Dynamic multi-objective optimization method and device, equipment and medium

Abstract

The invention relates to a dynamic multi-objective optimization method and device, equipment and a medium. The method comprises the following steps: establishing an event model of a multi-objective optimization event; if it is detected that the environmental information changes, a first group and a second group are obtained based on a multi-objective evolutionary algorithm and a historical optimal set, an original optimal set of an event model is determined according to the first group and the second group, the first group is obtained based on a representative individual prediction algorithm, and the second group is obtained based on an inflection point prediction algorithm; otherwise, taking the Pareto optimal solution of the event model at the current moment as an original optimal set; and inputting the original optimal set into a social optimization learning model, and outputting a target optimal set of the event model through the social optimization learning model. According to the method, when the change of the environment information of the multi-target optimization event is detected, the target optimal set is output through the social optimization learning model by improving the population diversity and improving the precision of the Pareto optimal solution from the perspective of the population diversity.

Description

Technical Field

[0001] The present invention relates to the field of computer technology, and in particular to a dynamic multi-objective optimization method, device, equipment and medium. Background Art

[0002] Many problems in industrial production and scientific computing (such as cloud computing task scheduling, photovoltaic module cooling, mineral processing operations, and dynamic design of optimal controllers) can be summarized as multi-objective optimization problems (MOPs). These problems are influenced by dynamic factors such as production conditions and the operating environment, causing their objective functions and constraints to be highly dynamic over time and in response to environmental changes. As a result, solutions to these problems are often not effective in the long term. Consequently, existing dynamic multi-objective optimization methods often suffer from poor adaptability and slow convergence.

[0003] However, existing dynamic multi-objective optimization methods cannot effectively track changes when dealing with complex environmental changes, and suffer from insufficient population diversity and low prediction accuracy. Therefore, there is an urgent need for a new dynamic multi-objective optimization method that can effectively handle dynamic multi-objective problems and quickly adapt to environmental changes. Summary of the Invention

[0004] The first object of the present invention is to provide a dynamic multi-objective optimization method, device, equipment and medium.

[0005] According to one aspect of the present application, a dynamic multi-objective optimization method is provided, which includes: establishing an event model of a multi-objective optimization event, wherein the multi-objective optimization event corresponds to event information, and the event information includes environmental information and a historical optimal set; if a change in environmental information is detected, a first group and a second group are obtained based on a multi-objective evolutionary algorithm and a historical optimal set, and the first group and the second group are used as the original optimal set of the event model, wherein the multi-objective evolutionary algorithm includes a representative individual prediction algorithm and an inflection point prediction algorithm, the first group is obtained based on the representative individual prediction algorithm, and the second group is obtained based on the inflection point prediction algorithm; otherwise, the Pareto optimal solution of the event model at the current moment is used as the original optimal set; the original optimal set is input into a social optimization learning model, and the target optimal set of the event model is output through the social learning optimization model, and the target optimal set is used as the current optimal set of the multi-objective optimization event.

[0006] According to another aspect of the present application, a dynamic multi-objective optimization device is provided, which includes: a modeling module, which establishes an event model of a multi-objective optimization event, wherein the multi-objective optimization event corresponds to event information, and the event information includes environmental information and a historical optimal set; a prediction module, which, if a change in environmental information is detected, obtains a first group and a second group based on a multi-objective evolutionary algorithm and a historical optimal set, and determines an original optimal set of the event model based on the first group and the second group, wherein the multi-objective evolutionary algorithm includes a representative individual prediction algorithm and an inflection point prediction algorithm, the first group is obtained based on the representative individual prediction algorithm, and the second group is obtained based on the inflection point prediction algorithm; otherwise, the Pareto optimal solution of the event model at the current moment is used as the original optimal set; an optimization module, which inputs the original optimal set into a social optimization learning model, outputs a target optimal set of the event model through the social learning optimization model, and uses the target optimal set as the current optimal set of the multi-objective optimization event.

[0007] According to another aspect of the present application, a computer device for dynamic multi-objective optimization is provided, comprising a memory and a processor, wherein the memory stores a computer program that can be loaded by the processor and execute the above-described method.

[0008] According to another aspect of the present application, a computer-readable storage medium is provided, storing a computer program that can be loaded by a processor and execute the above method.

[0009] Compared with the prior art, the present application provides a dynamic multi-objective optimization method, which detects whether the environmental information of the multi-objective optimization event has changed. If the environmental information has changed, the algorithm is performed based on multiple objectives, and the historical optimal set is used to determine the first group and the second group. The original optimal set is determined based on the first group and the second group. When the environmental information changes, from the perspective of population diversity, the accuracy of the Pareto optimal solution is improved by increasing the population diversity. When the environmental information has not changed, the Pareto optimal solution at the current moment is directly used as the original optimal set. Furthermore, in order to improve the accuracy, the original optimal set is input into the social optimization learning model, and the target optimal set is output through the social optimization learning model, so that the target optimal set is used as the current optimal set of the multi-objective optimization event. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 A flow chart of a method for dynamic multi-objective optimization according to an embodiment of the present application is shown; Figure 2 A schematic diagram of an original optimal solution according to an embodiment of the present application is shown; Figure 3 A schematic diagram of an inflection point algorithm according to an embodiment of the present application is shown; Figure 4A schematic diagram of a crossover operation according to an embodiment of the present application is shown; Figure 5 A schematic diagram of a mutation operation according to an embodiment of the present application is shown; Figure 6 The reverse distance comparison chart of the four algorithms with different iteration numbers on the FDA1 test function is shown; Figure 7 The figure shows the distribution of the results of the algorithm on the test function FDA2 at time t=5; Figure 8 This is the distribution of the results of the algorithm on the test function FDA2 at time t=10; Figure 9 This is the distribution of the results of the algorithm on the test function FDA2 at time t=15; Figure 10 This is the distribution of the results of the algorithm on the test function FDA2 at time t=18; Figure 11 This is the distribution of the results of the algorithm on the test function FDA2 at time t=20; Figure 12 A schematic diagram of a device structure for dynamic multi-objective optimization according to another embodiment of the present application is shown; Figure 13 It is a schematic diagram of the structure of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0011] The present application is described in further detail below with reference to the accompanying drawings.

