknesses of each component shown in the drawings are arbitrary, and the present invention does not limit the dimensions and thicknesses of each component. To make the illustrations clearer, some components are appropriately exaggerated in the drawings.

[0055] This application provides a multi-objective directed evolution method based on decision variable analysis to solve the problems of high computational complexity and insufficient search capability encountered in large-scale multi-objective optimization.

[0056] This application divides the solution process of LaMOPs into two stages: decision variable analysis and population-directed evolution. In the variable analysis stage, the convergence and diversity of decision variables are quantified, the intrinsic characteristics of decision variables are explored, and then large-scale decision variable grouping and dimensionality reduction are achieved based on the interdependence of convergent variables. In the population-directed evolution stage, convergent strategies and diversity strategies are designed and executed by utilizing the intrinsic characteristics of decision variables, thereby achieving fast and efficient search of the decision space.

[0057] A multi-objective directed evolution method based on decision variable analysis includes:

[0058] S1. Perform quantitative analysis on each decision variable in the multi-objective evolution method, calculate its convergence trend and diversity trend, and divide the decision variables into convergent variables and diversity variables.

[0059] Calculate the convergence tendency and diversity tendency for each decision variable:

[0060]

[0061] Wherein, C(x) i ) represents the decision variable x i The convergence trend, M represents the pre-set number of perturbations, m is used to identify the m-th perturbation, and X represents a solution, X m This indicates the decision variable x i The solution obtained from X after adding perturbation, where λ represents the weight vector, is a unit vector passing through the origin and having the same angle with each coordinate axis, and the coordinate axes represent the objective function in the multi-objective evolution method;

[0062]

[0063] Where D(x) i ) represents the decision variable x i The trend towards diversity.

[0064] like Figure 2 As shown, taking a multi-objective evolutionary algorithm with two objective functions as an example, Z in the figure... * Let PF represent the ideal solution, and let PF represent the Pareto optimal frontier for individual X, with respect to decision variable x. i After perturbation, we obtain X′. Therefore, we repeatedly perturb the decision variable x. i By perturbing, we can obtain the solution set G = {X1, X2, ..., X}. M}, decision variable x i The convergence trend C(x) i ) and diversity trend D(x i ) can be described as the forward distance and the deviation distance of the solution set G along the vector λ, respectively.

[0065] The decision variables are specifically divided into convergent variables and diversity variables as follows:

[0066] Calculate the intrinsic properties of each decision variable:

[0067] R(x i )=C(x i )-D(x i ) Formula (3)

[0068] Where R(x) i ) represents the decision variable x i The inherent properties of R(x) i If ) > 0, the decision variable x i It is determined to be a convergent variable, R(x) i ) represents the variable x i The convergence correlation; when R(x) i When ) < 0, the decision variable x i It was determined to be a diversity variable, |R(x) i | represents the variable x i The degree of diversity correlation.

[0069] Of course, the above-mentioned method for quantifying the intrinsic characteristics of decision variables can be based on the target space partitioning technique to comprehensively consider the convergence or divergence trends of individuals in different regions, and combined with the curve characteristics of the solution set G and the number of non-dominated levels, the mathematical representation of each parameter in formula (3) can be further optimized by using neural networks, reinforcement learning and other methods.

[0070] S2. Analyze the dependencies between convergent variables and divide the convergent variables into groups of independent variables;

[0071] Dependency analysis can be performed on each pair of convergent variables. The dependency relationship between variables can be based on link learning technology, which is a commonly used method for variable dependency analysis. Those skilled in the art will understand this, so it will not be elaborated here.

[0072] In this embodiment, a binary tree search algorithm is used to reduce time complexity, as follows:

[0073] Convergence variables are used as nodes to construct a binary search tree;

[0074] The variable to be detected is identified, and a binary search method is used to search for the dependency relationship between each node and the variable to be detected, starting from the root node of the binary search tree. This step is repeated until the dependency relationship of all convergent variables is detected. The dependency relationship between two variables is determined by the link learning method.

