Dynamic multi-objective optimization method based on region partition selection transfer learning

Abstract

The present application discloses a dynamic multi-objective optimization method based on regional division selection transfer learning, which relates to the field of artificial intelligence technology, including: generating an initial population; optimizing the initial population to obtain an initial Pareto optimal set; when the environment changes, evaluating the historical Pareto optimal set, and classifying the historical solutions into elite solutions and non-elite solutions; performing transfer learning on the elite solutions and non-elite solutions using an individual transfer learning method based on elitism and a manifold transfer learning method based on rapid evolution, respectively, to obtain a first predicted population and a second predicted population; combining the first predicted population and the second predicted population to form a real-time population; optimizing the real-time population to obtain a real-time Pareto optimal set. The present application evaluates the historical solutions, classifies the historical solutions into elite solutions or non-elite solutions, and then adopts the corresponding transfer method according to the type of historical solutions, thereby reducing the negative transfer generated when using transfer learning.

Description

Technical Field

[0001] The present application relates to the field of artificial intelligence technology, and in particular to a dynamic multi-objective optimization method based on region partitioning and selection transfer learning. Background Art

[0002] Dynamic Multi-Objective Evolutionary Algorithm (DMOEA) is a method for optimizing multiple objective functions simultaneously. This method has made significant progress in obtaining good accuracy. Compared with traditional multi-objective optimization methods, dynamic multi-objective optimization methods need to deal with the complexity of dynamic characteristics and multi-objective optimization at the same time, so they face greater challenges. In dynamic multi-objective optimization, the response mechanism can quickly guide the population to search for the Pareto Optimal Frontier (POF) or Pareto Optimal Set (POS) in the new environment when the environment changes. According to the different response mechanisms, dynamic multi-objective optimization methods are mainly divided into three categories: memory-based dynamic multi-objective optimization methods, diversity-based dynamic multi-objective optimization methods, and prediction-based dynamic multi-objective optimization methods.

[0003] Memory-based dynamic multi-objective optimization methods rely on historical information and experience, and use the memory mechanism of the population to adapt to environmental changes, thereby better guiding future searches. However, memory maintenance and search increase the computational cost and may reduce the algorithm speed. Diversity-based dynamic multi-objective optimization methods focus on maintaining the diversity of the population, thereby avoiding the phenomenon of premature convergence without finding the POS due to insufficient diversity. However, because maintaining population diversity will cause certain interference to the search process, resulting in a slow convergence rate. In recent years, prediction-based dynamic multi-objective optimization methods have been widely studied, aiming to use historical information to predict possible POS / POF locations in new environments. Although prediction-based dynamic multi-objective optimization methods can use the regularity of problem changes to predict new solutions in appropriate environments, less accurate predictions may lead to performance degradation to a certain extent.

[0004] The independent and identically distributed (IID) assumption in traditional prediction strategies cannot be met in practical problems, so it may lead to evolutionary deviations. Recently, the introduction of transfer learning (TL) has liberated this condition. For non-IID cases, transfer learning can search the latent space and improve the efficiency of solving. However, negative transfer may occur when the transfer method is not suitable for the transfer task. Negative transfer may lead to deviation from the search path and seriously reduce efficiency. Therefore, how to reduce the occurrence of negative transfer to save the running time of dynamic multi-objective optimization methods is an important problem that needs to be solved. Summary of the invention

[0005] The embodiment of the present application provides a dynamic multi-objective optimization method based on region partition selection transfer learning, which is used to solve the problem in the prior art that negative transfer may cause deviation from the search path, thereby seriously reducing efficiency.

[0006] The embodiment of the present application provides a dynamic multi-objective optimization method based on region division selection transfer learning, including:

[0007] Generate initial population POP 0;

[0008] For the initial population POP 0 The multi-objective optimization method based on decomposition is used for optimization to obtain the initial Pareto optimal set POS 0;

[0009] The initial Pareto optimal set POS 0 saved in memory Q middle;

[0010] When the environment changes, the estimator is used to adjust the memory Q The historical Pareto optimal set in POS Evaluate and convert the historical Pareto optimal set POS The historical solutions in are classified into elite solutions and non-elite solutions;

[0011] The elite solution is transferred using the individual transfer learning method based on elitism to obtain the first prediction population POP t1 ;

[0012] The non-elite solution is transferred using the manifold transfer learning method based on rapid evolution to obtain the second prediction population POP t2 ;

[0013] Combined with the first predicted population POP t1 and the second predicted populationPOP t2 , get the real-time population POP t ;

[0014] Real-time population POP t The multi-objective optimization method based on decomposition is used for optimization to obtain the real-time Pareto optimal set. POS t .