[0012] refer to Figure 1 The embodiment of the present invention provides a method for dynamic multi-objective optimization, which includes steps S11, S12, and S13. In step S11, an event model of a multi-objective optimization event is established, wherein the multi-objective optimization event corresponds to event information, and the event information includes environmental information and a historical optimal set; in step S12, if a change in environmental information is detected, a first group and a second group are obtained based on a multi-objective evolutionary algorithm and a historical optimal set, and an original optimal set of the event model is determined based on the first group and the second group, wherein the multi-objective evolutionary algorithm includes a representative individual prediction algorithm and an inflection point prediction algorithm, the first group is obtained based on the representative individual prediction algorithm, and the second group is obtained based on the inflection point prediction algorithm; otherwise, the Pareto optimal solution of the event model at the current moment is used as the original optimal set; in step S13, the original optimal set is input into a social optimization learning model, and the target optimal set of the event model is output through the social learning optimization model, and the target optimal set is used as the current optimal set of the multi-objective optimization event.

[0013] Specifically, in step S11, an event model for a multi-objective optimization event is established. Each multi-objective optimization event corresponds to event information, including environmental information and a historical optimal set. In some embodiments, multi-objective optimization events include, but are not limited to, cloud resource scheduling and photovoltaic module cooling. In some embodiments, environmental information is associated with the multi-objective optimization event. For example, if the multi-objective optimization event is cloud resource scheduling, the environmental information may include resources, tasks, and requirements. In some embodiments, the historical optimal set includes, but is not limited to, solutions based on historical environmental information (e.g., Pareto optimal solutions, Pareto frontiers, and inflection point solutions on the Pareto frontier corresponding to each time instant). In some embodiments, an event model of a multi-objective optimization event (e.g., a mathematical model of a dynamic multi-objective optimization problem (DMOP)) can be expressed as follows: a DMOP with n decision variables and m objective functions can be described as follows: minf(x, t) = {f1(x, t), f2(x, t), …, fm(x, t)}, gi(x, t) ≤ 0 (i = 1, …, p), hj(x, t) = 0 (j = 1, …, q); where f(x, t) = {f1(x, t), f2(x, t), …, fm(x, t)} is the target vector consisting of the n objective functions, and gi(x, t) and hj(x, t) are the inequality and equality constraints of the problem. t is a discrete time series, defined as: t = {t1, t2, …, tnt}, , among which nt, Denote the degree of change and the number of iterations, respectively; x = (x1, x2, …, xn) represents the n-dimensional decision vector, or the solution to the objective function F(x, t), whose domain is Ω; m represents the dimensionality of the objective space; F = (f1, f2, …, fn) represents the m-dimensional objective vector being optimized; p and q represent the number of equality and inequality constraints, respectively. A Pareto Optimal Set (POS): At time t, if no individual x'∈Rn dominates individual x, then x is a Pareto optimal solution of the DMOP at time t. At time t, all Pareto optimal solutions of the event model constitute POSt, denoted as: POSt = {x|∣∄x′∈Ω, f(x′,t)≺f(x,t)}. The mapping of POSt to the objective space at time t is called POFt, denoted as: POFt = {F(x,t)|x∈POSt}.

[0014] In step S12, if a change in environmental information is detected, a first population and a second population are obtained based on a multi-objective evolutionary algorithm and a historical optimal set. The original optimal set of the event model is determined based on the first and second populations. The multi-objective evolutionary algorithm includes a representative individual prediction algorithm and an inflection point prediction algorithm. The first population is obtained based on the representative individual prediction algorithm, and the second population is obtained based on the inflection point prediction algorithm. For example, the multi-objective optimization event is cloud resource scheduling, and environmental information includes resources, tasks, and requirements. If a change is detected in at least one of the resources, tasks, and requirements in the environmental information, the environmental information is determined to have changed. In this embodiment, to increase population diversity and thereby improve prediction accuracy, a new population (the first population) is generated using the representative individual prediction algorithm, and a new population (the second population) is generated using the inflection point prediction algorithm. In some embodiments, the first and second populations are combined using a first hybrid strategy to generate the original optimal set. For example, final_Set = (δ × RI) + ((1 - δ) × KI), where final_Set is the original optimal set, RI is the first population, KI is the second population, and δ is a proportion parameter representing the proportion of new individuals generated by the representative individual prediction in the original optimal set. In some embodiments, the value of δ can be determined experimentally. In some embodiments, the first group includes but is not limited to the Pareto optimal solution of the representative individual at the next moment predicted by the representative individual prediction algorithm, and the second group includes but is not limited to the optimal Pareto optimal solution at the next moment predicted based on the inflection point prediction algorithm. In some embodiments, in order to further increase the diversity of the group, when a change in environmental information is detected, the original optimal set also includes a third group and a fourth group. In some embodiments, the third group includes the Pareto optimal solution of the event model at the previous moment, and the fourth group includes a random solution of the event model. For example, a random generation strategy is used to randomly generate a random solution to the event model. In some embodiments, if the original optimal set includes the first group, the second group, the third group, and the fourth group, the original optimal set can be generated according to the second hybrid strategy. For example, as Figure 2As shown, part I represents the first population generated by the representative individual prediction algorithm; part II represents the second population generated by the inflection point prediction algorithm; part III represents the Pareto optimal solution at the previous moment; and part IV represents a random solution generated randomly during the algorithm's execution. In some embodiments, the second hybrid strategy includes, but is not limited to, allocating a certain proportion to each of the first, second, third, and fourth populations. For example, the fourth population is allocated the smallest proportion, the third population the second largest proportion, and the first and second populations the largest proportions. This hybrid population generation strategy can fully utilize environmental information, enabling the algorithm to better adapt to environmental changes. In a dynamic environment, population diversity plays an important role in solving dynamic multi-objective optimization problems. To maintain population diversity and robustness of prediction results, this embodiment proposes a population generation method based on a hybrid prediction strategy. This method generates a portion of new individuals based on the representative individual prediction method and a portion of new individuals based on the inflection point prediction method. To rationally allocate the proportion of populations generated by each prediction algorithm, this embodiment exemplifies the formula for the composition of the population generated by each prediction method (final_Set = (δ × RI) + ((1 - δ) × KI)). In some embodiments, if the environmental information has not changed, the Pareto optimal solution at the current moment is directly input into the social optimization learning model as the original optimal set, and the target optimal set is output through the social optimization learning model.

