A dynamic multi-objective evolutionary method based on transfer learning and special point strategy

Abstract

The embodiment of the application provides a dynamic multi-objective evolutionary method based on migration learning and special point strategy, and relates to the field of evolutionary computation.The method comprises the following steps: analyzing a dynamic multi-objective optimization scene, and obtaining an initial population of the optimization scene;optimizing the initial population by using a multi-objective estimation distribution method, and obtaining a front optimization set of the initial population;obtaining a special point according to the front optimization set;when the decision variable changes, mapping the special point to a high-dimensional space based on a migration learning method of joint distribution adaptation to obtain the special point at the next moment;optimizing the initial population at the next moment by using the multi-objective estimation distribution method, and obtaining a front optimization set of the initial population at the next moment.Through the special point, the accurate prediction of the special point under a new environment is realized, other individuals are randomly generated, the population diversity is increased, and therefore the convergence speed and convergence precision of the algorithm under the new environment are improved.

Description

Technical Field

[0001] This invention relates to the field of evolutionary computation, and in particular to a method for solving a monthly centralized bidding mechanism based on a co-evolutionary algorithm. Background Technology

[0002] In many optimization fields such as production scheduling, artificial intelligence, combinatorial optimization, engineering design, large-scale data processing, urban transportation, reservoir management, network communication, data mining, and capital budgeting, we often encounter many complex dynamic and static optimization problems that are closer to real life. In the past few decades, people have mostly focused on the study of static objective problems. Only in recent years have dynamic objective problems attracted more and more researchers' interest.

[0003] Currently, research on dynamic multi-objective problems is still limited, and internationally it is only in its early stages, with few available theories. Most of these findings focus on designing algorithms for discrete-time variables or directly applying static multi-objective optimization algorithms to solve dynamic multi-objective problems. However, dynamic multi-objective problems are challenging due to the presence of multiple time-dependent, conflicting objectives, and the fact that Pareto efficiency (also known as the Pareto effect, referring to an ideal state of resource allocation) changes over time. Dynamic optimization problems are currently mainly categorized into three types: 1) Maintaining population diversity: Methods such as Grevenstette's stochastic migration evolution strategy, Morrison's hypermutation method, and Gan Ruan et al.'s diversity maintenance strategy are effective ways to improve population diversity; 2) Memory-based methods: For dynamic evolutionary algorithms, adding previously obtained better solutions and restarting these solutions for evolution when needed significantly improves the algorithm's efficiency and search capability in changing environments. Memory is generally divided into two types: implicit memory using redundant representations and explicit memory stored by introducing additional memory sets. Examples include Ryan's method using additional diploid implicit memory and Collins' gene hierarchical structure memory method. Although these implicit memory methods allow evolutionary algorithms to indirectly store some useful information, it is uncertain whether the algorithm can effectively use this information. 3) Prediction-based methods: For example, Iason H et al. proposed a forward-looking approach based on solving dynamic single-objective optimization evolutionary algorithms; Aimin Zhou et al. proposed a dynamic multi-objective evolutionary algorithm based on population prediction; Arrchana Muraganantham et al. proposed an algorithm based on Kalman filter prediction; and Juan Zou et al. proposed a prediction strategy based on center points and inflection points. These methods can respond quickly after environmental changes, but the accuracy of prediction remains a major challenge.

[0004] Currently, most dynamic multi-objective optimization algorithms predict that the solution sets of the model under different environments follow independent and identically distributed rules. This assumption undoubtedly simplifies the complexity of the problem. However, changes in the frontier may lead to different distributions of the solution sets under different environments, which is very difficult for traditional machine learning to solve. Min Jiang et al. proposed a dynamic multi-objective optimization algorithm based on transfer learning. Using the transfer learning method of transfer component analysis (TCA), the frontier at the current time step is mapped to a high-dimensional space to obtain the initial population at the next time step. This method effectively improves the quality of the obtained solutions, but the computation is very complex.

[0005] The design of an evolutionary algorithm for solving dynamic multi-objective optimization problems should first consider the following key issues: 1) How to enable the algorithm to effectively track the Pareto optimal solution set under different times (environments); 2) How to enable the algorithm to quickly and accurately obtain the Pareto optimal solution of the multi-objective problem under different times (environments). Summary of the Invention

[0006] In view of the above problems, embodiments of the present invention are proposed to provide a dynamic multi-objective evolution method based on transfer learning and special point strategy to overcome or at least partially solve the above problems.