[0015] The dynamic multi-objective optimization method based on region partition selection transfer learning in this application has the following advantages:

[0016] According to the selection strategy, the historical solutions are evaluated and classified as elite solutions or non-elite solutions, and then the corresponding migration method is adopted according to the type of historical solutions. In order to verify the performance of the proposed method, the dynamic multi-objective optimization method (Division Slection Transfer-learning DynamicMulti-objective Optimization Evolutionary Algorithm, DST-DMOEA) based on the division selection transfer learning of this application was compared with several advanced DMOEA methods. The results show that the DST-DMOEA method of this application reduces the negative transfer generated when using transfer learning to solve dynamic multi-objective optimization problems (Dynamic Multi-objective Optimization Problems, DMOPs), and the running speed of the method is significantly improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0018] Figure 1 A flowchart of a dynamic multi-objective optimization method based on region partitioning and transfer learning provided in an embodiment of the present application. DETAILED DESCRIPTION

[0019] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0020] Figure 1 A flowchart of a dynamic multi-objective optimization method based on region partitioning and transfer learning provided in an embodiment of the present application. An embodiment of the present application provides a dynamic multi-objective optimization method based on region partitioning and transfer learning, including:

[0021] S100, generate the initial population POP 0.

[0022] S110, for the initial population POP 0 The multi-objective optimization method based on decomposition is used for optimization to obtain the initial Pareto optimal set POS 0.

[0023] For example, the Multi-objective Optimization Evolutionary Algorithm based on Decomposition (MOEA / D) can effectively solve complex optimization problems. The core principle of MOEA / D is to set the initial population to be optimized. POP 0 is decomposed into multiple single-objective optimization sub-problems, and these sub-problems are solved by co-evolution. Multi-objective optimization is performed in a neighborhood search-based framework, where each population interacts with a neighborhood, and the neighborhood information is used to guide the evolution of the population, ultimately obtaining the global Pareto optimal set. The main process of MOEA / D includes the following steps:

[0024] (1) Problem decomposition: The initial population POP 0 is decomposed into multiple single-objective optimization sub-problems, making each sub-problem as simple as possible while retaining the initial population POP 0 key information.

[0025] (2) Population initialization: Use random generation or other heuristic methods to initialize a set of initial solutions for each subproblem.

[0026] (3) Neighborhood search: Each initial solution evolves through neighborhood search according to the subproblem to which it belongs.

[0027] (4) Population update: Update the population based on the results of the neighborhood search to generate a new generation of solutions.

[0028] (5) Neighborhood exchange: Neighborhood exchange is performed under a certain number of iterations or other conditions so that information can be shared between populations.

[0029] (6) Termination condition: According to the preset termination condition, such as reaching the maximum number of iterations, reaching the convergence threshold, etc., determine to stop the iteration and output the final Pareto optimal set.

[0030] S120, the initial Pareto optimal set POS 0 saved in memory Q middle.

[0031] S130, when the environment changes, using the estimator to Q The historical Pareto optimal set in POS Evaluate and convert the historical Pareto optimal set POS The historical solutions in are classified into elite solutions and non-elite solutions.

[0032] Exemplarily, S130 specifically includes: randomly sampling a population in the decision space, calculating the objective function value of the sampled population; using the sampled population as an input feature matrix of the estimation model, using the objective function value of the sampled population as a label for training the estimation model, training the estimation model, and obtaining an estimator; converting the historical Pareto optimal set POS As the test set input estimator, use the estimator to predict the estimated value of the objective function of the test set; according to the estimated value of the objective function, the historical Pareto optimal set POS Perform non-dominated sorting on the historical solutions in to obtain a non-dominated solution set, and select elite solutions and non-elite solutions from the non-dominated solution set.