[0015] In step S13, the original optimal set is input into the social optimization learning model, which then outputs the target optimal set for the event model. This target optimal set serves as the current optimal set for the multi-objective optimization event. The Social Learning Optimization Algorithm (SLO) is a swarm intelligence algorithm that simulates the evolution of human social intelligence. This social optimization learning model employs a three-layer co-evolutionary space algorithm. The three co-evolutionary spaces of the SLO algorithm form an evolutionary closed loop, exhibiting a robust optimization and co-evolutionary mechanism and excellent optimization performance. However, existing SLO algorithms cannot be directly applied to solving DMOPs (dynamic multi-objective optimization problems). In this embodiment, the SLO algorithm is improved based on the characteristics of DMOPs, and an operator suitable for dynamic multi-objective optimization problems is designed. For a detailed description of the social optimization learning model, please refer to the corresponding embodiments below and will not be elaborated here. In some embodiments, the target optimal set includes, but is not limited to, a target Pareto optimal solution, which is used as the Pareto optimal solution at the next moment. Here, those skilled in the art can understand that the target Pareto frontier and the target inflection point solution of the target Pareto frontier can be obtained based on the target Pareto optimal solution.

[0016] In some embodiments, the historical optimal set includes the Pareto optimal solution of the event model at each moment, and the first group is obtained based on the representative individual prediction algorithm, including steps S111 (not shown), step S112 (not shown), and step S113 (not shown). In step S111, a representative individual set is obtained based on the SGEA algorithm and the network clustering algorithm, wherein the representative individual set at time t-2 is , at time t-1 , at time t In step S112, for each representative individual, the representative individual at the current moment is adjusted by comparing the evolution value of the representative individual from time t-2 to time t-1 with the Euclidean distance between the representative individual at time t and time t-1, thereby obtaining the adjusted representative individual at the current moment; in step S113, the representative individual at the next moment is obtained based on the adjusted representative individual at the current moment and the representative individual prediction formula, and the representative individual set consisting of the representative individuals at the next moment is used as the first group. Here, the representative individual prediction formula includes: , here, Including the representative individual at the next moment, Including the adjusted representative individual at the current moment, the Including Gaussian perturbations, is the disturbance variance, Including the evolution value of the representative individual from time t-2 to time t-1. Here, those skilled in the art will understand that the SGEA (Strength Pareto Evolutionary Algorithm) algorithm is a classic multi-objective optimization algorithm proposed by Zitzler and Thiele in 1999. In some embodiments, the grid clustering algorithm includes the Clique (CLustering In QUEst) grid clustering algorithm. Clique is a density-based grid clustering algorithm that is particularly suitable for processing high-dimensional data. The Clique algorithm divides the data space into grid cells and identifies clusters based on the point density in the cells. The Cliuqe grid clustering method combines the advantages of density-based clustering methods and grid clustering methods, can process high-dimensional data in large DMOPs problems, and has high clustering efficiency and good clustering effects. This clustering method first sets parameters such as the density threshold and the number of grid cells, and divides the initialized population into k non-overlapping rectangular cells. It then calculates the local density of each grid cell and determines whether the density of each grid cell exceeds the density threshold. If the density threshold is exceeded, the grid cell is marked as dense, and the cluster of the cluster is found based on the minimum description length (MDL) principle and greedy thinking. Finally, the representative individuals in the final dense grid cell are obtained. For example, the representative individual set obtained based on SGEA and Clique grid clustering includes: inputting the density threshold threshold, the number of grid cells k, the grid width grid_width, an empty queue GH_density, initializing the population G, and outputting the representative individual set. The method involves the following steps: Step 1: Initialize the population G using the SGEA algorithm and divide it into k rectangular cells; Step 2: Calculate the density threshold_grid for each grid; Step 3: Determine whether threshold_grid is greater than threshold (density threshold). If threshold_grid > threshold, add the network to the empty queue GH_density; Step 4: Select a grid with higher density and find the optimal cluster using a greedy algorithm; Step 5: Output the final set of selected representative individuals. In solving dynamic multi-objective optimization problems, each representative individual has its own evolutionary direction, determined by the individual itself and its parents. Furthermore, the evolutionary direction of representative individuals helps construct new POS (Pareto optimal solution) scenarios. The representative individuals obtained using this method perform well in describing POS. Therefore, predicting new individuals based on representative individuals can effectively track POS trends.In some embodiments, since the Pareto optimal solution of the event model at each time is known and a representative individual set is extracted, the representative individual set can be represented at time t-2. , at time t-1, it can be expressed as , at time t can be expressed as , here, Represents the Pareto optimal solution of the i-th representative individual at time t. In some embodiments, time t represents the current moment. Further, for each representative individual, by comparing the evolution value of the representative individual from time t-2 to time t-1 with the Euclidean distance of the representative individual between time t and time t-1, the adjustment direction of the representative individual at the current moment can be determined (for example, accelerating the evolution in the evolution direction, or slowing down the evolution in the evolution direction). For the specific description of this part, please refer to the corresponding embodiment below, which will not be repeated here. Further, after obtaining the adjusted representative individual at the current moment, the representative individual at the current moment is brought into the representative individual prediction formula, and the representative individual at the next moment is output through the representative individual prediction formula, and the representative individual set composed of the representative individuals at the next moment is used as the first group. For example, the first group includes the Pareto optimal solution of the representative individual at the next moment predicted by the representative individual prediction algorithm. In some embodiments, .

[0017] In some embodiments, Including the evolution value of the representative individual from time t-2 to time t-1, Including the Euclidean distance between the representative individual at time t and time t-1, step S112 includes: if , adjusting the representative individual at the current moment based on an accelerated adjustment formula, wherein the accelerated adjustment formula includes: Otherwise, the representative individual at the current moment is adjusted based on a slowdown adjustment formula, wherein the slowdown adjustment formula includes: , here, Including the adjusted representative individual at the current moment, the Including representative individuals before adjustment, Including the acceleration factor, >0, Including the representative individual at time t-1, Including mitigation factors, >0, Including the representative individual at time t-2. For example, to calculate the evolution value of each representative individual at time t-2 and time t-1, the calculation formula is: , here, This includes the evolution value of the i-th representative individual from time t-2 to time t-1. Based on the position of the representative individual at time t-1 and the position of the representative individual at time t, the Euclidean distance between the representative individuals at time t-1 and time t is calculated to obtain the evolution value of the representative individual at time t. The calculation formula is as follows: .like , then it indicates that the representative individual is moving towards the optimal POS direction. Therefore, the speed of the representative individual in this direction should be accelerated during the movement of the representative individual, and the representative individual at the current moment should be adjusted based on the acceleration adjustment formula. In some embodiments, Used to increase the speed of individual movement towards the optimal direction. < , it indicates that the representative individual is moving away from the optimal POS direction. Therefore, during the evolution process, the movement of the individual in this direction will be suppressed, and the representative individual at the current moment will be adjusted based on the slowdown adjustment formula. In some embodiments, Used to slow down individuals moving in the wrong direction.

