Large-scale multi-objective optimization method and device based on GAN

Abstract

The invention relates to the technical field of computers, in particular to a GAN-based large-scale multi-objective optimization scheme. Comprising the following steps: randomly initializing a population and operation parameters of a multi-objective optimization problem; selecting a preset number of non-dominated solutions from the population as reference solutions through a non-dominated sorting algorithm; converting a multi-objective optimization problem into a series of single-objective optimization sub-problems by performing bidirectional weight vector association with upper and lower boundary points of a decision space according to symmetric points of a non-dominated reference solution about center symmetry in the decision space; using the current population as a parent population to train a GAN model and generate a child population; and preferentially updating the population between the parent population and the child population through an environment selection mechanism until a preset termination condition is met, and outputting a final solution set. According to the method, the original problem is simplified, the globally optimal solution can be more effectively searched in the low-dimensional space, the high-quality filial generation is generated by training the GAN model, the population diversity is improved, and more high-quality solutions are provided for selection.

Description

Technical Field

[0001] This application relates to the field of computer technology, and particularly to a large-scale multi-objective optimization method and device based on GAN. Background Art

[0002] Currently, in the field of large-scale multi-objective optimization problems (LSMOPs), with the increase in the number of decision variables and the number of optimization objectives, the performance of traditional multi-objective evolutionary algorithms (MOEAs) significantly degrades when dealing with problems having thousands or even more decision variables. Large-scale multi-objective optimization problems are usually accompanied by a complex objective function structure and a huge set of constraint conditions, which makes it difficult to efficiently apply traditional solution strategies.

[0003] To address these challenges, existing research has proposed various strategies, including large-scale multi-objective evolutionary algorithms based on divide-and-conquer, problem transformation, and novel search strategies. However, each method has its limitations. For example, the "divide-and-conquer" strategy simplifies the problem by grouping decision variables, but this method requires a large amount of time and the number of function evaluations for effective grouping, and improper grouping may seriously affect the algorithm performance. On the other hand, the "problem transformation" strategy attempts to shorten the parent decision vector to simplify the offspring generation process, but this may lead to the loss of information on the global optimal solution of the original problem, affecting the comprehensiveness of the final result. Finally, the method based on the novel search strategy attempts to conduct a more extensive exploration in the entire decision variable space, but this also means a higher computational cost.

[0004] Due to the "curse of dimensionality" brought about by the growth of the decision variable dimension, existing multi-objective optimization algorithms are difficult to search the entire high-dimensional decision space within a limited time, resulting in insufficient algorithm search capabilities. Therefore, traditional optimization algorithms are difficult to obtain the global optimal solution when dealing with large-scale multi-objective optimization problems and have a slow convergence rate in practical engineering applications. Summary of the Invention

[0005] In view of this, it is necessary to provide a large-scale multi-objective optimization method and device based on GAN to solve problems such as unsatisfactory effects and insufficient algorithm search capabilities when existing methods deal with large-scale multi-objective optimization problems.

[0006] A large-scale multi-objective optimization method based on GAN includes:

[0007] Randomly initialize the population and operating parameters of the multi-objective optimization problem;

[0008] Select a preset number of non-dominated solutions from the population as reference solutions through the non-dominated sorting algorithm;

[0009] According to the symmetric points of the non-dominated reference solutions that are centrosymmetric about the center in the decision space, through bidirectional weight vector association with the upper and lower boundary points of the decision space, convert the multi-objective optimization problem into a series of single-objective optimization sub-problems;

[0010] Use the current population as the parent population to train the GAN model and generate the offspring population;

[0011] Through the environmental selection mechanism, preferentially update the population between the parent and offspring populations until the preset termination condition is met and output the final solution set.

[0012] Preferably, after converting the multi-objective optimization problem into a series of single-objective optimization sub-problems, it further includes:

[0013] Generate new solutions by constructing direction vectors in the decision space, and select excellent individuals through the environmental selection mechanism to update the population.

[0014] Preferably, it includes: combining the direction vector with the reference solution in a linear combination to generate new solutions.