[0033] Specifically, the estimation model is established based on Support Vector Regression (SVR). The embodiment of the present application constructs an estimator through SVR to screen historical solutions of different degrees of quality. SVR has a powerful nonlinear modeling capability and can accurately capture the nonlinear relationship of the objective function, thereby providing an accurate estimate of the objective function.

[0034] Furthermore, in order to ensure the diversity of solutions, after obtaining the elite solutions and non-elite solutions, the elite solutions or non-elite solutions whose congestion degree exceeds the congestion setting value are deleted. At the same time, if the number of elite solutions or non-elite solutions exceeds the first number setting value, a part of the elite solutions or non-elite solutions are randomly deleted; if the number of elite solutions or non-elite solutions is less than the second number setting value, the elite solutions and non-elite solutions are reselected from the non-dominated solution set, where the second number setting value is less than the first number setting value.

[0035] S140, transfer learning is performed on the elite solution using the individual transfer learning method based on elitism to obtain the first predicted populationPOP t1 .

[0036] Exemplarily, S140 specifically includes: taking the elite solution and the solution obtained in the previous environment as samples, and sequentially inputting them into multiple weak classifiers h p ; Use the basic classifier to classify the weak classifier h p The parameters and weights of the adjusted weak classifiers are adjusted. h p Combining to form a strong classifier h f ; Using strong classifier h f Filter elite solutions to obtain the first predicted population POP t1 .

[0037] The Elite Meritocracy Individual Transfer-learning (EMIT) method based on elitism adopts the idea of ​​Transfer Adaptive Boosting (Transfer Adaboost) to obtain part of the high-quality prediction population by constructing a classifier using the information of the elite solution. The main contribution of EMIT is to combine individual transfer learning with elitism. On the one hand, this method reduces the possibility of negative transfer through the guidance information of the elite solution. On the other hand, compared with the existing methods, the EMIT proposed in this application is essentially a sample-based transfer method, which does not require complex feature transformation, thereby avoiding a large amount of computing resource consumption.

[0038] Furthermore, the base classifier uses the Transfer Adaboost method to boost the weak classifier h p In the process of transfer learning, the elite solution and the solution obtained in the previous environment are regarded as the first target domain. D ta1 and the first source domain D so1 For each domain, non-dominated solutions are labeled as +1 and dominated solutions are labeled as -1. The whole process uses the base classifier to iteratively adjust a set of weak classifiers. h p Parameters and weights, and then the weak classifiers with different weights h p Combined to form a strong classifier h f Finally, using the strong classifier h f Select solutions from the elite solutions to form the first prediction populationPOP t1 . Combined strong classifiers h f The specific steps are as follows:

[0039] Initialize the weight vector as shown in formula (1):

[0040] (1)

[0041] in, Represents an individual x The initial weight vector, x represents the individuals of the initial population, represents individuals belonging to the first source domain, represents individuals belonging to the first target domain, and the symbol Indicates belonging to.

[0042] Iteratively use the base classifier to generate j Weak classifier , j The label indicating the number of iterations, calculating the weak classifier In the first target domain D ta1 The error rate on , as shown in formula (2):

[0043] (2)

[0044] Among them, the symbol Indicates belonging to, It represents the proportion of a single individual weight vector to the overall weight vector, as shown in formula (3). is the loss function, which is calculated as shown in formula (4):

[0045] (3)

[0046] (4)

[0047] Among them, the symbol Indicates belonging to, Represents an individual x No. j The weight vector of times, Indicates the label of the solution. For each domain, the non-dominated individuals are labeled +1 and the dominated individuals are labeled -1. Indicates absolute value.

[0048] Compute weak classifiers The coefficient of , as shown in formula (5):

[0049] (5)

[0050] ln represents the natural logarithm. Use formula (6) to update the weight vector;

[0051] (6)

[0052] in, Represents an individual x No. j +1 weight vector, e is a natural constant, symbol Indicates belonging to.

[0053] Use formula (7) to get the strong classifier h f :

[0054] (7)

[0055] in, represents the symbolic function, N is the total number of iterations.

[0056] In order to obtain a strong classifier h f After EMIT, the elite solutions are input into the strong classifier, and the solutions identified as good by the strong classifier will be selected to form the first prediction population.

[0057] S150, transfer learning is performed on non-elite solutions using the manifold transfer learning method based on rapid evolution to obtain the second prediction population POP t2 .