[0075] Compared to directly performing pairwise dependency analysis between convergent variables, binary search trees and binary search can reduce the time complexity from the traditional O(n) to O(n) time complexity. 2 m) is reduced to O(mnlogn).

[0076] Convergent variables can be manually divided into multiple groups based on their dependencies. Variables within the same group have dependencies on each other, while variables in different groups do not. Alternatively, a graph search method can be used, as follows:

[0077] Treat each convergent variable as a vertex, and connect convergent variables with dependencies with edges to obtain an undirected graph of variables;

[0078] A depth-first search (or breadth-first search) algorithm is used to find all maximal connected subgraphs in the undirected graph of variables. The convergent variables in each maximal connected subgraph are grouped as variables to complete the grouping of convergent variables.

[0079] S3. Initialize the first and second populations;

[0080] In the dual-population directed evolution stage, this application maintains two populations evolving in complementary directions: a convergent optimization population (CP) and a diversity optimization population (DP). The CP employs mating selection, crossover, and mutation operators oriented towards the convergent evolution direction for population reproduction, combined with a convergence-priority environmental selection mechanism to maintain population convergence. The DP employs mating selection, crossover, and mutation operators oriented towards the diversity evolution direction for population reproduction, combined with a diversity-priority environmental selection mechanism to maintain population diversity. The CP and DP share evolutionary information through offspring sharing. The first population is designated as the convergent optimization population (CP), and the second population as the diversity optimization population (DP).

[0081] S4. The first population performs evolutionary operations based on a convergence strategy, and the second population performs evolutionary operations based on a diversity strategy. The first and second populations share offspring. This step is repeated until the optimal solution is obtained.

[0082] ① In the mating selection process of a convergent optimization population (CP), a convergent individual selection strategy is used; in the mating selection process of a diversity optimization population (DP), a diverse individual selection strategy is used. In multi-objective optimization evolutionary algorithms, there are various individual selection strategies. Those skilled in the art can understand which are convergent and which are diverse individual selection strategies, and they will not be listed here. In this embodiment, the binary tournament method is used to design the individual selection operation, as follows:

[0083] (1) Using the target cumulative function C(x) and density estimation function D(x) as the target, compare the Pareto dominance relationship between individuals p and q. If p and q do not dominate each other, proceed to step (2); otherwise, eliminate the dominated individuals.

[0084] (2) In the convergent individual selection strategy, compare the convergence trends of individuals p and q, and retain the individuals with strong convergence. If they cannot be compared, proceed to step (3). In the diverse individual selection strategy, compare the diversity trends of individuals p and q, and retain the individuals with strong diversity. If they cannot be compared, proceed to step (3).

[0085] (3) Randomly select individuals from individuals p and q.

[0086] ② When performing a crossover operation between a convergence optimization population (CP) and a diversity optimization population (DP), the crossover operator is designed as follows:

[0087] (1) In the design of crossover operators oriented towards convergence, the parent individuals are selected based on the above convergence mating selection strategy. Each group of convergence variables in the parent is regarded as a whole, and the crossover operation of the parent solution is performed on the group by using recombination operators (such as SBX, DE, etc.).

[0088] (2) In the crossover operator design for diversity optimization, the parent individuals are selected based on the above-mentioned diversity mating selection strategy. All diversity-related variables in the parent are regarded as a whole, and the crossover operation is performed on the parent solution using the recombination operator.

[0089] ③ When performing mutation operations on convergent optimization populations (CP) and diversity optimization populations (DP), mutation operators are designed using the roulette wheel method based on the intrinsic characteristics of the decision variables.

[0090] In the design of the mutation operator in the convergence strategy, the mutation probability is set to:

[0091]

[0092] Wherein, P(x i ) represents the variable x i The mutation probability, R(x) i ) represents the variable x i The inherent characteristics of the decision variables; n represents the number of convergent variables among the decision variables; CV and DV represent the set of convergent variables and the set of diversity variables, respectively;

[0093] In the design of mutation operators in diversity strategies, the mutation probability can be set as follows:

[0094]

[0095] Where h represents the number of diversity variables in the decision variables.