[0015] Preferably, after generating new solutions, it further includes:

[0016] Evaluate the new solutions using the hypervolume indicator evaluation criterion;

[0017] Select excellent individuals according to the evaluation results and use the environmental selection mechanism to update the population.

[0018] Preferably, the environmental selection mechanism includes preferentially selecting according to the fitness value and diversity index of individuals to update the population.

[0019] Preferably, constructing the direction vector in the decision space includes:

[0020] Construct the direction vector according to the direction from the non-dominated solution and its symmetric point to other non-dominated solutions, and the direction of mutual pointing between non-dominated reference solutions.

[0021] Preferably, using the current population as the parent population to train the GAN model and generate the offspring population, it further includes: applying the differential evolution algorithm to optimize the offspring population.

[0022] Preferably, the GAN model is the WGAN-GP model.

[0023] Preferably, using the trained GAN model to generate new offspring solutions, it further includes: optimizing the generated new offspring solutions through the differential evolution algorithm.

[0024] A large-scale multi-objective optimization device based on GAN, comprising:

[0025] An initialization module, configured to randomly initialize the population and operating parameters of the multi-objective optimization problem;

[0026] A non-dominated sorting module, configured to select a preset number of non-dominated solutions from the population as reference solutions through a non-dominated sorting algorithm;

[0027] A problem transformation module, configured to transform the multi-objective optimization problem into a series of single-objective optimization sub-problems by performing two-way weight vector association with the upper and lower boundary points of the decision space according to the symmetric points of the non-dominated reference solutions that are centrosymmetric about the center in the decision space;

[0028] A model training and generation module, configured to use the current population as the parent population to train the GAN model and generate the offspring population;

[0029] An environmental selection module, configured to preferentially update the population between the parent and offspring populations through an environmental selection mechanism until a preset termination condition is met and the final solution set is output.

[0030] Compared with the prior art, the beneficial effects of this application are as follows: This application transforms large-scale multi-objective optimization into single-objective optimization, which not only simplifies the original problem but also enables more effective search for the global optimal solution in the low-dimensional space. Guiding the generation of new solutions through two types of direction vectors not only improves the diversity of the offspring solutions but also ensures the balance between the effective exploration and utilization of the algorithm. Finally, by training the GAN model to generate high-quality offspring, the population diversity is improved, providing more high-quality solutions for selection. This application overcomes the difficulties encountered by traditional algorithms in dealing with high-dimensional decision variables and reduces the computational cost at the same time. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 is a schematic flowchart of a large-scale multi-objective optimization method based on GAN provided in the first embodiment of this application.

[0032] Figure 2 is a schematic flowchart of another large-scale multi-objective optimization method provided in the first embodiment of this application.

[0033] Figure 3 is a schematic diagram of an approximate Pareto front obtained on the LSMOP2 benchmark function provided in the embodiment of this application;

[0034] Figure 4 is a schematic diagram of an approximate Pareto front obtained on the ZDT1 benchmark function provided in the embodiment of this application;

[0035] Figure 5It is a flowchart showing the process of the large-scale multi-objective optimization method based on GAN provided in the second embodiment of this application;

[0036] Figure 6 It is a schematic structural diagram of a voltage transformer provided in an embodiment of this application;

[0037] Figure 7 It is a schematic structural diagram of the large-scale multi-objective optimization device 300 based on GAN provided in an embodiment of this application. Detailed implementation manners

[0038] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings required for use in the embodiments will be briefly introduced below. Obviously, the accompanying drawings in the following description are some embodiments of this application. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can also be obtained based on these drawings.

[0039] With the "curse of dimensionality" brought about by the growth of the dimensionality of decision variables, existing multi-objective optimization algorithms are difficult to search the entire high-dimensional decision space within a limited time, resulting in insufficient search capabilities of the algorithms. For large-scale multi-objective optimization problems, a set of solution sets with good convergence and diversity on the Pareto front needs to be obtained, but existing algorithms cannot balance the convergence and diversity of the solution sets to be solved.