[0058] Exemplarily, S150 specifically includes: taking the non-elite solution as the source domain, segmenting the source domain into multiple manifolds; randomly generating a population as the target domain; mapping the multiple manifolds and the target domain to the starting point on the Grassmann manifold respectively. S 0 and end point S 1. Starting point S 0 and end point S The curve between 1 is the geodesic flow of the source domain and the target domain; select multiple intermediate points on the geodesic flow, map the training data and the test data on the intermediate points, obtain the corresponding mapping data, and obtain the second prediction population according to the mapping data POP t2 .

[0059] The rapid evolution manifold transfer learning method (REMT) in the embodiment of the present application adopts the sample geodesic flow (SGF) in manifold transfer learning. The SGF method continuously learns from the knowledge of non-elite solutions and retains most of the knowledge, and applies it to the target domain to obtain high-quality solutions, thereby guiding the population search to the true Pareto frontier.

[0060] The specific steps of the transfer learning method based on geodesic flow are as follows: Local Principal Component Analysis (LPCA) is used to cluster the elite solutions and randomly generated populations. d The source domain and target domain are obtained in the feature subspace, which are respectively referred to as the second source domain and the second target domain ,in , , express n × d Dimensional matrix. for The orthogonal complement of express n × nd dimensional matrix, and ,when k =0 Indicates that the mapping starts from the second source domain, k =1 Indicates that the mapping ends at the second target domain. , the geodesic from the second source domain to the second target domain is expressed by formula (8):

[0061] (8)

[0062] in, represents the mapping function from the second source domain to the second target domain, k Represents the gradual change parameter from the second source domain to the second target domain, ranging from 0 to 1. , and is a set of standard orthogonal matrices, which are given by a set of orthogonal complementary singular values, as shown in formula (9):

[0063] (9)

[0064] Superscript T represents transpose, represents a diagonal matrix,V represents a right singular matrix. and They are respectively and Composition dimensional diagonal matrix, i= 1,2,…, d , is the angle between the second source domain and the second target domain, , i The label of the angle.

[0065] After obtaining the geodesic model, the midpoint of the training data and test data mapped to the geodesic can be calculated according to formula (10):

[0066] (10)

[0067] in, is the training data or the test data, express n dimensional matrix, is the characteristic data at the middle point, y corresponds to a position on the geodesic flow p ,Location p The number of is predefined, superscript T Indicates transpose.

[0068] The specific steps of transfer learning include: First, non-elite de-clustering into m -1-dimensional manifold: ,…, ,in m is the number of targets. For each cluster, construct the geodesic flow Then the data in each manifold y Mapped onto the geodesic flow, we get the mapping data of the second source domain In a dynamic environment, the second source domain and the second target domain may have similar mapping data on the manifold. Therefore, it is possible to find a mapping data of the second target domain , the mapping data on the manifold Mapping data with the second source domain Infinitely close, superscript T This is a single-objective optimization problem. Any single-objective optimization algorithm can be used to solve this problem. This application uses the interior point method to solve this single-objective optimization problem. Mapping data The second predicted population POP t2 .

[0069] S160, combined with the first predicted populationPOP t1 and the second predicted population POP t2 , get the real-time population POP t .

[0070] S170, for real-time population POP t The multi-objective optimization method based on decomposition is used for optimization to obtain the real-time Pareto optimal set. POS t .

[0071] For example, in obtaining the real-time Pareto optimal set POS t After that, the real-time Pareto optimal set POS t Stored in memory Q middle.

[0072] If the memory Q The remaining capacity is greater than or equal to the real-time Pareto optimal set POS t The amount of data will be real-time Pareto optimal set POS t Directly stored in memory Q If the memory Q The remaining capacity is less than the real-time Pareto optimal set POS t The amount of data will be stored in memory Q The earliest population stored in the memory is deleted. Q The remaining capacity increases to be greater than or equal to the real-time Pareto optimal set POS t When the amount of data is POS t Stored in memory Q middle.

[0073] The DST-DMOEA proposed in the embodiment of the present application improves the optimization performance by reusing the solutions obtained at the previous moment. The knowledge of the historical solutions has a certain guiding effect on the new solutions. Solutions of different quality have different guiding effects on the new solutions due to their different characteristics. Therefore, by retaining and reasonably transforming these historical solutions, a better real-time population can be generated.