[0007] To address the aforementioned problems, embodiments of the present invention disclose a dynamic multi-objective evolutionary method based on transfer learning and special point strategies, comprising:

[0008] For dynamic multi-objective optimization scenario analysis, an initial population of the optimization scenario is obtained, which includes dynamic objectives, decision variables and constraints;

[0009] The initial population is optimized using a multi-objective estimation distribution method to obtain the front-end optimization set of the initial population;

[0010] Special points are obtained based on the aforementioned front-end optimization set;

[0011] When the decision variables change, the transfer learning method based on joint distribution adaptation maps the special points to a high-dimensional space to obtain the special points at the next time step.

[0012] The minimum value among the special points at the next time step is used as the lower limit, and the maximum value among the special points at the next time step is used as the upper limit to generate the initial population at the next time step.

[0013] The initial population at the next time step is optimized using a multi-objective estimation distribution method to obtain the front-end optimization set of the initial population at the next time step.

[0014] Preferably, the step of the transfer learning method based on joint distribution adaptation mapping the special points to a high-dimensional space to obtain the special points at the next time step includes:

[0015] The special points of the initial population are obtained as source data, and the special points at the next time step are obtained as target data;

[0016] Principal component analysis is used to obtain a high-dimensional space based on the source data and the target data, and a first optimization objective is established.

[0017] Using the maximum difference as a distance metric to measure the different distributions of the source data and the target data, an edge distribution fit is constructed to obtain a second optimization objective.

[0018] A model is built based on the source data, and pseudo-labels corresponding to the target data are constructed. Based on the pseudo-labels, a conditional distribution adaptation is constructed to obtain the third optimization target.

[0019] By combining the first optimization objective, the second optimization objective, and the third optimization objective, the final optimization objective is obtained.

[0020] The final optimization objective is converged to obtain the best fit matrix between the source data and the target data;

[0021] Based on the optimal fit matrix and the special point, the special point at the next time step is obtained.

[0022] Preferably, the step of optimizing the initial population using a multi-objective estimation distribution method to obtain the front-end optimization set of the initial population includes:

[0023] Extract information from the initial population to construct a probability model;

[0024] Gaussian sampling is performed on the probability model to obtain the solution set;

[0025] A selection operation is performed on the initial population and the solution set to obtain the front-end optimization set of the initial population.

[0026] The embodiments of the present invention have the following advantages:

[0027] The present invention is based on a method of transfer learning and special point strategy. It assumes that the population at different times follows related but different conditional distributions and probability distributions. It introduces a transfer learning method based on joint distribution adaptation. Based on the special points at the current time, it can accurately predict the special points in the new environment, randomly generate other individuals, increase the population diversity, and thus improve the convergence speed and convergence accuracy of the algorithm in the new environment. Attached Figure Description

[0028] Figure 1 This is a flowchart of the steps of a dynamic multi-objective evolutionary method based on transfer learning and special point strategy according to the present invention;

[0029] Figure 2 This is a flowchart illustrating the steps of obtaining the specific point at the next moment in one embodiment of the present invention;

[0030] Figure 3 This is a special point in a two-dimensional target space according to the present invention;

[0031] Figure 4 This invention relates to FDA4 and FDA5 under a C1 parameter setting. iso Trend chart of IGD, the algorithm's reverse generation distance evaluation index;

[0032] Figure 5 This invention relates to a C1 parameter setting for dMOP2. iso With dMOP2 dec A comparison chart of the actual frontier and the acquired frontier. Detailed Implementation

[0033] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0034] Example 1

[0035] Reference Figure 1 The diagram illustrates a flowchart of a dynamic multi-objective evolutionary method based on transfer learning and special point strategies according to the present invention, which may specifically include the following steps:

[0036] Step S101: Analyze the dynamic multi-objective optimization scenario and obtain the initial population of the optimization scenario. The initial population includes the dynamic objective, decision variables, and constraints.

[0037] When analyzing dynamic multi-objective scenarios, such as dynamic path planning, the optimization objectives in the planning scheme generally need to consider the shortest distance, the shortest time, and good road conditions. However, during the vehicle's journey, decision variables that affect the optimization objectives, such as traffic accidents and traffic control, occur randomly. This requires the optimization algorithm to adjust the optimization results based on real-time information and perform dynamic online optimization to achieve the optimal driving route.

