Dynamic multi-objective optimization method and device based on CITI

Abstract

The invention provides a dynamic multi-objective optimization method and device based on CITI, and relates to the technical field of artificial intelligence. The method comprises the following steps: randomly generating an initial population for a dynamic multi-objective optimization problem, and optimizing the initial population by adopting a basis algorithm; detecting whether the environment is changed or not by adopting a population evaluation mechanism; and for the change, an initial population of a new environment is generated by adopting a dynamic multi-objective optimization algorithm CITI of a migration and interpolation strategy driven by cluster individual change, and then a control strategy is obtained. The sub-populations divided based on the individual change characteristics are more beneficial to strengthening the search task of the individuals in the cluster, so that other individuals are better guided to evolve towards a new environment. The NNI interpolation strategy can utilize adjacent point information to approximately fit geometric features of a new environment PF to improve the distributivity. Learning excellent non-dominated solutions of different historical populations helps to enhance the reliability of knowledge migration and make DMOA applicable to different types of changes.

Description

Technical Field

[0001] The present invention relates to the field of artificial intelligence technology, and particularly to a dynamic multi-objective optimization method and device based on CITI. Background Art

[0002] The dynamic multi-objective optimization problem is a special type of multi-objective optimization problem. It not only has multiple conflicting objectives, but also its decision variables, constraint conditions, and objective functions change with the environment. Such problems are very common in practical applications, for example, factory layout, path optimization, planning problems, and production scheduling.

[0003] DMOPs (Dynamic Multiobjective Optimization Problems) are extremely challenging to solve due to the uncertainty of their internal systems. General static multi-objective optimization algorithms are difficult to quickly respond to environmental changes and thus difficult to timely track the dynamic PF (Pareto Frontier). In response, some scholars re-evolve the initial population for each new environment to improve the algorithm's response ability. The prediction-based method is one of the most popular research methods in DMOAs (Dynamic Multiobjective Optimization Algorithms). It predicts the initial population of the new environment based on the historical PS (Pareto Set) or PF movement trajectory. This method has stronger robustness than the diversity method and the memory method when solving different types of dynamic multi-objective optimization problems. Initially, scholars established a single linear prediction model related to time series for the centroid of the historical population, individual sequence, or some key points to obtain the initial population. However, when facing complex non-linear changing objective functions, these methods cannot evolve individuals in a promising direction, so they often result in a large deviation between the obtained PF and the actual PF.

[0004] Currently, the research focus of prediction-based dynamic multi-objective optimization algorithms is more on non-linear prediction mechanisms. They use a variety of linear strategies, machine learning methods, or transfer learning methods in combination to explore the complex relationships of environmental changes. Among them, the clustering-based prediction method is a relatively common non-linear prediction algorithm. This type of method uses the clustering idea in machine learning to divide the population into multiple clusters, and uses the individual knowledge in the clusters of similar environments to predict each region of the new environmental population. Therefore, they refine the local search tasks of individuals, which can promote the evolution of potential individuals in promising directions. In recent years, numerous clustering-based response strategies have been proposed. For example, Yan et al. proposed a manifold-based prediction method, which divides the population into multiple local manifolds through principal component analysis. Subsequently, in two adjacent environments, the local manifolds that are closer to each other obtain new initial individuals through the centroid prediction method. Xu et al. proposed a prediction method based on population center prediction and induced mutation. This algorithm first uses Kmeans to cluster the population and uses the cluster centers to guide the movement of individuals within the clusters. Secondly, it generates an exploration population and mutates the promising non-dominated individuals based on the PF results. Li et al. combined the clustering method with the transfer method. It uses the analytic hierarchy process to divide the population and trains the excellent individuals within the clusters through some weak classifiers. Subsequently, this algorithm integrates a strong classifier according to the training error through TrAdaboost to predict good solutions from a large number of initial solutions. However, the existing clustering-based prediction strategies still have the following deficiencies:

[0005] Existing methods cluster the population by considering the neighboring positions of individuals in the decision space or the transformation subspace. However, due to the dynamic changes of PF, this may cause individuals with different types of change characteristics to be divided into the same cluster, resulting in the obtained cluster information not being highly representative.

[0006] The algorithms usually assume that individuals in different clusters have similar evolutionary trends, and they use the same prediction methods for individuals in each cluster, such as prediction based on the population centroid, linear prediction, etc. However, this convergent search method cannot enable individuals in various clusters to accurately explore each region of the PS and is prone to falling into local optima.

[0007] For complex-changing DMOPs, the initial population based only on sub-population prediction is difficult to achieve a balanced distribution and convergence in the objective space due to the limitations of the prediction direction. Summary of the Invention

[0008] To solve the technical problem that most of the control strategies of the existing control systems cluster the population according to the static positions of individuals in a certain space and adopt the same prediction mechanism for each sub-population. However, with the dynamic changes of the environment, this static division method may lead to individuals with different change characteristics being divided into the same cluster. At the same time, the same evolution trend of each cluster makes the individuals within the cluster prone to convergence and seriously hinders the prediction performance of the algorithm, the embodiments of the present invention provide a dynamic multi-objective optimization method and device based on CITI. The technical solutions are as follows:

[0009] On the one hand, a dynamic multi-objective optimization method based on CITI is provided. This method is implemented by a dynamic multi-objective optimization device, and the method includes:

[0010] S1. Construct a dynamic multi-objective optimization problem for the control system.

[0011] S2. For the dynamic multi-objective optimization problem, randomly generate an initial population, and use the base algorithm to optimize the initial population to obtain the optimized initial population.

[0012] S3. Use the evaluation mechanism of the population to detect whether the environment has changed.

[0013] If the environment has changed, use the dynamic multi-objective optimization algorithm CITI with a migration and interpolation strategy driven by the change of clustered individuals to generate the initial population of the new environment, and then obtain the control strategy.

[0014] If the environment has not changed, use the base algorithm to optimize the population, and then obtain the control strategy.

[0015] S4. Complete the control task according to the control strategy.

[0016] Optionally, the dynamic multi-objective optimization algorithm CITI with a migration and interpolation strategy driven by the change of clustered individuals includes: a prediction strategy CIF guided by the change trend of the objectives of clustered individuals, a nearest neighbor interpolation method NNI, and a prediction strategy DDA for dual-source domain adaptation.

[0017] Generating the initial population of the new environment by using the dynamic multi-objective optimization algorithm CITI with a migration and interpolation strategy driven by the change of clustered individuals in S3 includes:

[0018] S31. Use the prediction strategy CIF guided by the change trend of the objectives of clustered individuals to predict new individuals and generate a new initial population X CIF .

[0019] S32. According to the new initial population X CIF and the nearest neighbor interpolation method NNI, generate a new initial population X NNI .

[0020] S33. Generate a new initial population X CIF according to the new initial population X DDA and the dual-source domain adaptation prediction strategy DDA.

[0021] S34. Select using the environmental selection mechanism of NSGA-II based on the new initial population X CIF , the new initial population X NNI and the new initial population X DDA to obtain the initial population of the new environment.