[0018] In some embodiments, a second population is obtained based on an inflection point prediction algorithm, including steps S121 (not shown), S122 (not shown), S123 (not shown), and S124 (not shown). In step S121, the Euclidean distance between the inflection point solution of the event model at time t and time t-1 is determined; in step S122, the inflection point solution at time t+1 is determined based on the moving direction and Euclidean distance of the inflection point solution from time t-1 to time t; in step S123, the Pareto front at time t+1 is determined based on the inflection point solution at time t+1 and the Pareto front of the event model at time t; in step S124, the Pareto optimal solution at time t+1 is determined based on the Pareto front at time t+1, and the Pareto optimal solution is used as the second population. The inflection point selection method based on the minimum Manhattan distance has obvious advantages in finding global inflection point solutions. Compared with other inflection point selection strategies, this method has the advantages of collective information analysis and optimization performance analysis. In a dynamic environment, the direction of inflection point movement is as follows: Figure 3 As shown. Determining the direction of inflection point movement is crucial for inflection point prediction in order to guide the group to a promising search area. To this end, this embodiment utilizes the MMD inflection point selection method and calculates the movement direction in the following manner. For example, assume is the inflection point solution at time step t, is the inflection point solution obtained at time t-1. The position of the inflection point can be calculated according to the following formula: , here, Including inflection point solution and The Euclidean distance between them. In some embodiments, in multiple targets, the moving direction of the inflection point solution on the Pareto front can be determined by dynamic analysis. The dynamic analysis is usually based on Pareto front data at different times. For example, Pareto front data at different times are collected to identify inflection point solutions (in some embodiments, inflection point solutions include but are not limited to solutions with obvious turning points or changes). In some embodiments, the identification method includes but is not limited to the slope change method (for example, calculating the slope change between adjacent solutions, and the place where the slope change is larger usually corresponds to the inflection point solution). Further, the movement of the inflection point solution is tracked (for example, the position of each inflection point solution at different times is recorded), and the moving direction of the inflection point solution is analyzed through the recorded moving path (for example, vector analysis, trend analysis, etc.). Here, those skilled in the art will understand that the method for determining the moving direction of the inflection point solution described above is only an example, and other existing or future methods that may appear, if applicable to the present application, are also within the scope of protection of the present application and are included herein by reference. In some embodiments, after determining the Euclidean distance and moving direction of the inflection point solution from time t-1 to time t, the position of the inflection point solution at time t+1 is determined based on the Euclidean distance and moving direction (for example, at time t+1, the inflection point solution moves the same Euclidean distance along the same moving direction). Furthermore, the Pareto front at time t+1 is determined based on the inflection point solution at time t+1 and the Pareto front of the event model at time t (for example, the Pareto front at time t can be directly moved to the position of the inflection point solution at time t+1). Furthermore, based on the Pareto front at time t+1, the Pareto optimal solution at time t+1 can be directly determined, and this Pareto optimal solution is used as the second population.

[0019] In some embodiments, the method further includes step S125 (not shown) before determining the Pareto front at time t+1 based on the inflection point solution at time t+1 and the Pareto front of the event model at time t. In step S125, the inflection point solution at time t+1 is input into a regression model, and the regression model outputs an adjusted inflection point solution at time t+1. Here, the regression model includes: , here, Including the inflection point solution at time t+1 based on Euclidean distance, Including the adjusted inflection point solution at time t+1, Including the linear regression coefficient of the i-th target, Including the nonlinear coefficient of the i-th dimension, u includes the environmental change intensity coefficient, It includes the time difference between time t and time t-1. The moving direction of the inflection point solution can guide an individual to move towards a search area where a better solution set is likely to be found. The regression model can be used to test both the strength and direction of variable relationships, and can control other irrelevant variables when variables enter the regression equation to obtain the variable relationship, making the obtained variable relationship more accurate than correlation analysis. In some embodiments, to improve the prediction accuracy, in this embodiment, the initially predicted inflection point solution at time t+1 is substituted into the regression model for adjustment to obtain the adjusted inflection point solution at time t+1, thereby improving the prediction accuracy. In some embodiments, the parameter u is determined by the ratio of the environmental change intensity to the environmental change frequency. More precisely, this parameter is actually the above-mentioned Euclidean distance determined because directly reflects the movement amplitude and change trend of the inflection point solution in a dynamic environment. In some embodiments, the larger it is, the larger u is. In this embodiment, a regression model is added during the movement of the inflection point, and based on the environmental change intensity, the predicted inflection point is obtained.

[0020] In some embodiments, the social learning model includes a micro space, a learning space, and an update space. Step S13 includes: inputting the original optimal set into the micro space, performing crossover and mutation operations through the micro space, and outputting a first set; inputting the first set into the learning space, performing learning and training operations through the learning space, and outputting a second set; inputting the second set into the update space, performing an update operation through the update space, and outputting the target optimal set. Here, those skilled in the art can understand that the Social Learning Optimization Algorithm (SLO) is a swarm intelligence algorithm that simulates the intelligent evolution process of human society. In some embodiments, a genetic mutation process is performed within the micro space of SLO. The operations within the micro space mainly include a roulette-based selection operation, a crossover operation, and a mutation operation. In some embodiments, the crossover operation includes: Let X1 and X2 be two m-dimensional individuals, rand be a random number within the interval (0,1), and pc be the crossover rate. If r<pc, then the crossover operation is performed. The crossover operation is as Figure 4 shown, where S represents the dimension and I represents the number of targets. When the mth target in X1 and the mth target in X2 are cross-swapped, new individuals X3 and X4 are obtained. To adapt to environmental changes, the crossover rate pc can be adjusted according to dynamic environmental conditions to improve the evolutionary adaptability of the population. In some embodiments, the mutation operation includes: The embodiment of the present invention adopts a single-point mutation operation. Let X be an m-dimensional individual, rand be a random number in (0,1), and pm be the mutation probability. Each dimension value of the individual has the same mutation probability. If r<pm, then the mutation operation is performed, as Figure 5As shown. The mutation operation plays a key role in enhancing population diversity. By dynamically adjusting the mutation probability pm, the adaptability of the population can be improved when different environments change. After the mutation, the crowding distance of the entire set is recalculated to ensure that the individual evolves in the direction of the global optimal solution. In some embodiments, in the DMOPs problem, in order to ensure that individuals evolve in the direction of a better Pareto solution set and ultimately obtain the optimal Pareto solution set, the embodiment of the present invention compares the crowding distance in the learning space, takes individuals with larger crowding distances as learning objects, and guides other individuals to evolve in these directions, and outputs the second set through the learning space. For a detailed introduction to this part, please refer to the corresponding embodiments below, which will not be repeated here. In some embodiments, the update space mainly performs update operations (Update) and influence operations (influence) in the social learning optimization algorithm, the purpose of which is to guide the population to evolve in a good direction, thereby improving the efficiency of population evolution. For a detailed introduction to this part, please refer to the corresponding embodiments below, which will not be repeated here.