[0040] To solve the above technical problems, this application proposes a large-scale multi-objective optimization method based on GAN. Please refer to Figure 1 - Figure 2 , Figure 1 It is a flowchart showing the process of a large-scale multi-objective optimization method based on GAN provided in the first embodiment of this application, Figure 2 It is a flowchart showing the process of another large-scale multi-objective optimization method provided in the first embodiment of this application. The large-scale multi-objective optimization method based on GAN includes the following steps:

[0041] S101: Randomly initialize the population and operating parameters of the multi-objective optimization problem.

[0042] First of all, an initial population needs to be created. This population consists of multiple individuals (solutions), and each individual represents a potential solution to the optimization problem. At the same time, some parameters required for the operation of the algorithm also need to be initialized, such as the population size, termination conditions, etc.

[0043] In addition, before creating the initial population, the optimization variables and optimization objectives can be determined based on the actual problem to be solved. For example, estimating the time-varying ratio error of a voltage transformer (VT) in a power system is a typical large-scale multi-objective optimization problem. The determined optimization variables and optimization objectives can include defining decision variables (e.g., the true voltage values of each phase at different times), the data collected from the voltage transformer, the ratio error of the voltage transformer, and its variation over time as optimization objectives, and establishing a corresponding mathematical model to describe these problems.

[0044] S102: Select a preset number of non-dominated solutions from the population as reference solutions through the non-dominated sorting algorithm.

[0045] Use the non-dominated sorting algorithm (such as the method in NSGA-II) to sort the population and select a certain number of non-dominated solutions as reference solutions (non-dominated solutions), that is, for each non-dominated solution in a given solution set, no other solution can perform better in all objectives or at least perform better in one objective without making other objectives worse.

[0046] In a multi-objective optimization problem, usually there is no single best solution because improving the performance of one objective may lead to a decrease in the performance of another objective. Therefore, what needs to be found is a set composed of multiple non-dominated solutions, and these solutions together constitute the so-called Pareto Front. Each point on the Pareto Front represents a trade-off solution, under which it is impossible to improve another objective without sacrificing at least one objective.

[0047] For example, in the problem of voltage transformer error estimation, different solutions may correspond to different levels of ratio error and its variation. Some solutions may perform well in reducing the ratio error but poorly in controlling its variation over time, and vice versa. By identifying non-dominated solutions, those solutions that provide the best balance point can be found.

[0048] S103: Perform problem transformation: According to the symmetric points of the non-dominated reference solutions that are centrosymmetric in the decision space, through bidirectional weight vector association with the upper and lower boundary points of the decision space, transform the multi-objective optimization problem into a series of single-objective optimization sub-problems.

[0049] Based on a number of non-dominated solutions selected as the reference solution set, each reference solution and its centrosymmetric point in the decision space are used to construct direction vectors. The association between the direction vectors and the weight variables is to assist in solving large-scale multi-objective optimization problems. Specifically, this association is to transform the original large-scale multi-objective optimization problem into a single-objective optimization problem and conduct effective search in the constructed low-dimensional space.

[0050] Specifically, the following steps may be included:

[0051] Perform vector association: Select N s solutions from the current population as the reference solution set, and construct two direction vectors v l and v u for each reference solution. The two direction vectors point to the lower bound and the upper bound of the decision space respectively.

[0052] Calculate the two direction vectors of each reference solution:

[0053] v l = s1 - o

[0054] v u = t - s1

[0055] where s1 is the reference solution selected from the current population through non-dominated sorting, and o and t are the lower bound point and the upper bound point of the decision space respectively.

[0056] Associate weight variables: The role of the weight variables is to adjust the importance or intensity of the direction vectors, thereby affecting the search direction and depth. Associate the direction vectors with the weight variables and calculate the two weight variables of each reference solution:

[0057]

[0058] where l max = ||t - o||, λ 11 and λ 12 are two weight variables. In some embodiments of the present application, the values of the weight variables can be set to [0, 0.5].