[0096] ④ When performing environment selection operations for convergent optimization populations (CP) and diversity optimization populations (DP), the environment selection operation design in the convergent strategy uses a convergent environment selection strategy, that is, environment selection for CP is based on a convergence index. Conversely, the environment selection operation design in the diversity strategy uses a diversity environment selection strategy, that is, environment selection for DP is based on a diversity index. There are various evaluation indices, and those skilled in the art will understand which are convergence indices (such as I). ε+ What are diversity indicators (such as SDE, L, etc.)? P (e.g., norms, etc.), which will not be listed here.

[0097] This application also provides a multi-objective directed evolution system based on decision variable analysis. Based on the aforementioned multi-objective directed evolution method based on decision variable analysis, it includes a decision variable quantitative analysis module and a population-oriented optimization module.

[0098] The decision variable quantitative analysis module performs the following steps:

[0099] For each decision variable in the multi-objective evolutionary method, a quantitative analysis is performed to calculate its convergence trend and diversity trend, and the decision variables are divided into convergence variables and diversity variables.

[0100] Analyze the dependencies between convergent variables and divide them into groups of independent variables;

[0101] The population-oriented optimization module performs the following steps:

[0102] Initialize the first and second populations;

[0103] The first population performs evolutionary operations based on a convergence strategy, while the second population performs evolutionary operations based on a diversity strategy. The first and second populations share offspring, and this process is repeated until the optimal solution is obtained.

[0104] The specific content of the above-mentioned decision variable quantitative analysis module and population-oriented optimization module is the same as that of the multi-objective directed evolution method based on decision variable analysis mentioned above, and will not be repeated here.

[0105] A typical application scenario of this invention is task offloading in an edge computing environment. The specific application process is as follows: First, using indicators such as energy consumption, resource depletion, data communication traffic, and task completion latency as the problem optimization objectives (i.e., objective functions), and the remaining available computing capacity of the edge server as constraints, a multi-objective constrained optimization model is established for an "edge-end" fusion scenario; then, using the number of tasks to be offloaded as the chromosome length and the task number as the gene location, the encoding of individuals in the population is achieved; finally, CP and DP are initialized based on the encoding method, and then... Figure 1 The dual-population directed evolution process is subjected to quantitative analysis of decision variables, directed mating selection, and directed crossover mutation until the termination condition of the algorithm is met. The output is a Pareto optimal solution set with multiple conflicting indicators such as energy consumption, resource loss, data communication traffic, and task completion delay as optimization objectives.

[0106] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A multi-objective directed evolutionary method based on decision variable analysis for task offloading optimization in edge computing environments, characterized in that, include: For each decision variable in the multi-objective evolutionary method, a quantitative analysis is performed to calculate its convergence trend and diversity trend, and the decision variables are divided into convergence variables and diversity variables. Analyze the dependencies between convergent variables and divide them into groups of independent variables; Initialize the first and second populations; The first group performs evolutionary operations based on a convergence strategy, and the second group performs evolutionary operations based on a diversity strategy. The first and second groups share offspring, and this step is repeated until the optimal solution is obtained. In an edge computing environment, energy consumption, resource loss, data communication traffic, and task completion latency are used as optimization objectives, while the remaining available computing capacity of the edge server is used as a constraint. In this context, the chromosome length of an individual in the population represents the number of tasks to be unloaded, and the gene location represents the task number. Quantitative analysis of each decision variable in the multi-objective evolutionary method is specifically performed as follows: Calculate the convergence tendency and diversity tendency for each decision variable: in, Representing decision variables The convergence trend This indicates the preset number of perturbations. Used to identify the first Secondary disturbance. To represent a solution, Indicates the decision variable After adding perturbation, The solution obtained The weight vector is a unit vector passing through the origin and having the same angle as each coordinate axis, where the coordinate axes represent the objective function in the multi-objective evolution method. in, Representing decision variables The trend of diversity; The decision variables are specifically divided into convergent variables and diversity variables as follows: Calculate the intrinsic properties of each decision variable: in, Representing decision variables Its inherent characteristics, if Decision variables It is determined to be a convergent variable; when At that time, decision variables It was identified as a diversity variable.