[0074] Take the vehicle path optimization problem as an example. When dealing with a vehicle path planning problem in a dynamic environment, the goal is to plan the optimal driving route for a group of vehicles under dynamic traffic conditions to minimize multiple goals such as total driving time, fuel consumption and carbon emissions. The specific process is as follows:

[0075] 1. Generate a set of initial vehicle paths ( POP 0), these paths can be generated randomly or based on some heuristic algorithms, and each path represents a solution.

[0076] 2. Use MOEA / D to decompose the vehicle path planning problem into multiple single-objective sub-problems (for example, minimizing the travel time of a specific vehicle), and then co-evolve these sub-problems to finally obtain a set of initial optimal paths ( POS 0).

[0077] 3. Obtain the initial optimal path set POS 0 is stored in memory Q It is convenient for use in subsequent environmental changes.

[0078] 4. When traffic conditions change (such as road congestion, weather changes, etc.), the estimator built using SVR evaluates the data stored in Q The historical Pareto optimal set in POS , classifying these historical solutions into elite solutions (e.g., paths that are still better) and non-elite solutions (e.g., paths that are likely to be more affected).

[0079] 5. Perform transfer learning on the paths classified as elite solutions. Use the elite solutions and the solutions in the previous environment to build multiple weak classifiers and combine them into a strong classifier. This strong classifier will help predict high-quality paths in the new environment ( POP t1 ).

[0080] 6. Perform manifold-based transfer learning on non-elite solutions. Generate a second set of predicted paths ( POP t2 ).

[0081] 7. The first predicted population POP t1 and the second predicted population POP t2 Combine to form a real-time population POP t , this population represents the potential optimal vehicle paths under the current traffic conditions.

[0082] 8. Real-time population POP t Perform multi-objective optimization based on decomposition again to generate real-time Pareto optimal sets POS t , which is the optimal vehicle path set under the current environment. Finally, POS t Stored in memory Q If the memory QIf the capacity is insufficient, the old data will be replaced according to certain rules.

[0083] The method of this application effectively combines multi-objective optimization and transfer learning techniques to adapt to the vehicle path planning problem in a dynamic environment. By adjusting the vehicle path in real time, the system can continuously find the optimal solution in a complex traffic environment, thereby minimizing the total driving time, fuel consumption and carbon emissions.

[0084] Experimental Description

[0085] The DST-DMOEA proposed in this application is compared with the latest DMOEA to verify the effectiveness of this method in dealing with DMOPs. All compared algorithms are evaluated based on 17 DMOPs selected from two test functions: 1. Dynamic Function (DF) test function; 2. Dynamic Multi-objective Optimization Problem (dMOP) test function. The DF test function contains 14 problems (DF1-DF14), and the dMOP test function contains 3 problems (dMOP1-dMOP3). The dynamics of the test functions involved in the comparison are reflected in the dynamic POF or POS that may exist in different environments, and these 17 different test functions can better represent different problems in real scenarios, which can effectively compare the performance of DMOEA.

[0086] In this experiment, the following metrics are used to evaluate the performance of various algorithms.

[0087] 1. MIGD: Inverted generational distance (IGD) is an effective method to evaluate the convergence and diversity of an algorithm. It reflects the difference between the true POF and the obtained POF, while MIGD is the average value of IGD.

[0088] 2. MHV: Hyper Volume (HV) is used to quantify the convergence and distribution of the algorithm solution, and MHV is the average value of HV.

[0089] In order to enhance the persuasiveness of the algorithm and ensure the fairness of the experiment, this application uses MOEA / D as the baseline algorithm. When solving dynamic problems, MOEA / D has high adaptability in dynamic environments and has been widely proven in experiments. The DST-DMOEA algorithm proposed in this application is compared with several popular DMOEAs, including Memory-driven Manifold Transfer Learning DynamicMulti-objective Optimization Evolutionary Algorithm (MMTL-DMOEA), Knee-points Transfer Dynamic Multi-objectiveOptimization Evolutionary Algorithm (KT-DMOEA), Individual Transfer-learning Dynamic Multi-objective OptimizationEvolutionary Algorithm (IT-DMOEA), Steady state GenerativeEvolutionary Algorithm (SGEA) and Support Vector Regression Dynamic Multi-objective Optimization Evolutionary Algorithm (SVR-DMOEA). All algorithms choose MOEA / D as the static optimizer. In the experiment, the dimension of the decision variables of DMOPs is set to 10, the population size of the dynamic bi-objective optimization problem is set to 100, and the population size of the dynamic tri-objective optimization problem is set to 150.