[0059] Construct sub-problems:

[0060] Based on the above constructed direction vectors and weight variables, transform the original large-scale multi-objective optimization problem into a series of low-dimensional single-objective optimization sub-problems. This step essentially simplifies the complex multi-objective optimization problem into a more easily handled form, facilitating the efficient search for the global optimal solution. In fact, the "sub-problems" in the present application refer to a series of new solutions generated based on the reference solutions, rather than the single-objective optimization sub-problems themselves.

[0061] Based on the above steps, the expressions of the sub-problems constructed are as follows:

[0062]

[0063] Similarly, the symmetric point s1' of s1 is:

[0064]

[0065] s1' = 2 * CenterPoint - s1 = o - t - s1

[0066] Construct two sub-problems z 11 ′ and z 12 ′ as:

[0067]

[0068] That is, the constructed sub-problems are:

[0069] z′(Λ) = (z 11 (λ 11 ), z 11 ′(λ 11 ′),..., z r2 (λ r2 ), z r2 ′(λ r2 ′))

[0070] where Λ = {λ 11 , λ 11 ′,..., λ r2 , λ r2 ′} is the reconstructed decision space. After the completion of the reconstruction of the sub-problems, the optimization of the decision vector of the original problem is transformed into the optimization of the weight vector in the reconstructed decision space. That is, the original problem is transformed from a D-dimensional multi-objective optimization problem into a (4 × Ns)-dimensional single-objective optimization problem. The new optimization problem can be re-expressed as:

[0071] maximize G(Λ) = HV(Z'(Λ))

[0072] subject to

[0073] Here, the hypervolume indicator (HV) is used to evaluate these sub-problems, and finally the fitness value of the objective vector is obtained. Among them, HV is used to measure the size of the objective space region covered by a set of non-dominated solutions (i.e., the solutions on the Pareto front). The higher the HV value, the better the convergence (close to the true Pareto front) and the better the diversity (covering a wider objective space) of the solution set.

[0074] Furthermore, after the problem transformation, the present application can also incorporate a direction guidance strategy: after converting the large-scale multi-objective optimization into a single-objective optimization, it is possible to search for and generate offspring solutions in the constructed low-dimensional space, that is, by constructing direction vectors in the decision space to generate promising offspring solutions (new solutions). These direction vectors guide the generation of new solutions, aiming to improve the diversity of the population and the global search ability. In the present application, there can be two methods for generating direction vectors - one is from the dominated solution to the non-dominated solution, and the other is from one non-dominated solution to another non-dominated solution. The combined effect of these two methods improves the diversity of the population and the exploration ability. In this embodiment, new potential solutions are effectively explored and developed throughout the multi-objective optimization process, rather than being limited to the transformed single-objective optimization problem, which helps to maintain good convergence and diversity throughout the optimization process and ultimately helps to find a solution set close to the true Pareto front.

[0075] Specifically, the steps of the direction guidance strategy for generating offspring are as follows:

[0076] Divide the current population into two parts: the dominated solution set and the non-dominated solution set. For example, P n is the non-dominated solution set, and P d is the dominated solution set.

[0077] Randomly select one as the starting point p n in the non-dominated solution set P star , and randomly select N d solutions in the dominated solution set P s , and calculate their symmetric points together as the ending point to construct an evolutionary direction vector from the non-dominated solution to the dominated solution to generate offspring and improve convergence.

[0078] Randomly select one as the starting point in the non-dominated solution set P n , and randomly select N n -p star solutions in the non-dominated solution set P s -|P d | and the remaining dominated solutions as the ending point, where |P d | is the number of the dominated solution set, to construct an evolutionary direction from the non-dominated solution to the non-dominated solution to improve the population diversity.

[0079] By constructing multiple direction vectors, the algorithm's ability to search for the global optimal solution is enhanced, avoiding being trapped in local optima.

[0080] Furthermore, after generating a new solution set in each iteration, it can be evaluated by indicators such as HV to determine whether these new solutions are better than the solutions in the current population or provide new and valuable information. In the embodiments of the present application, the HV indicator is used to help judge whether the newly generated solutions improve the overall quality of the population, including two aspects: convergence and diversity. In this way, the algorithm can be effectively guided to evolve in the direction of finding better Pareto front solutions.