[0038] Dynamic multi-objective optimization problems are prevalent in various fields, and ultimately, these problems can all be abstracted into the following mathematical model, taking minimization as an example:

[0039]

[0040] sta i ≤x i ≤b i

[0041] Where F(x,t) is the objective function, t∈[t0,t... s [x] represents the time variable, x = (x1, x2, ..., xn) n )∈R n Let a be an n-dimensional decision variable. i b i Let x be the upper and lower limits of the decision variable x in the i-th dimension, where i = 1, 2, ..., n.

[0042] Step S102: Optimize the initial population using a multi-objective estimation distribution method to obtain the front-end optimization set of the initial population;

[0043] The initial population is optimized using a rule-based multi-objective estimation distribution algorithm (RM-MEDA) to obtain the front-end optimization set of the initial population; the front-end optimization set obtained in this embodiment of the invention includes, but is not limited to, the RE-MEDA algorithm.

[0044] Step S1021: Extract information from the initial population to construct a probability model;

[0045] Obtain individuals from the initial population, randomly select K individuals, and generate K multidimensional spaces based on these individuals;

[0046] The initial population is clustered into K subpopulations; convergence is performed based on the mean and covariance of the subpopulation point sets to obtain the probability model;

[0047] Step S1022: Perform Gaussian sampling on the probability model to obtain the solution set;

[0048] Gaussian sampling is the only way for the RM-MEDA algorithm to generate new individuals. Its advantages include rotation invariance, translation invariance, linear invariance, and scale transformation invariance, which gives it a great advantage in solving complex variable correlations.

[0049] Step 1023: Perform a selection operation on the initial population and the solution set to obtain the front-end optimization set of the initial population.

[0050] The selection operation in this embodiment of the invention is a non-dominated sorting selection operation, which includes two calculation processes: constructing a partially ordered set and calculating the cluster distance.

[0051] Constructing the partially ordered set involves dividing the initial population and the solution set into disjoint Pareto fronts based on the dominance relationships between individuals. The clustering distances of the individuals are calculated, and high-performing individuals with low clustering density are retained for the next generation. These high-performing individuals with low clustering density constitute the front optimization set of the initial population. The clustering distance of an individual is obtained by summing the distance differences between its two neighboring individuals at each sub-objective.

[0052] Step S103: Obtain special points based on the front-end optimization set;

[0053] The special points include boundary points and inflection points; for the minimization problem, the boundary point refers to the minimum value in each dimension of the target space, and the number of boundary points is equal to the dimension of the target space.

[0054] Taking a two-dimensional target space as an example, special points such as Figure 3As shown, assuming the obtained boundary points are A and B, the straight line they form is L. The perpendicular lines from other points to line L represent distances, and the point with the greatest distance to line L is the inflection point. The mathematical expression for line L is shown in Formula 1 below:

[0055] Formula 1: ax + by + c = 0

[0056] The distance from a point (x, y) to a line is expressed by Formula 2:

[0057] Formula 2:

[0058] Step S104: When the decision variable changes, the special point is mapped to a high-dimensional space based on joint distribution adaptation transfer learning to obtain the special point at the next time step.

[0059] When the decision variables in the initial race change, for example, when a traffic accident occurs during vehicle travel, the decision variables change, and the dynamic objectives, such as the shortest distance, the shortest time, and good road conditions, need to be re-estimated.

[0060] Joint distribution adaptation (JDA) is used to jointly adapt the marginal and conditional distributions of source and target data during dimensionality reduction. The source data refers to the special points, which are known data (modeling data with known labels); the target data refers to the special points at the next time step, which are unknown data to be tested. Furthermore, the marginal distributions and conditional distributions of the source and target data are different.