[0021] In some embodiments, a first set includes multiple first Pareto optimal solutions, and a learning training operation is performed through a learning space, including: determining a first target Pareto optimal solution based on the crowding distance of each first Pareto optimal solution in the multiple first Pareto optimal solutions, wherein the crowding distance of the first target Pareto optimal solution satisfies a first target condition; determining a learning object based on the first target Pareto optimal solution, and the current individual in the first set performs an imitation learning operation based on the first target Pareto optimal solution to obtain a second set, wherein the second set includes multiple second Pareto optimal solutions; performing an update operation through an update space, including: determining a second target Pareto optimal solution and a second candidate Pareto optimal solution based on the fitness value of each second Pareto optimal solution in the multiple second Pareto optimal solutions, wherein the fitness value of the second target Pareto optimal solution satisfies the second target condition, and the fitness value of the second candidate Pareto optimal solution satisfies a third target condition; updating the second candidate Pareto optimal solution based on the second target Pareto optimal solution and an update formula, wherein the update formula includes: , here, Including the second candidate Pareto optimal solution, Including the second objective Pareto optimal solution, Including update interval parameters, Including ideal Pareto optimal solutions, Including random Pareto optimal solutions in the second set. In some embodiments, based on the crowding distance of the individual, multiple individuals with crowding distances that meet the requirements (for example, the first target Pareto optimal solution) are selected to form a learning group with the current individual to perform imitation learning; based on the perturbation learning factor of the sine function, the individual is simulated for observation learning. In some embodiments, the first target condition includes but is not limited to the crowding of the first target Pareto optimal solution being equal to or greater than the target threshold, or the first target Pareto optimal solution being a plurality of first Pareto optimal solutions in the first set that are ranked in the top N in terms of crowding. As mentioned above, for imitation learning, in human society, individuals usually randomly imitate the excellent individuals around them. Based on this phenomenon, the embodiment of the present invention uses crowding distance to find multiple individuals with larger crowding distances, form a learning group with the current individual, and perform imitation learning. The imitation learning operation is shown in the following formula: Fnew= xFcurrent+ xFstudy, where σ is the coefficient of the retained part, ξ is the learning perturbation factor, Fnew represents the new individual formed after the individual operates in the learning space, Fcurrent represents the current individual, and Fstudy represents the learning object (for example, the first objective Pareto optimal solution). The calculation formula for Fstudy is as follows: Fstudy = (Fbetter + (r1 − r2)) × rand + Fcurrent, where rand is a random number between (0, 1), r1 and r2 are random individuals after stratification of the non-dominated set, Fbetter represents the individual with high crowding, and Fcurrent represents the current individual. As mentioned above, in observational learning, individuals learn from the performance of other individuals by observing them. To simulate the learning volatility of individuals in observational learning, embodiments of the present invention introduce a perturbation learning factor based on a sine function. The observational learning operation is expressed as follows: sri′ = rand × Fcurrent + (1 − sin(a)) × (Fbetter − Fcurrent), where sri′ represents a random number between (0, 1), Fcurrent represents the current individual, Fbetter represents the best individual, and sin(a) represents a sine function with parameter a set to a = rand(2, π). The perturbation factor of the sine function effectively increases the diversity of the population, thereby ensuring the convergence speed and optimization efficiency of the algorithm in the later stages and reducing the risk of falling into a local optimum. In some embodiments, the update space in social learning optimization algorithms is based on the cultural influence of human intelligence during evolution. Therefore, operations within this space are mainly divided into update operations (Update()) and influence operations (influence()), whose purpose is to guide the population to evolve in a positive direction, thereby improving the efficiency of population evolution. In DMOPs, the update operation mainly replaces the poor individuals in the belief space with the excellent individuals at each goal extracted from the learning space, thereby achieving knowledge update and accumulation. In some embodiments, excellent individuals include but are not limited to optimal Pareto solutions with smaller fitness values, and poor individuals include but are not limited to optimal Pareto solutions with larger fitness values. The second target condition includes but is not limited to optimal Pareto solutions in the second set whose fitness values are less than a second threshold, or optimal Pareto solutions in the second set that are within a certain range of the reciprocal of the fitness values (for example, arranged in ascending order of fitness). The third target condition includes but is not limited to optimal Pareto solutions in the second set whose fitness values are equal to or greater than the third threshold, or optimal Pareto solutions in the second set that are within a certain range of the top fitness values (for example, arranged in ascending order of fitness). The formula is as follows: ai = p × β, where ai represents the number of excellent individuals on the i-th target; p represents the population size; and β is the selection probability. In the function tested in this embodiment of the present invention, β = rand(0.15, 0.2).The influence operation is to use the knowledge in the belief space to replace the individuals with poor fitness values in the microspace, guide the population to evolve in a good direction, and improve the convergence speed of the algorithm. The formula is as follows: , here, the Including the second candidate Pareto optimal solution, the Including the second objective Pareto optimal solution, the Including the ideal Pareto optimal solution, the Including the random Pareto optimal solution in the second set, j∈[0,a], r∈[0,a]; ε is an update interval parameter, and in the embodiment of the present invention, ε=10, that is, iterates 10 times and performs an influence operation once.

[0022] The embodiment of the present invention selects a public dynamic multi-objective test function to verify the method proposed by the present invention. The selected function sets include the FDA test function set, the dMOP test function set and the F5-F10 test function set. Among them, the test problems of FDA and dMOP are linearly correlated between decision variables, and F5-F10 are test problems with nonlinear correlation between decision variables. FDA4 and F8 are problems with three objectives, and the others are problems with two objectives. During the iteration process of F9-F10, the environment changes more dramatically, and it is a test problem that is more difficult to converge than other test problems.