[0081] Furthermore, after generating promising offspring solutions (new solutions), the population can be updated by selecting excellent individuals through an environmental selection mechanism. The generated new solutions will then be screened by the environmental selection mechanism to determine which solutions can enter the next-generation population. This process takes into account not only the quality of the solutions (i.e., their performance on all objectives) but also factors such as the diversity of the population.

[0082] Furthermore, finally, the differential evolution algorithm is used for single-objective optimization. In addition to the bidirectional weight vector constructed from the S1 reference solution, the bidirectional weight vector constructed from the symmetrically generated S1' will cover the entire search space more widely and without overlap, improving the efficiency of finding the optimal solution.

[0083] Furthermore, the above process can be repeated until a preset termination condition is met, such as the maximum number of iterations, the upper limit of the function evaluation times, etc.

[0084] S104: Use the current population as the parent population to train the GAN model and generate an offspring population.

[0085] Use the data of the current population to train the GAN model, and then use the trained model to generate new predicted values, that is, potential high-quality offspring solutions. As an implementation manner of the present application, the GAN model can adopt the WGAN-GP network model as the generation model.

[0086] Specifically, it can include:

[0087] Normalize the decision variables of the current population:

[0088]

[0089] where i = 1,..., D, D is the number of decision variables, o and t are the lower and upper bound points of the decision space respectively. When the model is in the training stage, for each iteration of the training of the generator network, the discriminator network performs epochD iterations. Among them, the parameters of the discriminator network are updated through the loss function loss D and the parameters of the generator network are updated through the loss function loss G For an input value X, the generated value is Define ε ∈ U(0, 1) is a random number in [0, 1]. Given a value of λ, the loss function is:

[0090]

[0091] where Y, are the values of the discriminator for X, respectively, denotes for the gradient. For mini-batch data, different values of ε are used and the average loss is calculated. The gradient penalty improves stability by penalizing gradients with large magnitudes, and the value of controls the magnitude of the gradient penalty added to the discriminator loss. Here, the Adam optimizer can be used to update the parameters of the neural network according to the gradient information. Then, m samples of D dimensions that follow a normal distribution

[0092] O = o + Y ⊙ (t - o)

[0093] where o and t are the lower and upper bound points of the decision space respectively. The predicted value Y is dot-multiplied with (t - o) and added to o to obtain the value of the final offspring in the decision space.

[0094] After training, the generator can generate new offspring solutions, which are usually of higher quality than those obtained by random generation or simple mutation. Further, these generated offspring solutions will also be further processed, such as optimized by the differential evolution algorithm, to ensure their effectiveness and diversity.

[0095] The solution set after being processed by the differential evolution algorithm will be evaluated again, and excellent individuals will be selected through the environmental selection mechanism to form the next generation population to ensure their effectiveness and diversity.

[0096] S105: Optimally update the population between the parent and offspring populations through the environmental selection mechanism until the preset termination condition is met and the final solution set is output.

[0097] Through the environmental selection mechanism, selection is made between the parent and offspring populations to determine which individuals can enter the next generation population. Considering the quality (fitness) and diversity of the solutions, it ensures the continuous evolution of the population and gradually approaches the true Pareto front.

[0098] As Figure 3 shown, it is a schematic diagram of the approximate Pareto front obtained by the embodiment of the present application on the LSMOP2 benchmark function; which includes 2 objectives and 1000 decision variables. AsFigure 4 As shown, it is a schematic diagram of the approximate Pareto front obtained on the ZDT1 benchmark function provided by the embodiments of the present application; it includes 2 objectives and 1000 decision variables. Combining this embodiment and Figure 3 、 Figure 4 it can be seen that the present application can quickly and effectively search for the global optimal solution. Among them, ZDT refers to a set of multi-objective optimization test functions, which are often used to evaluate the performance of multi-objective evolutionary algorithms (MOEAs). ZDT1 is a relatively simple test function with a convex Pareto front. It consists of two objectives. The first objective is a linear combination of decision variables, and the second objective depends on a non-linear function of all decision variables. Usually, the standard ZDT1 function has only 30 decision variables. Therefore, the present application processes 1000 decision variables, demonstrating the excellent ability of the algorithm of the present application in large-scale optimization problems.