[0022] Optionally, predicting new individuals using the prediction strategy CIF guided by the change trend of clustering individual objectives in S31 to generate a new initial population X CIF includes:

[0023] S311. Obtain the populations POS t and POS t-1 of the first two environments, and remove the duplicate individuals in the population POS t and the population POS t-1 respectively.

[0024] S312. Compare the sizes of the two populations after removing duplicate individuals, and find the corresponding non-dominated solutions from the population with a smaller size for each non-dominated solution in the population with a larger size based on the Euclidean distance to form sample pairs.

[0025] S313. Calculate the Euclidean distance ED i and the angular distance AD i of the sample pairs, and construct the feature matrix of each individual according to the Euclidean distance ED i and the angular distance AD i .

[0026] S314. Cluster the feature matrix using the Kmeans method.

[0027] S315. Divide the subpopulations according to the clustering results, and calculate the cluster center C i = [mED i , mAD i (i = 1, 2, 3) for each subpopulation, and construct the cluster center matrix C according to the cluster centers of all subpopulations.

[0028] S316. Remove the duplicate individuals in the subpopulations.

[0029] S317. Design a prediction mechanism based on the cluster center matrix, and predict new individuals according to the subpopulations after removing duplicate individuals and the prediction mechanism to form the population P1.

[0030] S318. Perform non - dominated sorting on the new individuals in population P1, and save the non - dominated individuals to the new initial population X CIF .

[0031] S319. Determine whether the number of non - dominated solutions in population P1 is less than the preset threshold; if so, select N / 2 individuals from the dominated individuals for update according to the rank of non - dominated sorting and the crowding distance, and perform non - dominated sorting on the updated individuals and the individuals in the new initial population X CIF and put the non - dominated individuals into the new initial population X CIF .

[0032] Optionally, the prediction mechanism includes:

[0033] When the parameters mED i and mAD i of the cluster center of the sub - population are both the minimum values of each column in the cluster center matrix C, predict the new individual using the following formula (1):

[0034]

[0035] In the formula, represents the new individual, represents the individual at time t in the i - th cluster, represents the centroid of, represents the set composed of all solutions of the sub - population subp i in the i - th cluster at time t, represents the centroid of, represents the set composed of all solutions of the sub - population subp i in the i - th cluster at time y - 1, N(0,σ 2 ) represents a random number subject to a normal distribution with a mean of 0 and a variance of σ 2 .

[0036] When the parameter mED i of the cluster center of the sub - population is the second - minimum value of the first column in the cluster center matrix C or mAD i is the second - minimum value of the second column in C, and mAD i is the minimum value of the second column in C or mED i is the second - minimum value of the first column in C, and, mAD i is the maximum value of the second column in C and mED i is the minimum or second - minimum value of the first column in C, predict the new individual using the following formulas (2)(3):

[0037]

[0038] Wherein, α represents the crossover coefficient, represents the individual in the population at time t - 1 that has the nearest Euclidean distance to, r represents a random number between [0, 1], and n t represents the change intensity of the environment, and τ t represents the change frequency of the environment, and β represents the mutation coefficient.

[0039] When the parameter mED of the cluster center of the sub - population i is the maximum value of the first column in the cluster center matrix C, the new individual is predicted using the following formula (4):

[0040]

[0041] Wherein, part represents sampling L promising small regions at intervals of part for each non - dominated solution at time y within the cluster.

[0042] Optionally, generating a new initial population X CIF according to the new initial population X NNI and the nearest - neighbor interpolation method NNI includes:

[0043] S321. Generating a target vector f CIF for each individual in the new initial population X i , and the target vectors of all individuals form F CIF ; the number of targets is m.

[0044] S322. Quantifying the target vector f i to obtain the quantified target vector f i '.

[0045] S323. Calculating the cosine distance disf ij between two target points.

[0046] S324. For a 2 - target problem when disf ij < 10 -10 and for a 3 - target problem when disf ij < 10 -4 , removing the duplicate target points f i '.

[0047] S325. For the removed target points, calculating the adjacent points of each target point in the quadrants from Q2 to .

[0048] S326. Determining the interpolation region according to the cosine distance between the target points and the adjacent points.

[0049] S327. Determine the number of target points to be inserted according to the cosine distance between the target point and the adjacent points.

[0050] S328. Determine whether there are other neighbor points of the target points after culling except the end points.

[0051] If so, insert new target points.

[0052] If not, update the vector and insert new target points.

[0053] S329. Update the boundary points, establish a linear inverse inference model, and map the new target points to the decision space according to the linear inverse inference model to obtain the new initial population X NNI .

[0054] Optionally, determine the area to be interpolated according to the cosine distance between the target point and the adjacent points through the following formula (5):

[0055]

[0056] In the formula, disf i,k represents the cosine distance between the target point and the adjacent points.

[0057] Determine the number of target points to be inserted according to the cosine distance between the target point and the adjacent points through the following formula (6):

[0058]

[0059] In the formula, Num represents the number of target points to be inserted.

[0060] Insert new target points through the following formula (7):

[0061]

[0062] In the formula, f new represents the new target point, f i represents the target end point of the i-th area to be inserted, f j represents the other target end point of the i-th area to be inserted, λ represents the equal division coefficient, used to determine the concave-convex position of the target point, represents the cross product enhancement term.

[0063] Optionally, in S33, according to the new initial population X CIF and the dual-source domain adaptive prediction strategy DDA, generate the new initial population X DDA , including:

[0064] S331. Use the new initial population X CIF as the target domain D T .

[0065] S332. Determine whether the number of environmental changes is greater than or equal to 3.

[0066] If it is equal to 3, then select N T = min(|POS1|, |POS2|) individuals from population POS1 and population POS2 respectively according to the crowding distance to obtain the dual-source domain D Si (i = 1, 2).

[0067] If it is greater than 3, then calculate the centroid of the historical environmental population and the centroid of the target domain of the Euclidean distance; select two populations POS n1 and POS n2 from the historical environmental population according to the Euclidean distance, and select N n1 and population POS n2 from population POS T = min(|POS n1 |, |POS n2 |) individuals to obtain the dual-source domain D Si (i = 1, 2).

[0068] S333. Migrate the individuals in the dual-source domain D Si to the target domain D Ti to obtain the new initial population X DDA .

[0069] On the other hand, a dynamic multi-objective optimization device based on CITI is provided. This device is applied to the dynamic multi-objective optimization method based on CITI. The device includes:

[0070] A construction module for constructing the dynamic multi-objective optimization problem of the control system.

[0071] An optimization module for randomly generating an initial population for the dynamic multi-objective optimization problem and optimizing the initial population using a base algorithm to obtain the optimized initial population.

[0072] A generation module for detecting whether the environment has changed by using the evaluation mechanism of the population.

[0073] If the environment has changed, then use the dynamic multi-objective optimization algorithm CITI with the migration and interpolation strategy driven by the change of clustered individuals to generate the initial population of the new environment, and then obtain the control strategy.