[0061] Preferably, in the implementation of the present invention, reference is made to Figure 2 The flowchart illustrating the steps of obtaining the special point at the next moment according to an embodiment of the present invention includes:

[0062] Step S1041: Obtain the special points of the initial population as source data, and the special points at the next moment as target data;

[0063] Step S1042: Using principal component analysis, a high-dimensional space is obtained based on the source data and the target data, and a first optimization objective is established;

[0064] Principal component analysis (PCA) obtains a novel feature representation by minimizing the reconstruction error of the input data. The learning objective of PCA is to obtain an orthogonal transformation matrix A that maximizes the variance of the embedded data, which can be represented by the first optimization objective:

[0065] Formula 3:

[0066] Where X = [x1,…,xn]∈Rm×n is the source data matrix; It is the center matrix, n is the sum of the number of samples of the source data ns and the target data nt, l is an n×n matrix of all 1s, XHXT covariance matrix is ​​calculated, and tr(·) represents the trace of the matrix.

[0067] The optimal problem can be calculated by performing eigenvalue decomposition on XHXTA=AΦ, where Φ=diag(φ1,…,φk)∈Rk×k are the k largest features, and their k-dimensional feature representation can be obtained by Z=[z1,…,zn]=ATX.

[0068] Step S1043: Using the maximum difference as a distance metric for the different distributions of the source data and the target data, constructing an edge distribution fit through a first optimization objective, and obtaining a second optimization objective;

[0069] The dimensionality reduction achieved by PCA did not eliminate the distributional differences between the source data and the target data. To reduce the distributional differences between the source data Ps(X(s)) and the target data Pt(X(t)), the maximum mean discrepancy (MMD) is used as a distance metric to calculate the distance between the k-dimensional embedded data samples of the source data and the target data. The MMD distance is expressed as:

[0070] Formula 4:

[0071] Introducing the kernel method, we simplify Formula 4 to obtain Formula 5, the second optimization objective.

[0072] Formula 5: (D s D t ) = tr(A T XM0X T A) (5)

[0073] By minimizing equation (4), the marginal distribution between the domains of equation (3) is maximized in the new representation Z = A. T X is brought closer, where A is the transformation matrix, X is the data after merging the source and target domains, and M0 is the MMD matrix.

[0074] Formula 6:

[0075] Step S1044: Build a model based on the source data, construct pseudo-labels corresponding to the target data, construct conditional distribution adaptation based on the pseudo-labels and the first optimization objective, and obtain the third optimization objective.

[0076] Reducing the marginal distribution between the source data and the target data does not guarantee a reduction in the difference in conditional distribution between them. The source data minimizes the conditional distribution Q. s (y s |x s ) and the target data minimized conditional distribution Q t (y t |x t The differences between these factors are crucial for distribution adaptation.

[0077] The target data is unknown test data, unlabeled data, i.e., Q. t (y t |x t (It cannot be directly modeled. Based on the concept of sufficient statistics in statistics, Q is used.) t (x t |y t To approximate Q t (y t |x t The base classifier trained on the labeled source data is then applied to the unlabeled target data to obtain pseudo-target labels. This process is iterated to improve the accuracy of the pseudo-labels. The MMD distance between classes is the third optimization objective, as shown in Formula 7.

[0078] Formula 7:

[0079] Where M c As shown in Formula 8:

[0080] Formula 8:

[0081] Step S1045: After merging the second optimization objective and the third optimization objective, merge them with the first optimization objective to obtain the final optimization objective;

[0082] Combining Equations 4 and 7, we obtain the optimization objective for joint distribution fitting as Equation 9.

[0083] Formula 9:

[0084] in It is a regularization term that ensures the optimization problem is clearly defined.

[0085] The optimization objective formula 9 for joint distribution adaptation and the first optimization objective formula 3 for principal component analysis are combined, and the optimization objective is unified into formula 10.

[0086] Formula 10:

[0087] Based on Rayleigh quotient, Equation 10 is transformed into Equation 11.

[0088] Formula 11:

[0089] Using the Lagrange method, Equation 11 is transformed into Equation 12, yielding the final optimization objective.

[0090] Formula 12:

[0091] Step S1046: Converge the final optimization objective to obtain the best fit matrix between the source data and the target data;

[0092] The steps for converging the final optimization objective are as follows:

[0093] To solve the eigenvalue decomposition problem described in Equation 12, select the k smallest eigenvectors to construct the fitness matrix A, where Z = A T X;

[0094] based on Train a standard classifier f to update pseudo-labels

[0095]

[0096] Construct the MMD matrix according to Formula 8. Continue until convergence, and obtain the optimal fit matrix.