[0099] In summary, in the GAN-based large-scale multi-objective optimization method provided by the embodiments of the present application, initializing the population and non-dominated sorting provide preliminary high-quality reference solutions, laying a foundation for subsequent problem transformation and direction guidance strategies; problem transformation simplifies the search space, enabling the direction guidance strategy to more effectively generate new solutions in the simplified space; the WGAN-GP model generates high-quality offspring, and the differential evolution algorithm further optimizes these solutions, improving the diversity and convergence of the population; finally, the population is continuously updated through the environmental selection mechanism to approach the true Pareto front.

[0100] Next, in combination with a specific embodiment, the GAN-based large-scale multi-objective optimization method provided by the present application is further introduced, especially an optimization design example for estimating the time-varying ratio error of a voltage transformer (VT) in a power system to estimate the ratio error of the voltage transformer in real time and accurately, ensuring the stable operation of the power system. Please refer to Figure 5 - Figure 6 , Figure 5 is a schematic flowchart of the GAN-based large-scale multi-objective optimization method provided by this embodiment, Figure 6 is a schematic structural diagram of the voltage transformer provided by this embodiment. The method includes the following steps:

[0101] S201: Determine the optimization variables and optimization objectives according to the structure and working characteristics of the voltage transformer.

[0102] Take the total time-varying ratio error (Ratio Error, RE) of all uncalibrated VTs and its sum over time as the optimization objective, and establish the following mathematical model for the optimization problem:

[0103]

[0104] The specific definitions are as follows:

[0105] First, define the decision variable x:

[0106] x = (x 1,1 ,..., x 1,T ,..., x K,1 ,..., x K,T )

[0107] where x i,j represents the true voltage value of the i-th phase at time j. Then define the data d i collected from the voltage transformer of the i-th phase:

[0108]

[0109] where d p,q represents the p-th measurement data at time q. Then define the ratio error e i of the voltage transformer:

[0110]

[0111] where represents the ratio error of the k-th phase of the i-th group of voltage transformers at time j. Define the change Δe i of the ratio error over time as:

[0112]

[0113] where is the change in RE of the k-th phase of the i-th group of voltage transformers at time j. The objective function f1 reflects the matching degree between the true voltage value and the measured value, aiming to minimize the total RE of all voltage transformers. The objective function f2 reflects the relationship between the true voltage value and the measured value over time, aiming to minimize the variance of the RE changes of different voltage transformers.

[0114] S202: Define function parameters.

[0115] For example, define the maximum number of calculations FE max = 100000, initialize each parameter, and set N s to 20; randomly initialize and generate a population P of N = 100 individuals according to the problem, and calculate their objective values.

[0116] S203: Sort the current population using the non-dominated sorting algorithm.

[0117] Divide the population into a non-dominated solution set P n and a dominated solution set P d .

[0118] S204: Constructor problem: From the non-dominated solution set P n Select N s The solutions are used as reference solution sets, and two direction vectors are constructed for each reference solution and its symmetric point, and are associated with two weight variables to construct subproblems. The subproblems are then optimized to generate the sub-generation solution P1.

[0119] S205: Construct non-dominated solutions to guide the evolution direction vector of the dominated solutions to generate offspring.

[0120] P n and P d Quantity is used to judge, if P n The number of d , then in P n Randomly select a starting point from the P d Randomly select N s -|P d | solutions and the remaining dominant solutions as the end point, construct non-dominated solutions to point to the evolutionary direction dominated by non-dominated solutions to guide the generation of offspring and improve population diversity. d Select N s The solution is obtained by calculating its symmetric point as the end point, constructing a non-dominated solution to guide the dominant solution evolution direction vector to generate offspring to improve convergence. Generate offspring solution P2.

[0121] S206: Select excellent offspring through environmental selection strategy.

[0122] The parent population P and the generated child populations P1 and P2 are selected, and N individuals are selected as the new parent population P.

[0123] S207: Iterate until the preset conditions are met.