[0074] If the environment has not changed, then optimize the population using the base algorithm to obtain the control strategy.

[0075] A control module for completing the control task according to the control strategy.

[0076] On the other hand, a dynamic multi-objective optimization device is provided. The dynamic multi-objective optimization device includes: a processor; a memory storing computer-readable instructions, which, when executed by the processor, implement any one of the above-mentioned dynamic multi-objective optimization methods based on CITI.

[0077] On the other hand, a computer-readable storage medium is provided. At least one instruction is stored in the storage medium, and the at least one instruction is loaded and executed by a processor to implement any one of the above-mentioned dynamic multi-objective optimization methods based on CITI.

[0078] The beneficial effects brought by the technical solutions provided in the embodiments of the present invention at least include:

[0079] In the present invention, a dynamic multi-objective optimization algorithm with a migration and interpolation strategy driven by clustering individual changes is proposed. Specifically, first, a prediction strategy guided by the target change trend of clustering individuals is proposed to enhance the prediction accuracy of subpopulations and guide other individuals to evolve in a promising direction. This strategy divides into different clusters according to the target change distance of similar individuals in adjacent environments and the angular deviation from the center as change features. According to the nature of individuals within the cluster, different prediction mechanisms are adopted to obtain new initial solutions. Secondly, a nearest neighbor interpolation method is designed to improve the distribution of the Pareto front. It interpolates some new objective points in the sparse region of the current Pareto front based on the maximum distance between reference vectors and adjacent objective point information. In addition, to promote the algorithm to be applicable to solving various types of changing DMOPs, a dual-source domain adaptive prediction strategy is proposed, which performs knowledge migration on the two historical environments most similar to the new environment based on multi-source domain transfer learning and integrates them into new initial solutions according to the contribution degree of the environments. The proposed algorithm is compared with 6 popular algorithms on the CEC2018 suite. The experimental results demonstrate the excellent optimization performance of the proposed algorithm. In addition, the proposed algorithm has good engineering applicability in the automotive speed control task. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0081] Figure 1 is a flowchart of a dynamic multi-objective optimization method based on CITI provided by an embodiment of the present invention;

[0082] Figure 2 is a CITI algorithm diagram provided by an embodiment of the present invention;

[0083] Figure 3 It is the execution flowchart of CITI based on the base algorithm (MOEA / D algorithm) provided by the embodiments of the present invention;

[0084] Figure 4 It is a schematic diagram of the process of dividing subpopulations based on individual change characteristics provided by the embodiments of the present invention (only the clustering results of 1 subpopulation are shown in the figure);

[0085] Figure 5 It is the CIF algorithm diagram provided by the embodiments of the present invention;

[0086] Figure 6 It is the NNI algorithm diagram provided by the embodiments of the present invention;

[0087] Figure 7 It is to find the target point f in the DMOP with 2 objectives provided by the embodiments of the present invention i Schematic diagram of adjacent target points;

[0088] Figure 8 It is the schematic diagram of the interpolation position provided by the embodiments of the present invention;

[0089] Figure 9 It is the DDA algorithm diagram provided by the embodiments of the present invention;

[0090] Figure 10 It is the unit step function curve diagram of CITI and 3 comparison algorithms PID systems in the case of t = 16 provided by the embodiments of the present invention;

[0091] Figure 11 It is the block diagram of a dynamic multi-objective optimization device based on CITI provided by the embodiments of the present invention;

[0092] Figure 12 It is the structural schematic diagram of a dynamic multi-objective optimization device provided by the embodiments of the present invention. Detailed implementation manners

[0093] The technical solutions in the present invention will be described below with reference to the accompanying drawings.

[0094] In the embodiments of the present invention, words such as "exemplarily" and "for example" are used to represent examples, illustrations or explanations. Any embodiment or design solution described as "example" in the present invention should not be construed as more preferred or more advantageous than other embodiments or design solutions. Exactly speaking, the use of the word "example" aims to present concepts in a specific way. In addition, in the embodiments of the present invention, the meaning expressed by "and / or" can be both, or either of the two can be selected.

[0095] In the embodiments of the present invention, "image" and "picture" can sometimes be used interchangeably. It should be noted that when the difference is not emphasized, their intended meanings are the same. "Of", "corresponding", and "corresponding to" can sometimes be used interchangeably. It should be noted that when the difference is not emphasized, their intended meanings are the same.

[0096] In the embodiments of the present invention, sometimes a subscript such as W1 may be written in a non-subscript form such as W1. When the difference is not emphasized, their intended meanings are the same.

[0097] To make the technical problems, technical solutions, and advantages to be solved by the present invention clearer, the following will be described in detail with reference to the accompanying drawings and specific embodiments.

[0098] The embodiments of the present invention provide a dynamic multi-objective optimization method based on CITI. This method can be implemented by a dynamic multi-objective optimization device, which can be a terminal or a server. As Figure 1 shown in the flowchart of the dynamic multi-objective optimization method based on CITI, the processing flow of this method can include the following steps:

[0099] S1. Construct the dynamic multi-objective optimization problem of the control system.

[0100] S2. For the dynamic multi-objective optimization problem, randomly generate an initial population, and use the base algorithm to optimize the initial population to obtain the optimized initial population.

[0101] S3. Use the evaluation mechanism of the population to detect whether the environment has changed.

[0102] If the environment has changed, then use the dynamic multi-objective optimization algorithm CITI with a migration and interpolation strategy driven by the change of clustered individuals to generate the initial population of the new environment, and then obtain the control strategy.

[0103] If the environment has not changed, then use the base algorithm to optimize the population, and then obtain the control strategy.

[0104] In a feasible implementation, as Figure 2The algorithm shown provides the pseudocode for the CITI execution process, which uses MOEA / D (Multi-objective Evolutionary Algorithm Based on Decomposition) as the basic SMOA (Static Multiobjective Optimization Algorithm). Specifically, the algorithm mainly goes through three processes, namely environment detection, environment response, and static multi-objective optimization. In line 1, N random solutions are generated to initialize the population. Lines 3 - 18 are the main optimization process of the CITI framework and end the operation when the termination condition is met. At the beginning of each iteration, the algorithm uses the evaluation mechanism of the population to detect changes in the environment (line 4). If the environment changes, the CITI prediction response strategy is initiated (lines 5 - 15). Since CITI requires a certain accumulation of historical information, when t ≤ 2, the algorithm only uses random solutions as the initial population InitPop. When t > 2, the initial individuals of the new environment are predicted through the CIF (line 9), NNI (line 10), and DDA (line 11) sub-strategies respectively. Line 12 uses the environmental selection mechanism of NSGA-II to select the best N solutions from the three strategies to form the initial population InitPop of the new environment. When no environmental changes are detected, the MOEA / D algorithm is used to optimize the population (line 16).

[0105] Figure 3 Shows the overall framework of CITI based on the base algorithm (MOEA / D algorithm).