[0090] Experimental results show that based on the MIGD metric, DST-DMOEA achieved 32 best results out of 51 test cases, MMTL-DMOEA achieved 3 best results, KT-DMOEA achieved 3 good results, IT-DMOEA achieved 2 good results, SGEA achieved 7 good results, and SVR-DMOEA achieved 4 good results. Among them, DST-DMOEA is significantly better than other competing algorithms on DF2, DF3, DF4, DF10, dMOP1, and dMOP2.

[0091] Compared with the IGD indicator, the HV indicator can better quantify the convergence and diversity of the solutions obtained by the algorithm. The experimental results show that the DST-DMOEA method proposed in this application has advantages over other methods in most cases. In addition, in most cases, the DST-DMOEA of this application can obtain initial solutions with better diversity and convergence compared with other DMOEAs. In addition, in most cases, the initial solution of DST-DMOEA is closer to the true POF than other comparison algorithms, which shows that DST-DMOEA can effectively reduce negative migration.

[0092] In order to prove the advantages of DST-DMOEA in terms of convergence and evolution speed, the average running time cost of different algorithms for 17 test functions is also compared in the experiment. From the experimental results, it can be seen that the running speed of DST-DMOEA is faster than MMTL-DMOEA, SGEA, and SVR-DMOEA in most cases. For a few test functions, the time cost of DST-DMOEA is comparable to KT-DMOEA and IT-DMOEA, which shows that DST-DMOEA can achieve excellent performance at a moderate time cost compared with these competitive DMOEAs. In summary, the running time of DST-DMOEA is the fastest among most of the tested algorithms, which shows that the hybrid migration strategy is very effective.

[0093] Although the preferred embodiments of the present application have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present application.

[0094] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is also intended to include these modifications and variations.

Claims

1. A dynamic multi-objective optimization method based on region partitioning and transfer learning, characterized in that: include: Generate initial vehicle paths POP 0; For the initial vehicle path POP 0 The multi-objective optimization method based on decomposition is used to optimize the initial optimal path set POS 0; The initial optimal path set POS 0 saved in memory Q middle; When the traffic conditions change, the memory is updated using an estimator. Q The historical Pareto optimal set in POS Evaluate and convert the historical Pareto optimal set POS The historical solutions in are classified into elite solutions and non-elite solutions; The paths classified as the elite solutions are transferred using the individual transfer learning method based on elitism to obtain high-quality paths. POP t1 ; The non-elite solution is transferred using a manifold transfer learning method based on rapid evolution to obtain a second set of prediction paths. POP t2 ; Combining the high quality paths POP t1 and the second set of predicted paths POP t2 , get the real-time population POP t , the real-time population POP t represents the potential optimal vehicle path under current traffic conditions; For the real-time population POP t The multi-objective optimization method based on decomposition is used for optimization to obtain the real-time Pareto optimal set. POS t , the real-time Pareto optimal set POS t is the optimal vehicle path set under the current environment; The elite solution is transferred using an individual transfer learning method based on elitism, including: The elite solution and the solution obtained in the previous environment are used as samples and input into multiple weak classifiers in sequence. h p ; The weak classifier is classified by using the basic classifier h p The parameters and weights of the adjusted multiple weak classifiers are adjusted. h p Combining to form a strong classifier h f ; Using the strong classifier h f Filter the elite solutions to obtain the high-quality paths POP t1 ; Wherein, the basic classifier is used to classify the weak classifier h p Methods for adjusting parameters and weights include: Initialize the weight vector as shown in formula (1): （1） in, Represents an individual x The initial weight vector, x represents the individuals in the initial path set, D so1 represents the first source domain, represents individuals belonging to the first source domain, represents individuals belonging to the first target domain, and the symbol Indicates belonging to; Iteratively use the base classifier to generate j Weak classifier , j The label indicating the number of iterations, calculating the weak classifier In the first target domain D ta1 The error rate on , as shown in formula (2): （2） Among them, the symbol Indicates belonging to, It represents the proportion of a single individual weight vector to the overall weight vector, as shown in formula (3). is the loss function, which is calculated as shown in formula (4): （3） （4） Among them, the symbol Indicates belonging to, Represents an individual x No. j The weight vector of times, Indicates the label of the solution. For each domain, the non-dominated individuals are labeled +1 and the dominated individuals are labeled -1. Indicates absolute value; Compute weak classifiers The coefficient of , as shown in formula (5): （5） ln represents the natural logarithm, and the weight vector is updated using formula (6); （6） in, Represents an individual x No. j +1 weight vector, e is a natural constant, symbol Indicates belonging to; The adjusted multiple weak classifiers h p Combining to form the strong classifier h f It is expressed by formula (7): （7） in, represents the symbolic function, N is the total number of iterations; The non-elite solution is transferred by using a manifold transfer learning method based on rapid evolution, including: Taking the non-elite solution as a source domain, segmenting the source domain into a plurality of manifolds; A set of paths is randomly generated as the target domain; Mapping the plurality of manifolds and the target domain to the starting point on the Grassmann manifold respectively S 0 and end point S 1. Starting point S 0 and end point S The curve between 1 is the geodesic flow of the source domain and the target domain; Select multiple intermediate points on the geodesic flow, map the training data and the test data on the intermediate points to obtain corresponding mapping data, and obtain the second set of predicted paths according to the mapping data POP t2 .