[0023] Performance Metrics: Inverted Generational Distance (IGD) measures the closeness between the true POF and the algorithm's POF, thereby evaluating the algorithm's convergence and diversity. The IGD metric is defined as follows: IGD = |PFt∗|1∑v∈PFt∗d(v,PFt), where PFt* is the standard POF at time t, PFt is the algorithm's POF at time t, and d(v,PFt) is the Euclidean distance between individual v on PFt* and the individual closest to v on PFt. IGD is evaluated by finding the closest point on the Pareto front PFt* to each individual on the algorithm's Pareto front and calculating the Euclidean distance between them. The Euclidean distances are then summed and averaged. Therefore, IGD not only evaluates the closeness between PFt* and PFt but also the distribution of individuals within PFt. Smaller IGD values indicate better convergence and a more uniform distribution of the Pareto front obtained by the algorithm.

[0024] Since the environment is dynamic, it is difficult to comprehensively measure the performance of the algorithm if only IGD is used. Therefore, the embodiment of the present invention also uses the MIGD indicator to measure the performance of the algorithm. The MIGD metric is a modified version of IGD and is defined as the average value of the IGD value within certain time steps during the operation. Assuming that the environment changes Tmax times, the average value of the IGD of all Tmax environments is: MIGD=Tmax1∑t=1TmaxIGDt. In order to verify the effectiveness of the dynamic multi-objective optimization method (SGEA) proposed in the embodiment of the present invention, the embodiment of the present invention first observed the impact of three representative dynamic multi-objective optimization methods on MIGD under different environmental change frequencies and environmental change intensities. The three algorithms are: (1) dynamic multi-objective evolutionary optimization prediction strategy based on feedback (MOEA / D-FPS); (2) dynamic multi-objective evolutionary algorithm based on environmental change intensity (IEC); (3) inflection point guided dynamic multi-objective optimization prediction method (KPEA). Among them, MOEA / D-FPS is a dynamic multi-objective optimization method based on two feedback mechanisms: correction feedback (CF) and effectiveness feedback (EF). IEC is an evolutionary algorithm based on the intensity of environmental change, effectively tracking the Pareto optimal set in dynamic multi-objective optimization. When an environmental change is detected, IEC divides individuals into micro- and macro-variation components based on the evolutionary information fed back by the Pareto optimal set in the current and historical environments, guiding the evolutionary direction. KPEA is an evolutionary algorithm that uses inflection point guidance for prediction. When an environmental change is detected, this algorithm relocates the inflection point and boundary solutions based on the movement of the global inflection point solution in the new environment, reducing computational cost. This embodiment of the present invention selected 11 dynamic multi-objective test functions for comparative testing of the above algorithms. The unique parameters of the MOEA / D-FPS algorithm, IEC algorithm, and KPEA algorithm can be set empirically. Other parameters are set as follows: population size of 100; number of algorithm iterations of 4000 generations; and degree of variation of 10. Furthermore, the four algorithms were analyzed for both fully converged and non-converged scenarios for the dynamic multi-objective optimization problem, with the environmental change frequency set to 10 and 30, respectively, while keeping all other parameters constant. Each of the four algorithms was run 20 times on the 11 test functions.

[0025] Feasibility Verification: The mean inverse distance (MIGD) test results of the four algorithms on 10 test functions show that, for a change frequency of 30, the SGEA algorithm proposed in this embodiment outperforms the other three algorithms in terms of mean inverse distance (MIGD) on 6 of the 11 test functions. The KPEA algorithm performs best on the FDA3 and dMOP2 test functions, while the MOEA / D-FPS algorithm performs better on the F5 and F6 test functions. For a change frequency of 10, the SGEA algorithm proposed in this embodiment outperforms the other three algorithms in terms of mean inverse distance (MIGD) on 7 test functions, with KPEA performing best on the dMOP1 and F8 test functions and IEC performing best on the F6 test function. Vertically, as the change frequency increases from 10 to 30, i.e., from low to high, the mean inverse distance (MIGD) of the SGEA algorithm proposed in this embodiment shows little difference, and even slightly decreases in some functions. This demonstrates the SGEA's improved adaptability to drastic environmental changes. Validation: To further illustrate the effectiveness of the SGEA algorithm proposed in this embodiment of the present invention, this embodiment of the present invention selected the FDA2 test function and conducted an in-depth analysis of the test results of the above four algorithms at the same time point when the environmental change frequency was 30. First, the values of the reverse distance index of the four algorithms at different times were compared. The results are as follows: Figure 6 As shown in the figure, the horizontal axis represents the number of iterations, and the vertical axis represents the IGD value. A smaller IGD value indicates better final experimental results; a more stable IGD value indicates faster convergence. The results show that the method proposed in the embodiment of the present invention reaches near stability after 5 iterations, with minimal fluctuations in the IGD value over time and a lower average value than the other three algorithms. The experimental results of the algorithm in the embodiment of the present invention are relatively close to the final results of the KPEA algorithm. However, in terms of experimental stability, the SGEA algorithm exhibits less volatility, and before reaching stability, the IGD decreases more steadily during the iterations, far below the KPEA value. The IEC value performs poorly in the FDA2 test function, indicating that it is not well-suited to the FDA2 test function. Furthermore, MOEA / D-FPS only reaches stability in the FDA2 test function after the 10th iteration, and after stabilization, its experimental results are far inferior to those of the algorithm in the embodiment of the present invention and the KPEA algorithm. Therefore, the algorithm in the embodiment of the present invention outperforms the other three algorithms in the FDA2 test function when the environmental change frequency is 30. In order to observe the distribution of solutions obtained by the four algorithms at different times, the values of the solutions obtained at 5, 10, 14, 18, and 20 moments in the target space are selected. The results are as follows: Figure 7-11 As shown in the figure. The red points in the figure are the optimal surfaces at different times, and the points are the solution sets obtained at different times. Figure 7and Figure 11 As can be seen, the SGEA algorithm proposed in this embodiment of the present invention achieves superior solutions to the corresponding solutions of the other three algorithms at these five time points, with good convergence and relatively uniform distribution, essentially covering the entire optimal surface. The results of the KPEA and IEC algorithms lag behind. The KPEA algorithm performs less well than the other algorithms in the early stages of iteration. Therefore, the solutions obtained by this embodiment of the present invention at the same time point demonstrate superior convergence and robustness to the other three algorithms.