[0106] Optionally, the dynamic multi-objective optimization algorithm CITI driven by the change of clustered individuals includes: the prediction strategy CIF guided by the change trend of clustered individual objectives, the nearest neighbor interpolation method NNI, and the prediction strategy DDA of dual-source domain adaptation.

[0107] The above step S3 may include the following steps S31 - S34:

[0108] S31. Use the prediction strategy CIF guided by the change trend of clustered individual objectives to predict new individuals and generate a new initial population X CIF .

[0109] Optionally, the above step S31 may include the following steps S311 - S319:

[0110] S311. Obtain the populations POS of the previous two environments t and POS t-1 , and respectively for the population POS tand the population POS t-1 Eliminate the duplicate individuals in it.

[0111] In a feasible implementation, the changing characteristics of the CIF clustered similar individuals enable the sub-populations to track the positions of the Pareto front according to their preference trends. Figure 4 Figure shows the schematic of the process of dividing sub-populations based on individual changing characteristics. In most cases, the populations in adjacent environments are the most relevant, and the historical experiences of the first two environments help to accelerate the convergence speed of individuals to the PS (Pareto Set) in the new environment. Therefore, in order to establish the temporal information of the current individuals, the most similar individuals are selected from POS t and POS t-1 from the two populations respectively for pairing. To avoid duplication of sample pairs, the duplicate individuals in POS t and POS t-1 are eliminated respectively before pairing.

[0112] S312. Compare the sizes of the two populations after eliminating duplicate individuals, and for each non-dominated solution in the larger population, find the corresponding non-dominated solution from the smaller population based on the Euclidean distance to form a sample pair.

[0113] In a feasible implementation, assume that the number of non-dominated solutions contained in POS t and POS t-1 are N t and N t-1 respectively. The population with more non-dominated solutions N max(N t , N t-1 ) max will be paired with the individuals in the other population. Specifically, for each non-dominated solution x i in the larger population size, find the non-dominated solution x j with the closest Euclidean distance to it from the other population to form a sample pair pair i =(x i , x j ), such as the two individuals circled by the gray background in Figure 4 .

[0114] S313. Calculate the Euclidean distance ED i and the angular distance AD i of the sample pair, and construct the feature matrix of each individual according to the Euclidean distance ED i and the angular distance AD i .

[0115] In a feasible implementation, the change characteristics of an individual are composed of two distances, namely, the Euclidean distance between similar individuals in the environments at times t and t-1, and the angular distance formed by the difference between these two individuals and the first-order difference of the centroid of the historical environmental population. On the one hand, the change in distance can describe the search range of an individual in different regions of the Pareto front and determine whether the individual is exploring or exploiting. The Euclidean distance of the i-th sample pair is defined as ED i , and it is calculated as follows:

[0116] ED i =||x i -x j ||2 (1)

[0117] On the other hand, the angular distance reflects the most likely evolutionary direction of the changing individual, which can avoid the problem of population convergence. The angular distance AD i of the i-th sample pair is calculated based on the vector difference of the i-th sample pair pair i and the vector difference of the population centroid:

[0118] AD i =1-cos(v,move i ) (2)

[0119] where move i represents the first-order difference between i in pair and ; v is the first-order difference between the population centroid at time t and the population centroid at time t-1. The ED i and AD i features can better reflect the potential search ability of an individual. Combine the two features of all individuals to form a feature matrix X:

[0120]

[0121] S314. Use the Kmeans method to cluster the feature matrix.

[0122] In a feasible implementation, use Kmeans to cluster the feature matrix X into 3 categories. The reason is that 3 categories can appropriately divide the population into high, low, and medium changes. Otherwise, too few or too many clustering numbers are likely to reduce the quality of the sub-population and affect the search task of the sub-population.

[0123] S315. Divide the sub-populations according to the clustering results, and calculate the cluster center C i =[mED i ,mAD i (i=1,2,3) for each sub-population, and construct a cluster center matrix C based on the cluster centers of all sub-populations.

[0124] The cluster centers C of all categories i =[mED i , mAD i (i = 1, 2, 3) are put into a matrix C, which is represented as:

[0125]

[0126] The present invention finds all individuals forming sample pairs according to the change characteristics [ED i1 , AD i2 within each cluster and their indexes on the X matrix, and puts them into the same sub-population subp i (i = 1, 2, 3).

[0127] S316. Remove duplicate individuals in the sub-population.

[0128] In a feasible implementation manner, the duplicate individuals in subp i are removed to ensure the uniqueness of the individuals.

[0129] S317. Design a prediction mechanism based on the cluster center matrix. According to the sub-population after removing duplicate individuals and the prediction mechanism, predict new individuals to form population P1.

[0130] In a feasible implementation manner, the sets formed by all solutions of subp i at times t and t - 1 within the i-th cluster are respectively denoted as and From Figure 4 it can be seen that individuals in different clusters have different change characteristics while the change forms of individuals within a cluster are similar. The ranking situations of each variable in C in each dimension appear a total of 9 kinds. Subsequently, the present invention classifies these 9 kinds of situations into 3 types of change characteristics and designs the following prediction mechanism.

[0131] (1) When mED i and mAD i are both the minimum values of each column in C, it indicates that the change of the sample pair within the cluster is most similar to the overall change of the two environmental populations. As shown in the individual evolution schematic diagram of the green area in Figure 4 , and the vector difference of the centroids can effectively guide the internal individuals in the cluster to track the small change area on POS t+1 . At the same time, also performs Gaussian perturbation to enhance the diversity of solutions. In summary, the prediction mechanism based on the cluster center can be mathematically represented as:

[0132]

[0133] In the formula, represents a new individual, represents the individual within the i-th cluster at time t, represents the centroid of represents the set formed by all solutions of the sub-population subp within the i-th cluster i at time t, represents the centroid of represents the set formed by all solutions of the sub-population subp within the i-th cluster i at time t - 1, N(0, σ 2 ) represents a random number following a normal distribution with a mean of 0 and a variance of σ 2 , and the standard deviation σ is calculated as:

[0134]

[0135] (2) When mED i (or mAD i ) is the second minimum value in the first column (or the second column) of C and mAD i (or mED i ) is the minimum value or the second minimum value in the second column (or the first column) of C; mAD i is the maximum value in the second column of C and mED i is the minimum value or the second minimum value in the first column of C. Figure 4 The blue area in describes the prediction of the sub-population on the situation

[0136] In this type, the change of individuals within the cluster has a relatively obvious difference from the overall change of the two environmental solutions, and using the overall change trend can no longer move the current individuals in a promising direction. Therefore, the individuals combine the information of other optimal individuals to exploit the effective area as much as possible. At the same time, the change distance of the centroid does not show the maximum difference, and in the most serious case, only the degree of deviation in direction is relatively large. It should also be noted that a too large range of search for individuals may slow down the convergence speed of PS. To enable the individuals within the cluster to adaptively track the change of the environment, the present invention uses the change intensity n t and the change frequency τ t to perform crossover and mutation on the non-dominated solutions and of the sample pairs within the cluster. The mathematical expression of the crossover strategy is:

[0137]

[0138] where α represents the crossover coefficient; r represents a random number between [0, 1]. According to different change intensities nt and the change frequency τ t , α can effectively control the generation position of the new solution. The mathematical expression of the mutation strategy is:

[0139]

[0140] where β represents the mutation coefficient, which is used to regulate the search range of individuals.