2. The dynamic multi-objective optimization method based on region partition selection transfer learning according to claim 1 is characterized in that: In obtaining the real-time Pareto optimal set POS t Then, the real-time Pareto optimal set POS t Stored in the memory Q middle.

3. The dynamic multi-objective optimization method based on region partition selection transfer learning according to claim 2 is characterized in that: If the memory Q The remaining capacity is greater than or equal to the real-time Pareto optimal set POS t The amount of data will be the real-time Pareto optimal set POS t Stored directly in the memory Q If the memory Q The remaining capacity is less than the real-time Pareto optimal set POS t The amount of data will be stored in the memory Q The earliest path set stored in the memory is deleted. Q The remaining capacity increases to be greater than or equal to the real-time Pareto optimal set POS t When the amount of data is POS t Stored in the memory Q middle.

4. The dynamic multi-objective optimization method based on region partition selection transfer learning according to claim 1, characterized in that: The historical Pareto optimal set is analyzed using the estimator POS An evaluation is performed to classify the historical solutions into the elite solutions and the non-elite solutions, including: Randomly sample a path set in the decision space and calculate the objective function value of the sampled path set; Taking the sampling path set as an input feature matrix of an estimation model, taking the objective function value of the sampling path set as a label for training the estimation model, training the estimation model, and obtaining the estimator; The historical Pareto optimal set POS Input the estimator as a test set, and use the estimator to predict the estimated value of the objective function of the test set; The historical Pareto optimal set is calculated based on the estimated value of the objective function. POS The historical solutions in are non-dominated sorted to obtain a non-dominated solution set, and the elite solution and the non-elite solution are selected from the non-dominated solution set.

5. The dynamic multi-objective optimization method based on region partition selection transfer learning according to claim 4 is characterized in that: After obtaining the elitist solution and the non-elite solution, the elitist solution or the non-elite solution whose congestion degree exceeds a congestion setting value is also deleted.

6. The dynamic multi-objective optimization method based on region partition selection transfer learning according to claim 4 is characterized in that: If the number of the elite solutions or the non-elite solutions exceeds a first quantity setting value, a portion of the elite solutions or the non-elite solutions is randomly deleted; if the number of the elite solutions or the non-elite solutions is lower than a second quantity setting value, the elite solutions and the non-elite solutions are reselected from the non-dominated solution set, wherein the second quantity setting value is less than the first quantity setting value.

7. The dynamic multi-objective optimization method based on region partition selection transfer learning according to claim 4 is characterized in that: The estimation model is established based on a support vector machine.

8. The dynamic multi-objective optimization method based on region partition selection transfer learning according to claim 1, characterized in that: The source domain is segmented into a plurality of manifolds using a local principal component analysis method.

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