[0026] In addition, an embodiment of the present invention further provides an electronic device, comprising: one or more processors; and a memory associated with the one or more processors, wherein the memory is used to store program instructions, and when the program instructions are read and executed by the one or more processors, the dynamic multi-objective optimization method disclosed in the above embodiment is executed. Figure 2 The schematic diagram of the structure of a device for dynamic multi-objective optimization according to an embodiment of the present application is shown, and the device includes a first module, a second module, and a third module. The first module is used to establish an event model for a multi-objective optimization event, wherein the multi-objective optimization event corresponds to event information, and the event information includes environmental information and a historical optimal set; the first module is used to obtain a first group and a second group based on a multi-objective evolutionary algorithm and a historical optimal set if a change in environmental information is detected, and to determine the original optimal set of the event model based on the first group and the second group, wherein the multi-objective evolutionary algorithm includes a representative individual prediction algorithm and an inflection point prediction algorithm, the first group is obtained based on the representative individual prediction algorithm, and the second group is obtained based on the inflection point prediction algorithm; otherwise, the Pareto optimal solution of the event model at the current moment is used as the original optimal set; the third module is used to input the original optimal set into a social optimization learning model, output the target optimal set of the event model through the social learning optimization model, and use the target optimal set as the current optimal set of the multi-objective optimization event. Here, the specific implementations corresponding to module 11, module 12, module 13, and module 14 are the same or similar to the specific embodiments of step S11, step S12, step S13, and step S14, and are therefore not described in detail but are included herein by reference. In addition to the methods and devices introduced in the above embodiments, the present application also provides a computer-readable storage medium, which stores computer code, and when the computer code is executed, the method described in any of the preceding items is executed. The present application also provides a computer program product, and when the computer program product is executed by a computer device, the method described in any of the preceding items is executed. The present application also provides a computer device, which includes: one or more processors; a memory for storing one or more computer programs; and when the one or more computer programs are executed by the one or more processors, the one or more processors implement the method described in any of the preceding items. As Figure 13As shown, the electronic device of an embodiment of the present invention is suitable for edge computing scenarios. The computer device 12 can serve as an edge node, executing a dynamic multi-objective optimization algorithm on a device close to the data source. The edge device can receive data from sensors, IoT devices, and other devices in real time and quickly adjust the optimization strategy based on environmental changes, thereby reducing data transmission latency and improving computing efficiency. The processing unit of the edge device can not only process data locally but also communicate with other edge nodes via a network adapter to form a collaborative computing network, further improving the system's processing power and response speed. The components of the computer device 12 may include, but are not limited to: one or more processors or processing units 16, system memory 28, and a bus 18 connecting different system components (including the system memory 28 and the processing units 16). The processing units 16 can be distributed across multiple heterogeneous edge nodes, including smart terminals, industrial control devices, wireless access points, etc., collaboratively executing dynamic multi-objective optimization tasks through the edge network, achieving distributed computing and resource sharing, and improving the overall computing power and efficiency of the system. The computer device 12 communicates with one or more edge networks (such as a local area network (LAN), wide area network (WAN), or wireless network) via a network adapter 20 to enable data sharing and task distribution among edge nodes. Through this architecture, edge devices can perform computing tasks locally and collaborate with other edge nodes to form a distributed computing system, further improving the system's real-time performance and scalability. The edge devices of the present invention can detect and respond to environmental changes in real time, using the SEGA algorithm to quickly adjust the optimization solution. The processing unit 16 executes various functional applications and data processing by running program modules stored in the system memory 28, ensuring real-time solutions for dynamic multi-objective optimization. Localized processing reduces reliance on remote cloud resources, significantly improving the system's response speed and processing capabilities, making it particularly suitable for the rapid response requirements of edge computing environments. The system memory 28 can include computer-readable media in the form of volatile memory, such as random access memory (RAM) 30 and / or cache memory 32. The computer device 12 may also include other removable / non-removable, volatile / non-volatile storage media, such as a storage system 34 for reading and writing non-removable non-volatile magnetic media. These storage systems can store program instructions and data used to execute the dynamic multi-objective optimization method. Program module 42 includes an operating system, application programs, and modules that implement the functions of the present invention, providing localized optimization calculations and task processing in distributed edge computing scenarios. Processing unit 16 executes the functions of dynamic multi-objective optimization by running programs stored in system memory 28, and rapidly adjusts optimization strategies based on dynamic environmental changes to ensure efficient system operation. It should be noted that the present application can be implemented in software and / or a combination of software and hardware, for example, using an application-specific integrated circuit (ASIC), a general-purpose computer, or any other similar hardware device.In one embodiment, the software program of the present application can be executed by a processor to implement the steps or functions described above. Similarly, the software program of the present application (including related data structures) can be stored in a computer-readable recording medium, such as RAM memory, a magnetic or optical drive, a floppy disk, or similar devices. In addition, some steps or functions of the present application can be implemented using hardware, for example, as circuits that cooperate with a processor to perform the various steps or functions. In addition, a portion of the present application can be implemented as a computer program product, such as computer program instructions, which, when executed by a computer, can invoke or provide the methods and / or technical solutions according to the present application through the operation of the computer. Those skilled in the art will understand that the computer program instructions can be stored in a computer-readable medium in forms including, but not limited to, source files, executable files, and installation package files. Accordingly, the ways in which computer program instructions can be executed by a computer include, but are not limited to: the computer directly executing the instructions, the computer compiling the instructions and then executing the corresponding compiled program, the computer reading and executing the instructions, or the computer reading and installing the instructions and then executing the corresponding installed program. Here, the computer-readable medium can be any available computer-readable storage medium or communication medium that is accessible to the computer. It is obvious to those skilled in the art that the present application is not limited to the details of the above exemplary embodiments, and that the present application can be implemented in other specific forms without departing from the spirit or basic features of the present application.

Claims

1. A dynamic multi-objective optimization method, characterized in that: The method comprises: Establishing an event model of a multi-objective optimization event, wherein the multi-objective optimization event corresponds to event information, and the event information includes environmental information and a historical optimal set; If a change in the environmental information is detected, a first population and a second population are obtained based on a multi-objective evolutionary algorithm and the historical optimal set, and an original optimal set of the event model is determined based on the first population and the second population, wherein the multi-objective evolutionary algorithm includes a representative individual prediction algorithm and an inflection point prediction algorithm, the first population is obtained based on the representative individual prediction algorithm, and the second population is obtained based on the inflection point prediction algorithm; otherwise, the Pareto optimal solution of the event model at the current moment is used as the original optimal set; The original optimal set is input into a social optimization learning model, the target optimal set of the event model is output through the social learning optimization model, and the target optimal set is used as the current optimal set of the multi-objective optimization event.