[0141] (3) When mED i is the maximum value in the first column of C. The characteristic of this type is that the objective values of individuals in the two cluster environments change significantly in different environments. Figure 4 The yellow area described is the situation of the individual evolution on. The individuals within the cluster need to explore more promising regions according to historical information to improve their tracking ability for the new environment PS. Inspired by the guided individual sampling, the present invention proposes an individual exploration method to more comprehensively traverse the promising positions of the new environment. To ensure the extensiveness of the search area, the maximum value of all solutions at time t within the cluster and the minimum value of all solutions at time t - 1 form a search range for the individual evolution within this sub-population. Each non-dominated solution at time t within the cluster samples L promising small regions at intervals of part within this range, and its mathematical expression is:

[0142]

[0143] Too many sampling points not only reduce the algorithm performance but also easily lead to a long running time. Therefore, in the present invention, L is set to:

[0144]

[0145] where represents the number of all non-dominated solutions at time t in the i-th cluster. At the same time, the prediction direction of the individual also depends on the centroid change of the sub-population, which can ensure that the individual converges in the accurate direction. The individual is predicted in this case as:

[0146]

[0147] In the formula, part represents that each non-dominated solution at time t within the cluster samples L promising small regions at intervals of part within the search range.

[0148] Furthermore, the solutions obtained by combining these 3 types are used to form the population P1.

[0149] S318. Perform non-dominated sorting on the new individuals in the population P1, and save the non-dominated individuals to the new initial population XCIF 。

[0150] In a feasible implementation, the individuals in P1 calculate their objective vectors in the new environment for performing non-dominated sorting and rank them as {h1, h2, …, h k}. The solutions of rank h1 can approximate the PS of the new environment.

[0151] S319. Determine whether the number of non-dominated solutions in population P1 is less than a preset threshold; if so, select N / 2 individuals from the dominated individuals for update according to the rank of non-dominated sorting and crowding distance, perform non-dominated sorting on the updated individuals and the individuals in the new initial population X CIF and put the non-dominated individuals into the new initial population X CIF .

[0152] In a feasible implementation, the effectiveness of the individuals in the new environment degrades as the rank decreases. The individuals in the new environment can, to a certain extent, guide other individuals to accurately track the changing PS. Therefore, to provide more information about the new environment for the subsequent two strategies, when the number of non-dominated solutions in P1 is less than a certain value, the potential dominated solutions in P1 also perform local learning from the two non-dominated solutions closest to their objective values. This way can avoid the loss of solution information to a certain extent. To reduce the computational efficiency, the present invention sequentially selects individuals according to the rank and crowding distance after rank h1 to update their current positions, and the corresponding mathematical expression is:

[0153]

[0154] Re-evaluate the objective values of these N / 2 individuals and perform non-dominated sorting with the solutions in the previous rank h1. Finally, store all the non-dominated solutions in the set X CIF . This set can effectively reflect the approximate information of the new environment. Figure 5 The pseudo-code of the CIF strategy is given.

[0155] The present invention proposes a CIF (Subpopulation Prediction Strategy based on Clustering of Individual Features, a prediction strategy guided by the changing trend of individual objectives), which can achieve a balance between exploration and exploitation of the new environment population. It is divided into different clusters based on the distance and angle change characteristics of individuals. Each cluster uses center-based prediction, mutation, and sample point sampling methods according to their search preferences.

[0156] S32. According to the new initial population X CIFAnd the nearest neighbor interpolation method NNI to generate a new initial population X NNI .

[0157] Optionally, the above step S32 may include the following steps S321 - S329:

[0158] S321. Generate a target vector f for each individual in the new initial population X CIF , and the target vectors of all individuals constitute F i ; the number of targets is m. CIF

[0159] In a feasible implementation manner, although the prediction strategy based on sub - populations can obtain partial population information of the new environment, limited by the monotonic search ability of individuals in the decision space, the convergence and distribution of the initial population on the Pareto front are relatively poor. This will slow down the convergence efficiency of the subsequent SMOA and affect the approximation of the final Pareto to the true PF. Therefore, in order to improve the distribution of the PF, the present invention proposes a nearest neighbor interpolation method to supplement the Pareto vacancy positions according to the existing Pareto distribution and guide the subsequent population evolution. Figure 6 The pseudo - code of the NNI strategy is given in

[0160] S322. Quantify the target vector f i to obtain the quantified target vector f i '.

[0161] In a feasible implementation manner, the NNI strategy measures the distribution of the PF based on the angle of the target vector. Taking the minimization problem as an example, to reduce the deviation of the two - target angle caused by the coordinate origin, based on the definition method of the scalarized sub - problem in the MOEA / D algorithm, each target point f i is changed to f i - f idea , where f idea represents the ideal point and f idea = min f i . The transformed target value is denoted as f i '.

[0162] S323. Calculate the cosine distance disf between two target points ij .

[0163] In a feasible implementation manner, the cosine distance disf between the i - th target and the j - th target ij is calculated as:

[0164] disf ij = 1 - cos(f i ', f j ') (13)​

[0165] S324. For the two-objective problem, when disf ij <10 -10 and for the three-objective problem when disf ij <10 -4 , the duplicate target points f i ′ are removed.

[0166] In a feasible implementation, for the two- and three-objective problems, when disf ij <10 -10 and disf ij <10 -4 , the target points in the crowded area are removed.

[0167] S325. For the removed target points, calculate the adjacent points of each target point in quadrant Q2 to quadrant .

[0168] In a feasible implementation, the present invention finds all neighbor points around the target point according to the quadrant relationship of the target space. Figure 7 Shows the process of determining the adjacent target points of the target point f i in the case of DMOP for two objectives. There are 2 m quadrants Q i (i = 1, …, 2 m ) for the m-dimensional objective. Assume that each target point f i is used as the origin of the coordinate system. As Figure 7 shown by the gray shaded part, there cannot be adjacent target points in quadrant Q1 (the values on each objective are greater than f i ) and the quadrant i centrally symmetric to f because the target points do not dominate each other. Therefore, f i only needs to find the target points with the minimum disf m in the remaining 2 ij - 2 quadrants to obtain the neighbor point f i,k , and its mathematical expression is:

[0169]

[0170] The cosine distance between the target point f i and the adjacent point f i,k is denoted as disf i,k . It should be emphasized that when f i is a boundary point, there is no neighbor point in a certain quadrant and the present invention assigns its cosine distance disf i,k to be inf.

[0171] S326. Determine the interpolation region according to the cosine distance between the target point and the adjacent points.