2. The multi-objective directed evolution method based on decision variable analysis according to claim 1, characterized in that, The analysis of the dependencies between convergence variables is as follows: Convergence variables are used as nodes to construct a binary search tree; The variable to be detected is determined, and the binary search method is used to search for the dependency relationship between each node and the variable to be detected, starting from the root node of the binary search tree. This step is repeated until the dependency relationship of all convergent variables is detected. The dependency relationship between two variables is determined by the link learning method.

3. The multi-objective directed evolution method based on decision variable analysis according to claim 1, characterized in that, The convergence variables are divided into independent variable groups as follows: Treat each convergent variable as a vertex, and connect convergent variables with dependencies with edges to obtain an undirected graph of variables; A search algorithm is used to find all maximal connected subgraphs in the undirected graph of variables. The convergent variables in each maximal connected subgraph are grouped as variables to complete the grouping of convergent variables.

4. The multi-objective directed evolution method based on decision variable analysis according to claim 1, characterized in that, The evolutionary operation includes a crossover operation. In the crossover operator design of the convergence strategy, the process of parent generation crossover generating offspring is as follows: Obtain the convergence variables and their groups, and perform crossover operations on each group of convergence variables separately; In the crossover operator design of the aforementioned diversity strategy, the process of parent generation crossover generating offspring is as follows: Obtain all diversity variables and perform cross operations on all diversity variables as a whole.

5. The multi-objective directed evolution method based on decision variable analysis according to claim 1, characterized in that, The evolutionary operation includes a mutation operation. In the design of the mutation operator in the convergence strategy, the mutation probability is set to: in, Representing variables The mutation probability, Representing variables The inherent characteristics; It represents the number of convergent variables among the decision variables; CV and DV represent the set of convergent variables and the set of diversity variables, respectively; In the design of the mutation operator in the diversity strategy, the mutation probability is set to: in, This indicates the number of diversity variables in the decision variables.

6. The multi-objective directed evolution method based on decision variable analysis according to claim 1, characterized in that, The evolutionary operation includes an individual selection operation. In the design of the individual selection operation in the convergent strategy, a convergent individual selection strategy is used. In the design of the individual selection operation in the diversity strategy, a diverse individual selection strategy is used.

7. A multi-objective directed evolution method based on decision variable analysis according to claim 6, characterized in that, The evolutionary operation includes an environment selection operation. In the design of the environment selection operation in the convergent strategy, a convergent environment selection strategy is used. In the design of the environment selection operation in the diversity strategy, a diverse environment selection strategy is used.

8. A multi-objective directed evolutionary system based on decision variable analysis for task offloading optimization in edge computing environments, characterized in that, The multi-objective directed evolution method based on decision variable analysis as described in any one of claims 1-7 includes a decision variable quantitative analysis module and a population directed optimization module: The decision variable quantitative analysis module performs the following steps: For each decision variable in the multi-objective evolutionary method, a quantitative analysis is performed to calculate its convergence trend and diversity trend, and the decision variables are divided into convergence variables and diversity variables. Analyze the dependencies between convergent variables and divide them into groups of independent variables; The population-oriented optimization module performs the following steps: Initialize the first and second populations; The first group performs evolutionary operations based on a convergence strategy, and the second group performs evolutionary operations based on a diversity strategy. The first and second groups share offspring, and this step is repeated until the optimal solution is obtained. In an edge computing environment, energy consumption, resource loss, data communication traffic, and task completion latency are used as optimization objectives, while the remaining available computing capacity of the edge server is used as a constraint. In this context, the chromosome length of an individual in the population represents the number of tasks to be unloaded, and the gene location represents the task number.

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