2. The method according to claim 1, characterized in that The historical optimal set includes the Pareto optimal solution of the event model at each moment, and the first group is obtained based on the representative individual prediction algorithm, including: obtaining a representative individual set based on the SGEA algorithm and the network clustering algorithm, wherein the representative individual set at time t-2 is , at time t-1 , at time t ; For each representative individual, by comparing the evolution value of the representative individual from time t-2 to time t-1 with the Euclidean distance between the representative individual at time t and time t-1, the representative individual at the current moment is adjusted to obtain the adjusted representative individual at the current moment; The representative individual at the next moment is obtained based on the adjusted representative individual at the current moment and the representative individual prediction formula, and the representative individual set consisting of the representative individuals at the next moment is used as the first group. Here, the representative individual prediction formula includes: , here, Including the representative individual at the next moment, Including the adjusted representative individual at the current moment, the Including Gaussian perturbations, is the disturbance variance, Includes the evolution value of the representative individual from time t-2 to time t-1.

3. The method according to claim 2, characterized in that Including the evolution value of the representative individual from time t-2 to time t-1, Including the Euclidean distance between the representative individual at time t and time t-1, adjusting the representative individual at the current moment by comparing the evolution value of the representative individual from time t-2 to time t-1 with the Euclidean distance between the representative individual at time t and time t-1, to obtain the adjusted representative individual at the current moment, including: like , adjusting the representative individual at the current moment based on an acceleration adjustment formula, wherein the acceleration adjustment formula includes: Otherwise, the representative individual at the current moment is adjusted based on a slowdown adjustment formula, wherein the slowdown adjustment formula includes: , here, the Including the adjusted representative individual at the current moment, the Including representative individuals before adjustment, the Including the acceleration factor, >0, Including the representative individual at time t-1, Including mitigation factors, >0, Includes representative individuals at time t-2.

4. The method according to claim 1, wherein Obtaining the second population based on the inflection point prediction algorithm includes: Determining the Euclidean distance between the inflection point solution of the event model at time t and time t-1; Determine the inflection point solution at time t+1 according to the moving direction of the inflection point solution from time t-1 to time t and the Euclidean distance; Determine the Pareto front at time t+1 according to the inflection point solution at time t+1 and the Pareto front of the event model at time t; The Pareto optimal solution at time t+1 is determined based on the Pareto front at time t+1, and the Pareto optimal solution is used as the second population.

5. The method according to claim 4, characterized in that Before determining the Pareto front at time t+1 based on the inflection point solution at time t+1 and the Pareto front of the event model at time t, the method further includes: The inflection point solution at time t+1 is input into a regression model, and the regression model outputs an adjusted inflection point solution at time t+1. Here, the regression model includes: , here, the Including the inflection point solution at time t+1 obtained based on the Euclidean distance, Including the inflection point solution at time t+1 after adjustment, the Including the linear regression coefficient of the i-th target, the Including the i-th dimension nonlinear coefficient, the u includes the environmental change intensity coefficient, the Includes the time difference between time t and time t-1.

6. The method according to claim 1, characterized in that The socialized learning model includes a microspace, a learning space, and an update space. Inputting the original optimal set into the social optimization learning model and outputting the target optimal set of the event model through the social learning optimization model include: Inputting the original optimal set into the microspace, performing a crossover operation and a mutation operation through the microspace, and outputting a first set; Inputting the first set into a learning space, performing a learning and training operation through the learning space, and outputting a second set; The second set is input into the update space, an update operation is performed through the update space, and a target optimal set is output.

7. The method according to claim 6, characterized in that The first set includes a plurality of first Pareto optimal solutions, and performing a learning and training operation through the learning space includes: determining a first target Pareto optimal solution according to the congestion distance of each first Pareto optimal solution among the multiple first Pareto optimal solutions, wherein the congestion distance of the first target Pareto optimal solution satisfies a first target condition; Determining a learning object according to the first target Pareto optimal solution, wherein the current individual in the first set performs an imitation learning operation according to the first target Pareto optimal solution to obtain the second set, wherein the second set includes multiple second Pareto optimal solutions; The performing the update operation through the update space includes: determining a second target Pareto optimal solution and a second candidate Pareto optimal solution according to the fitness value of each second Pareto optimal solution in the plurality of second Pareto optimal solutions, wherein the fitness value of the second target Pareto optimal solution satisfies a second target condition, and the fitness value of the second candidate Pareto optimal solution satisfies a third target condition; The second candidate Pareto optimal solution is updated according to the second target Pareto optimal solution and an update formula, wherein the update formula includes: , here, the Including the second candidate Pareto optimal solution, the Including the second objective Pareto optimal solution, Including update interval parameters, the Including the ideal Pareto optimal solution, the Include random Pareto optimal solutions in the second set.

8. A dynamic multi-objective optimization device, characterized in that: The device includes: A modeling module, configured to establish an event model of a multi-objective optimization event, wherein the multi-objective optimization event corresponds to event information, and the event information includes environmental information and a historical optimal set; a prediction module configured to, if a change in the environmental information is detected, obtain a first population and a second population based on a multi-objective evolutionary algorithm and the historical optimal set, and determine an original optimal set of the event model based on the first population and the second population, wherein the multi-objective evolutionary algorithm includes a representative individual prediction algorithm and an inflection point prediction algorithm, the first population is obtained based on the representative individual prediction algorithm, and the second population is obtained based on the inflection point prediction algorithm; otherwise, use the Pareto optimal solution of the event model at the current moment as the original optimal set; An optimization module is used to input the original optimal set into a social optimization learning model, output the target optimal set of the event model through the social learning optimization model, and use the target optimal set as the current optimal set of the multi-objective optimization event.

9. A computer device for dynamic multi-objective optimization, characterized in that: The method comprises a memory and a processor, wherein the memory stores a computer program that can be loaded by the processor and executes any one of the methods according to claims 1 to 7.

10. A computer-readable storage medium, characterized in that A computer program is stored which can be loaded by a processor and execute the method according to any one of claims 1 to 7.

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