[0172] In a feasible implementation, on the one hand, in order to evenly insert the target points between the existing Pareto fronts, the present invention hopes to find a compromise angle threshold to determine the region to be interpolated. Considering that the decomposed multi-objective optimization method can generate N reference vectors according to the population size. Therefore, based on the larger cosine distance between adjacent reference vectors, the minimum lower limit of target point interpolation is determined. On the other hand, for the DMOP with an interval in the PF, the present invention also sets the maximum upper limit of interpolation to prevent the characteristics of the PF from being damaged during the interpolation process. For 2- and 3-objective DMOPs, the mathematical expression of the interpolation region is:

[0173]

[0174] S327. Determine the number of target points to be inserted according to the cosine distance between the target point and the adjacent points.

[0175] In a feasible implementation, according to the minimum interval of the cosine value, a functional relationship between the existing cosine distance and the lower limit of the cosine distance in formula (19) is established to determine the number of target points to be inserted at this position. Based on various experimental tests in the early stage, it is found that the logarithmic function can better describe the relationship between them. Therefore, the number Num of interpolations between the target point f i and the adjacent point f i,k is set as:

[0176]

[0177] In the formula, Num represents the number of target points to be inserted.

[0178] S328. Determine whether there are other neighbor points of the target points after elimination except the endpoints.

[0179] If so, insert new target points.

[0180] If not, update the vector and insert new target points.

[0181] In a feasible implementation, the new target points are determined according to the target points near them. However, since the two endpoints f i and f i,k of the region to be interpolated may be boundary points or discontinuous points, therefore, the present invention is discussed in the following two cases.

[0182] When f i has neighbor points in 2 or more octants Q i (i = 2,..., 2 m -1). Figure 8Shows a schematic of determining the interpolation positions for 2-objective problems and 3-objective problems. Figure 8 Linearly insert Num points (blue circles) between f i and f i,k by the ratio coefficient λ to equally divide the line segment f i f i,k . Then, find at most 2 i -1 nearest neighboring points f i,k and f m-1 from among the numerous neighboring points of f i,g and f k,g (g ∈ {1, …, 2 m-1 -1}) (excluding f i,k and f i ) to determine the concavity and convexity of the area to be interpolated and increase the smoothness of the Pareto front. Figure 8 , the green vectors and are used to describe the concavity and convexity of the local area. Among them, calculate the average of the vector differences between neighboring points f i,g and f i and regulate this vector through the ratio coefficient λ and the mean of their distance ratio coefficients to form Similarly, the operation of f i,k is the same as that of f i to process and obtain the vector For 2-objective problems, it can be seen that after these two vectors are added to the linear prediction term, they can protect the characteristics of the Pareto front. However, Figure 8 describes that in the 3-objective space, only using the above method to obtain new points are the circles with gray shading. The concavity and convexity it shows have a certain deviation because the complexity of the spatial position relationship increases with the addition of one dimension. Therefore, for 3-objective problems, on the basis of the 2-objective interpolation method, a cross-product enhancement term is added. Figure 8 It is the red vector in is to perform a cross-product operation on and to generate a vector perpendicular to the plane where they are located, which can measure the deflection generated by these two directions. This helps to improve the accuracy of the concavity (or convexity) of the Pareto and the smoothness of the entire surface. In summary, the mathematical expressions for the interpolation positions of 2- and 3-objective DMOPs are:

[0183]

[0184] In the formula, f new represents the new objective point, f i represents the objective endpoint of the i-th area to be interpolated, f jrepresents the other target endpoint of the \(i\)-th area to be inserted, and \(\lambda\) represents the equal division coefficient. It is used to determine the concave and convex position of the target point. represents the cross product enhancement term.

[0185] Among them, \(\lambda\) represents the equal division coefficient, and its mathematical expression is:

[0186]

[0187] and It is used to determine the concave and convex position of the target point, and its mathematical expression is:

[0188]

[0189] Among them, \(\alpha_1\in[1.2,1.8]\). \(|f i,g |\) and \(|f k,g |\) respectively represent the number of adjacent points of \(f i \) and \(f i,k \). and are the ratio coefficients of the angular distance of the area to be inserted and the angular distance of their adjacent areas, and its purpose is to ensure and adapt to the range of the area formed by \(f i \) and \(f i,k . Their calculation expressions are:

[0190]

[0191] Among them, \(disf i,g \) and \(disf k,g \) respectively represent the angular distances of \(f i \) and \(f i,k \) from their respective adjacent target points.

[0192] When \(f i \) or \((f i,k )\) does not have any neighbor points other than the endpoint to be inserted \(f m \) or \((f i,k )\) in the octant \(Q_i(i = 2,\cdots,2 i -1)\). For the 2-target problem, its vector difference is assigned to 0. Due to the complexity of the 3-target space distribution, it cannot be operated in the same way as the 2-target problem. Therefore, considering obtaining or \(f i \) in the octant where \(f i,k \) is located, the 4th and 5th nearest neighbor points \(f i,h \) and \(f k,h(h = 4, 5). The main reason is that if a target point that is too close is selected, these adjacent target points may be reused when calculating another adjacent point. The concavity and convexity vector of the interpolation region or is the average vector difference between two target pseudo-points that are centrosymmetric with respect to f i and f i and is calculated as follows:

[0193]

[0194] Accordingly and are recalculated by formula (24). The remaining calculations are consistent with formula (21).

[0195] S329. Update the boundary points, establish a linear inverse extrapolation model, and map the new target points to the decision space according to the linear inverse extrapolation model to obtain the new initial population X NNI .

[0196] In a feasible implementation, the newly inserted target points are delimited to avoid generating extreme points, and its mathematical expression is:

[0197]

[0198] Furthermore, based on the original X CIF and their target F CIF values, a linear inverse extrapolation model is established, which can map the target vector in the target space back to the decision space. f new obtains the solution set X NNI through the established linear inverse extrapolation model.

[0199] The present invention designs a NNI (Nearest Neighbor Interpolation Strategy), aiming to improve the distribution uniformity of the currently obtained PF. This strategy judges the concavity and convexity of the PF based on the information of the nearest neighbor points to be interpolated in the bi-objective and tri-objective problems and inserts target points at uniform intervals to improve the accuracy of fitting the true PF.

[0200] S33. Generate a new initial population X CIF according to the new initial population X DDA and the dual-source domain adaptive prediction strategy DDA.

[0201] Optionally, the above step S33 may include the following steps S331-S333:

[0202] S331. Use the new initial population X CIF as the target domain D T。

[0203] S332. Determine that the number of environmental changes is greater than or equal to 3.

[0204] If it is equal to 3, then select N T = min(|POS1|, |POS2|) individuals from population POS1 and population POS2 respectively according to the crowding distance to obtain the dual-source domain D Si (i = 1, 2).

[0205] If it is greater than 3, then calculate the centroid of the historical environmental population and the centroid of the target domain of the Euclidean distance; select two populations POS n1 and POS n2 from the historical environmental population according to the Euclidean distance; select N n1 and population POS n2 from population POS T = min(|POS n1 |, |POS n2 |) individuals to obtain the dual-source domain D Si (i = 1, 2).