[0097] Step S1047: Based on the optimal fit matrix and the special point, obtain the special point at the next moment.

[0098] Based on the specific points mentioned in the next time step, the initial population for the next time step is generated.

[0099] Step S105: Use the minimum value among the special points at the next time step as the lower limit and the maximum value among the special points at the next time step as the upper limit to generate the initial population at the next time step.

[0100] Step S106: Use a multi-objective estimation distribution method to optimize the initial population at the next time step, and obtain the front-end optimization set of the initial population at the next time step.

[0101] The special points for the next time step are obtained using a strategy based on transfer learning and special points. Other individuals are obtained through random initialization. These two parts constitute the initial population for the next time step. The implementation process is as follows:

[0102] 1. Based on the leading edge F at time t t (·) and the test function F at time t+1 t+1 (·), randomly generate two sets of solutions Xs and Y t ;

[0103] 2. Calculate the objective function value F t (X s )and F t+1 (Y t These are used as training samples for the source and target domains, respectively.

[0104] 3. Obtain the fitness matrix A according to Formula 12;

[0105] 4. For each point p in the special set of points, do

[0106] k p ←[k(F t (X s (1)), p), ..., k(F) t+1 (Y t (n t )), p)] T

[0107] φ p ←W T k p

[0108] The mapping solution φ p The set PLS is defined as PLS = PLS ∪ {φ(p)};

[0109] end

[0110] 5. For each individual in PLS, l do

[0111] The interior-point method is used to find the individual closest to *l* in the mapping space as the solution for the next time step.

[0112]

[0113] end

[0114] 6. Using the obtained special points as upper and lower bounds, randomly generate other individuals, i.e., x. r =Min + r*(Max - Min);

[0115] 7. The initial population Pop-init at the next time step consists of the individuals obtained in steps 5 and 6, i.e., Pop-init = {x} ∪ {x} r}

[0116] Since the embodiments of this invention focus on general dynamic multi-objective optimization problems, the superiority of the algorithm is illustrated using internationally accepted test functions. The specific expression of the test function is shown in Table 5. In the table, PF and PS represent the Pareto front (PF) and the Pareto solution set (PS), respectively.

[0117] Table 5 Test Functions

[0118]

[0119]

[0120]

[0121] The closer the mapped population is to the true Pareto front in environment t, the faster the algorithm can converge to the true Pareto front.

[0122] To fully demonstrate the effectiveness of the algorithm, we analyzed it under three different environmental settings. The algorithm environment settings parameters used in this embodiment are shown in Table 6:

[0123] Table 6 Algorithm Parameter Settings

[0124]

[0125] To quantitatively analyze the convergence and distribution of the algorithm, two important indicators, dynamic reverse generation distance is used as the evaluation criterion, as shown in the following expression:

[0126]

[0127]

[0128]

[0129] Among them, P t* For the real Pareto frontier at time t, P t Let d(v,P) be the approximate Pareto front obtained by the algorithm at time t. t ) represents the point v on the true Pareto front and the closest approximation of the Pareto front.

[0130] Small European distance.

[0131] During 120 environmental changes under parameter C1 settings, test functions FDA4 and FDA5 were tested. iso The trend of the Inverse Generation Distance (IGD) index is shown in the figure. Figure 4 As can be seen from the figure, as environmental factors change, IGD fluctuates within a small range and tends to stabilize.

[0132] Figure 5 Give dMOP2 iso At environmental conditions t = 80, 90, 100, 105, 110 and dMOP2 dec The graph compares the true Pareto front and the approximate front obtained by the algorithm at t = 6, 11, and 20. The blue part represents the true Pareto front, and the red part represents the approximate Pareto front. It is clear from the graph that the approximate front almost coincides with the true front, indicating that the algorithm of this patent can achieve high convergence accuracy.

[0133] To quantitatively demonstrate the superiority of this patented algorithm, Table 7 presents the average back-generation distance evaluation index (MIGD) values ​​for different objective functions under three environmental settings. In each environment, the algorithm underwent 120 environmental changes. This patent divides these 120 environmental changes into three stages: stages 1-40 (stage 1), 41-80 (stage 2), and 81-120 (stage 3). The table clearly shows that the average MIGD values ​​obtained by the patented algorithm are very small, and the differences between each stage are minimal, indicating that the patented algorithm has high convergence accuracy and wide distribution, as well as high stability.