[0124] If the current number of function evaluations FE ≤ 0.5*FE max , then return to step S203 to continue iteration. Otherwise, execute step S208.

[0125] S208: Use the current population as training data for WGAN-GP to train the model and generate offspring.

[0126] Generate a random number rnd between 0 and 1. If rnd ≥ 0.5, use the current parent population P as the training data for the WGAN-GP neural network, train the model and generate N offspring solutions P3. Use the environmental selection strategy to select between the parent population P and the generated offspring population P3, and select N individuals optimally as the new parent population P. Conversely, if rnd < 0.5, use the differential evolution algorithm to generate offspring P4 from the parent population P, and then use the environmental selection strategy to select between the parent population P and the generated offspring population P4, and select N individuals optimally as the new parent population P.

[0127] S209: Iterate until the condition is met and output the optimal solution.

[0128] If the current number of function evaluations FE ≤ FE max , then return to step S208 to continue the iteration. Conversely, the algorithm iteration ends and the global optimal solution is output.

[0129] Please refer to Table 1. Table 1 shows the HV values obtained by this application and other comparison algorithms in estimating the ratio error problem TREE1-5 (Time-varying Ratio Error Estimation) of voltage transformers. The HV index measures the volume size covered by the non-dominated solution set generated by the optimization algorithm in the objective space. Specifically, the HV index measures the volume occupied by the solution set in the objective space relative to a reference point (usually the worst value of all objectives). Generally, the larger the HV index, the better the convergence and diversity of the surface algorithm. To reduce the influence of random errors on the calculation results, in this embodiment, each algorithm runs independently 20 times in each test case, and the mean value of the HV index obtained by each algorithm in each test case is calculated. To judge the significant differences between algorithms based on the results, a Wilcoxon signed-rank test at a 5% significance level is performed on the evaluation results of the competing algorithms, making the algorithm comparison more objective and persuasive. The symbols ‘+’, ‘-’, ‘=’ indicate that the algorithm is respectively better than, lower than, and close to the algorithm proposed in this application.

[0130] Table 1:

[0131]

[0132] As can be seen from Table 1, the method proposed in this application is significantly better than other algorithms in estimating the ratio error of voltage transformers, has stronger search ability, and can obtain the global optimal solution for the ratio error estimation of voltage transformers.

[0133] Based on the same inventive concept, this application also provides a GAN-based large-scale multi-objective optimization device 300, as Figure 7 shown in the structural schematic diagram of the GAN-based large-scale multi-objective optimization device 300, including:

[0134] An initialization module 301 for randomly initializing the population and operating parameters of a multi-objective optimization problem;

[0135] A non-dominated sorting module 302 for selecting a preset number of non-dominated solutions from the population as reference solutions through a non-dominated sorting algorithm;

[0136] A problem transformation module 303 for transforming a multi-objective optimization problem into a series of single-objective optimization sub-problems by performing two-way weight vector association with the upper and lower boundary points of the decision space according to the symmetric points of the non-dominated reference solutions that are centrosymmetric in the decision space;

[0137] A model training and generation module 304 for using the current population as the parent population to train a GAN model and generate an offspring population;

[0138] An environmental selection module 305 for preferentially updating the population between the parent and offspring populations through an environmental selection mechanism until a preset termination condition is met and the final solution set is output.

[0139] The above-mentioned initialization module 301, non-dominated sorting module 302, problem transformation module 303, model training and generation module 304, and environmental selection module 305 are used to execute the embodiments of the above steps S101 - S105 and any optional implementation manners thereof, which will not be elaborated in this embodiment.

[0140] The large-scale multi-objective optimization solution provided by this application first fully explores the large-scale decision space based on a problem transformation framework through a symmetric direction sampling strategy. Compared with the direction sampling strategy, the symmetric direction sampling strategy based on symmetry generates additional symmetric sampling directions, increasing the diversity of sampling directions and eliminating potential non-uniform searches caused by a single symmetric sampling direction. In addition, a direction guidance strategy is adopted to guide the generation of promising solutions through two types of direction vectors, ensuring the diversity of the generated offspring to avoid local optima. The two strategies are combined to optimize the population, balancing the exploration and exploitation of the algorithm and significantly improving the performance of the method.