[0206] S333. Migrate the individuals in the dual-source domain D Si to the target domain D Ti to obtain the new initial population X DDA 。

[0207] In a feasible implementation, since the historical information of the first two populations is limited, for problems with irregular or complex changes, their prediction accuracy for the new environment is slightly insufficient. To further enhance the DMOP of the algorithm to adapt to various environmental change types, the present invention proposes a dual-source domain adaptation method. DDA is proposed based on the multi-source domain migration idea, which learns the information of the two historical populations most similar to the new environment to predict the individuals in the new environment. Different from the single-source domain migration method, this method can obtain more comprehensive historical knowledge from multiple useful historical population knowledge and improve the generalization performance of knowledge in the new environment. Figure 9 Give the execution pseudocode of DDA.

[0208] When the number of environmental changes t = 3, DDA only performs domain adaptation through the first two environmental populations. When t > 3, DDA extracts useful knowledge from the historical environment. The target task of transfer learning is to obtain a high-quality solution, so the target domain D T is composed of the non-dominated solutions X CIF obtained by the CIF strategy. The source domain needs to extract useful knowledge for the new environment from the historical environment. The correlation between the source domain and the target domain is measured by the Euclidean distance of their centroids. The historical environmental populations POS1 to POSt The centroid and the centroid of the target domain Two populations with the closest Euclidean distance are defined as POS n1 and POS n1 . POS n1 and POS n1 The number of individuals contained in POS is N n1 and N n2 . Since multi-source domain migration requires synthesizing the individuals after mapping each source domain, the individual scale in each source domain is set to N T = min(|POS n1 |, |POS n2 |). The crowding distance mechanism is used to select N T individuals with good distribution from a larger-scale population. The individuals selected from POS n1 and POS n1 serve as the dual-source domain D of DDA Si (i = 1, 2). The dual-source domain adaptation process is as follows. First, each source domain and the target domain perform domain adaptation learning separately. The domain alignment method used in the present invention is SDA-IS (Subspace Distribution Alignment between Infinite Subspaces), which can apply the kernel trick to the integration of an infinite number of subspaces on the geodesic manifold from the source domain to the target domain and achieve feature alignment of subspace distributions. SDA-IS establishes a mapping matrix M s from the source domain to the target domain, that is For each individual x ∈ D in the source domain Si After migration, a corresponding new individual set x new ∈ D Ti is formed, and the calculation is as follows:

[0209] x new = x · M s (23)

[0210] Subsequently, D Si combines the migrated individuals in the two domains based on the contribution degree to D T to form a new set X DSDA , and its mathematical representation is:

[0211] X DSDA = ∑r i · DT i (24)

[0212] where r i represents the weight coefficient of the i-th source domain D Si and the target domain D T , and it is based on DSi The centroid C Si and the centroid C of the target domain T are obtained through a similarity relationship, and its mathematical representation is:

[0213]

[0214] The present invention proposes a DDA (Dual-source Domain Adaptation Mechanism, a prediction strategy for dual-source domain adaptation), which improves the performance of the algorithm in solving various types of DMOPs and the accuracy of predicting new environments. This strategy borrows the idea of multi-source domain migration, migrates the knowledge of the two most relevant historical environments to the new environment, and integrates them into a new solution according to their contribution degrees to the new environment.

[0215] S34. According to the new initial population X CIF , the new initial population X NNI and the new initial population X DDA , use the environmental selection mechanism of NSGA-II to select and obtain the initial population of the new environment.

[0216] S4. Complete the control task according to the control strategy.

[0217] The automotive speed control task refers to regulating and controlling the speed of the vehicle through a control system to ensure that the vehicle travels at a set speed. This control system can be implemented using PID (Proportional Integral Derivative), which performs feedback regulation through the speed error to ensure that the vehicle can stably maintain the target speed. However, in actual situations, affected by road conditions at different times, it is necessary to adjust the parameters of the control system in real time to meet the control requirements. Therefore, CITI is applied to this control task to optimize the system parameters.

[0218] The key parameters to be optimized in the PID system are the proportional control coefficient (K p ), the integral control coefficient (K i ), and the derivative control coefficient (K d ). In this task, two optimization objectives f1 and f2 are defined according to the response input of PID, where f1 is used to reflect the accuracy of speed control and f2 is used to evaluate the speed at steady state. The calculation expressions of f1 and f2 are:

[0219]

[0220] where (K p , K i , K d ) represent decision variables, and their respective value ranges are Kp ∈ [0.5, 5], K i ∈ [0.1, 1] and K d ∈ [8, 9]. |e(t)| represents the absolute error between the true output and the ideal value at steady state, and the ideal value of the system is set to 1. O m represents the rise time from the initial time to 0.9 of the ideal value for the first time. In the vehicle speed control task, the time-varying transfer function of the PID system is:

[0221]

[0222] where, a1(t) and a2(t) are time-related parameters, and and

[0223] CITI is applied to the vehicle speed control task with a PID system to verify its applicability to real problems. The IM, CT, and IMDMOEA algorithms are compared with CITI. The population size of all algorithms is set to 100. During the whole process, the system undergoes 20 environmental changes. The frequency τ of each environment t is set to 10. All algorithms run 30 independent experiments on the problem. Since the true PF of the real problem is unknown, the PFs obtained by integrating all algorithms are used to perform non-dominated sorting and select the objective points of non-dominated solutions to form an approximate reference point set.

[0224] Table 1 presents the MIGD results of CITI and three comparison algorithms on the PID system of the vehicle speed control task. represents that CITI is superior to other comparison algorithms at the 5% significance level of the Wilcoxon rank-sum test. CITI obtains the best MIGD result. This indicates that CITI shows good robustness and optimization accuracy in solving such problems.

[0225] Table 1 MIGD Results of CITI and Three Comparison Algorithms on the PID System of Vehicle Speed Control

[0226]

[0227] Due to the complexity of the dynamic PID system, they have a large change scale in each period, thus increasing the solution difficulty of DMOAs. To verify the response effect of the non-dominated solutions obtained by each algorithm on the PID system, Figure 10It shows the unit step function curves on the CITI and three comparison algorithms PID systems for the case of t = 16. It can be seen that the maximum threshold of CITI is lower than that of the other three algorithms and the curve fluctuates less than the other three algorithms. At the same time, CITI can make the system reach the steady state in a relatively short time. This indicates that CITI can provide better parameters for the system, so as to control the vehicle speed quickly and accurately. In summary, CITI shows good adaptability to this practical problem.