[0134] Table 7. MIGD values ​​for different objective functions under three different environments.

[0135]

[0136]

[0137] The present invention is based on a method using transfer learning and special point strategy. It assumes that the population at different times follows related but different conditional distributions and probability distributions. It introduces a transfer learning method based on joint distribution adaptation. Based on the special points of the Pareto solution set at the current time, it can accurately predict the special points of the Pareto solution set in the new environment, randomly generate other individuals, increase population diversity, and thus improve the convergence speed and convergence accuracy of the algorithm in the new environment.

[0138] It should be noted that, for the sake of simplicity, the method embodiments are all described as a series of actions. However, those skilled in the art should understand that the embodiments of the present invention are not limited to the described order of actions, because according to the embodiments of the present invention, some steps can be performed in other orders or simultaneously. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions involved are not necessarily essential to the embodiments of the present invention.

[0139] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0140] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, apparatus, or computer program products. Therefore, embodiments of the present invention can take the form of entirely hardware embodiments, entirely software embodiments, or embodiments combining software and hardware aspects. Furthermore, embodiments of the present invention can take the form of computer program products implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0141] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, terminal devices (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing terminal device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing terminal device, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0142] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing terminal device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0143] These computer program instructions can also be loaded onto a computer or other programmable data processing terminal equipment, causing a series of operational steps to be performed on the computer or other programmable terminal equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable terminal equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0144] Although preferred embodiments of the present invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the present invention.

[0145] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal device that includes said element.

[0146] The present invention provides a detailed description of a monthly centralized bidding mechanism solution based on a co-evolutionary algorithm. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A dynamic multi-objective evolutionary method based on transfer learning and special point strategy, applied to dynamic path planning, characterized in that, include: It is applied to vehicle path dynamic planning, analyzes dynamic multi-objective optimization scenarios, and obtains an initial population of the optimization scenario. The initial population includes dynamic objectives, decision variables, and constraints. The dynamic objectives include shortest distance, shortest time, and good road conditions. The decision variables include traffic accidents and traffic control. The initial population is optimized using a multi-objective estimation distribution method to obtain the front-end optimization set of the initial population; Special points are obtained based on the front-end optimization set; these special points include boundary points and inflection points; for minimization problems, boundary points refer to the minimum value in each dimension of the target space, and the number of boundary points is equal to the dimension of the target space; the point with the largest straight-line distance to the boundary points is the inflection point. When the decision variables in the initial population change, i.e., when a traffic accident occurs during the vehicle's movement, the dynamic target needs to be re-estimated. Based on the transfer learning method of joint distribution adaptation, the special points are mapped to a high-dimensional space to obtain the special points at the next time step. The transfer learning method based on joint distribution adaptation maps the special points to a high-dimensional space to obtain the special points at the next time step, including the following steps: The special points of the initial population are obtained as source data, and the special points at the next time step are obtained as target data; Principal component analysis is used to obtain a high-dimensional space based on the source data and the target data, and a first optimization objective is established. Using the maximum difference as a distance metric to measure the different distributions of the source data and the target data, an edge distribution fit is constructed to obtain a second optimization objective. A model is built based on the source data, and pseudo-labels corresponding to the target data are constructed. Based on the pseudo-labels, a conditional distribution adaptation is constructed to obtain the third optimization target. By combining the first optimization objective, the second optimization objective, and the third optimization objective, the final optimization objective is obtained. The final optimization objective is converged to obtain the best fit matrix between the source data and the target data; Based on the optimal fit matrix and the special point, the special point at the next time step is obtained; The minimum value among the special points at the next time step is used as the lower limit, and the maximum value among the special points at the next time step is used as the upper limit to generate the initial population at the next time step. A multi-objective estimation distribution method is used to optimize the initial population at the next time step, and the front-end optimization set of the initial population at the next time step is obtained. Dynamic online optimization is then performed to optimize the driving route.

2. The method according to claim 1, characterized in that, The step of optimizing the initial population using a multi-objective estimation distribution method to obtain the front-end optimization set of the initial population includes: Extract information from the initial population to construct a probability model; Gaussian sampling is performed on the probability model to obtain the solution set; A selection operation is performed on the initial population and the solution set to obtain the front-end optimization set of the initial population.

Images