[0141] This application also generates high-quality offspring based on the WGAN-GP neural network model, selects individuals with excellent convergence and diversity from historical data as the training set, ensures that the WGAN-GP model learns the distribution of high-quality solutions and generates excellent offspring, and improves the diversity of the population.

[0142] This application combines the above-mentioned strategies to ensure the global search accuracy. This algorithm can quickly and effectively search for the global optimal solution and has achieved excellent performance.

[0143] It should be understood that the above description of the specific embodiments of the present application is only for explaining the design concept and features of the present application, and its purpose is to enable those skilled in the art to understand the content of the present application and implement it accordingly. However, the scope of the present application is not limited to the above specific embodiments. All modifications made within the scope of the claims of the present application shall be covered by the protection scope of the present application.

Claims

1. A large-scale multi-objective optimization method based on GAN, characterized in that, including: Randomly initialize the population and operating parameters of the multi-objective optimization problem; Select a preset number of non-dominated solutions from the population as reference solutions through the non-dominated sorting algorithm; According to the symmetric points of the non-dominated reference solutions that are centrosymmetric in the decision space, through two-way weight vector association with the upper and lower boundary points of the decision space, convert the multi-objective optimization problem into a series of single-objective optimization sub-problems; Use the current population as the parent population to train the GAN model and generate the offspring population; Through the environmental selection mechanism, preferentially update the population between the parent and offspring populations until the preset termination condition is met and output the final solution set.

2. The large-scale multi-objective optimization method based on GAN according to claim 1, characterized in that After converting the multi-objective optimization problem into a series of single-objective optimization sub-problems, it further includes: Generate new solutions by constructing direction vectors in the decision space, and select excellent individuals through the environmental selection mechanism to update the population.

3. The large-scale multi-objective optimization method based on GAN according to claim 2, wherein, including: Combine the direction vector with the reference solution in a linear combination to generate a new solution.

4. The large-scale multi-objective optimization method based on GAN according to claim 3, characterized in that After generating the new solution, it further includes: Evaluate the new solution using the hypervolume indicator evaluation criterion; According to the evaluation results, select excellent individuals using the environmental selection mechanism to update the population.

5. The method for large-scale multi-objective optimization based on GAN according to claim 4, characterized in that The environmental selection mechanism includes preferentially selecting according to the fitness value and diversity index of individuals to update the population.

6. The large-scale multi-objective optimization method based on GAN according to claim 2, wherein Constructing the direction vector in the decision space includes: Construct the direction vector according to the direction from the non-dominated solution and its symmetric point to other non-dominated solutions, and the direction of mutual pointing between non-dominated reference solutions.

7. The large-scale multi-objective optimization method based on GAN according to claim 1, wherein Using the current population as the parent population to train the GAN model and generate the offspring population, it further includes: Apply the differential evolution algorithm to optimize the offspring population.

8. The GAN-based large-scale multi-objective optimization method according to any one of claims 1-7, characterized in that The GAN model is the WGAN-GP model.

9. The large-scale multi-objective optimization method based on GAN according to claim 8, characterized in that, Using the trained GAN model to generate new offspring solutions, it further includes: Optimize the generated new offspring solutions through the differential evolution algorithm.

10. A large-scale multi-objective optimization device based on GAN, characterized in that, including: Initialization module, used to randomly initialize the population and operating parameters of the multi-objective optimization problem; Non-dominated sorting module, used to select a preset number of non-dominated solutions from the population as reference solutions through the non-dominated sorting algorithm; Problem conversion module, used to convert the multi-objective optimization problem into a series of single-objective optimization sub-problems according to the symmetric points of the non-dominated reference solutions that are centrosymmetric in the decision space, through two-way weight vector association with the upper and lower boundary points of the decision space; Model training and generation module, used to use the current population as the parent population to train the GAN model and generate the offspring population; Environmental selection module, used to preferentially update the population between the parent and offspring populations through the environmental selection mechanism until the preset termination condition is met and output the final solution set.

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