[0228] In order to improve the guiding efficiency of the sub-population and the dynamic tracking ability of the population, the present invention proposes a dynamic multi-objective optimization algorithm with a migration and interpolation strategy driven by the change of clustered individuals, denoted as CITI. CITI consists of three components, namely: a prediction strategy guided by the change trend of the clustered individual objectives, a nearest neighbor interpolation method, and a prediction strategy with dual-source domain adaption. Specifically, CIF uses the distance and angle of similar individuals in adjacent periods to divide the current population into different sub-populations, which is beneficial to improving the representativeness of each cluster and distinguishing the differences between clusters. Based on the preference of individuals within the cluster, different prediction methods are used to move the individuals within the cluster in the direction of the new environment. This not only improves the search ability of individuals but also guides other individuals to evolve in a promising direction. In order to improve the distribution of PF, NNI determines the area to be interpolated in the current PF according to the maximum interval of the reference vector and inserts some new objective points through the information of adjacent points. In addition, in order to make full use of historical information to cope with various types of changes in DMOPs, the DDA algorithm borrows the idea of multi-source domain transfer learning, migrates the PSs of the two historical environments most similar to the new environment to the new environment respectively, and integrates the knowledge learned from these two domains according to their contribution degrees to the new environment to form the initial solution of the new environment.

[0229] On various types of configurations of CEC2018DF, CITI is compared with six popular DMOAs. The experimental results prove that the proposed CITI can show better optimization performance on complex DMOPs. In addition, CITI also has good applicability in the automotive speed control task. According to the experimental results, the present invention can discover some advantages of the proposed algorithm.

[0230] The sub-population divided based on the individual change characteristics is more conducive to strengthening the search tasks of individuals within the cluster, thus better guiding other individuals to evolve in the new environment.

[0231] The NNI interpolation strategy can approximate and fit the geometric characteristics of the PF in the new environment by using the information of adjacent points to improve the distribution.

[0232] Learning the excellent non-dominated solutions of different historical populations helps to enhance the reliability of knowledge transfer and make the DMOA applicable to problems with different types of changes.

[0233] In the embodiments of the present invention, a dynamic multi-objective optimization algorithm with a migration and interpolation strategy driven by the variation of clustering individuals is proposed. Specifically, first, a prediction strategy guided by the trend of the objective variation of clustering individuals is proposed to enhance the prediction accuracy of the sub-population and guide other individuals to evolve in a promising direction. This strategy divides into different clusters according to the objective variation distance of similar individuals in adjacent environments and the angular deviation from the center as variation characteristics. According to the nature of the individuals within the cluster, different prediction mechanisms are used to obtain new initial solutions. Second, a nearest neighbor interpolation method is designed to improve the distribution of the Pareto front, which interpolates some new objective points in the sparse region of the current Pareto front based on the maximum interval of the reference vectors and the information of adjacent objective points. In addition, to promote the algorithm to be applicable to solving various types of changing DMOPs, a dual-source domain adaptive prediction strategy is proposed, which performs knowledge transfer on the two historical environments most similar to the new environment based on multi-source domain transfer learning and integrates them into new initial solutions according to the contribution degree of the environments. The proposed algorithm is compared with 6 popular algorithms on the CEC2018 suite. The experimental results demonstrate the excellent optimization performance of the proposed algorithm. In addition, the proposed algorithm has good engineering applicability in the automotive speed control task.

[0234] Figure 11 It is a block diagram of a CITI-based dynamic multi-objective optimization device shown according to an exemplary embodiment. This device is used for the CITI-based dynamic multi-objective optimization method. Referring to Figure 11 , this device includes a construction module 310, an optimization module 320, a generation module 330, and a control module 340. Among them:

[0235] The construction module 310 is used to construct the dynamic multi-objective optimization problem of the control system.

[0236] The optimization module 320 is used to randomly generate an initial population for the dynamic multi-objective optimization problem, and optimize the initial population using the base algorithm to obtain the optimized initial population.

[0237] The generation module 330 is used to detect whether the environment has changed by using the evaluation mechanism of the population.

[0238] If the environment has changed, the dynamic multi-objective optimization algorithm CITI with a migration and interpolation strategy driven by the variation of clustering individuals is used to generate the initial population of the new environment, and then the control strategy is obtained.

[0239] If the environment has not changed, the base algorithm is used to optimize the population, and then the control strategy is obtained.

[0240] The control module 340 is used to complete the control task according to the control strategy.

[0241] In an embodiment of the present invention, a dynamic multi-objective optimization algorithm with a migration and interpolation strategy driven by clustering individual changes is proposed. Specifically, first, a prediction strategy guided by the target change trend of clustering individuals is proposed to enhance the prediction accuracy of the sub-population and guide other individuals to evolve in a promising direction. This strategy divides into different clusters according to the target change distance of similar individuals in adjacent environments and the angular deviation from the center as change characteristics. According to the nature of individuals within the cluster, different prediction mechanisms are used to obtain new initial solutions. Second, a nearest neighbor interpolation method is designed to improve the distribution of the Pareto front, which interpolates some new target points in the sparse region of the current Pareto front based on the maximum interval of the reference vector and the information of adjacent target points. In addition, to promote the algorithm to be applicable to solving various types of changing DMOPs, a dual-source domain adaptive prediction strategy is proposed, which performs knowledge migration on the two historical environments most similar to the new environment based on multi-source domain transfer learning and integrates them into new initial solutions according to the contribution degree of the environment. The proposed algorithm is compared with 6 popular algorithms on the CEC2018 suite. The experimental results demonstrate the outstanding optimization performance of the proposed algorithm. In addition, the proposed algorithm has good engineering applicability in the automotive speed control task.

[0242] Figure 12 is a schematic structural diagram of a dynamic multi-objective optimization device provided by an embodiment of the present invention, as Figure 12 shown, the dynamic multi-objective optimization device may include the above Figure 11 shown CITI-based dynamic multi-objective optimization device. Optionally, the dynamic multi-objective optimization device 410 may include a first processor 2001.

[0243] Optionally, the dynamic multi-objective optimization device 410 may further include a memory 2002 and a transceiver 2003.

[0244] Among them, the first processor 2001 is connected to the memory 2002 and the transceiver 2003, such as through a communication bus.

[0245] It should be understood that the first processor 2001 in the embodiments of the present invention may be a central processing unit (CPU), and the processor may also be other general-purpose processors, digital signal processors (DSPs), application specific integrated circuits (ASICs), field programmable gate arrays (FPGAs) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0246] The above are only the specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of changes or substitutions, which should all be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A dynamic multi-objective optimization method based on CITI, characterized in that, The method includes: S1. Construct a dynamic multi-objective optimization problem of the control system; S2. For the dynamic multi-objective optimization problem, randomly generate an initial population, and use a base algorithm to optimize the initial population to obtain an optimized initial population; S3. Use the evaluation mechanism of the population to detect whether the environment has changed; If the environment has changed, use the dynamic multi-objective optimization algorithm CITI with migration and interpolation strategies driven by clustering individual changes to generate an initial population in the new environment, and then obtain a control strategy; If the environment has not changed, use the base algorithm to optimize the population, and then obtain a control strategy; S4. Complete the control task according to the control strategy.

2. The dynamic multi-objective optimization method based on CITI according to claim 1, wherein The dynamic multi-objective optimization algorithm CITI with migration and interpolation strategies driven by clustering individual changes includes: a prediction strategy CIF guided by the trend of clustering individual objectives, a nearest neighbor interpolation method NNI, and a prediction strategy DDA for dual-source domain adaptation; The step of using the dynamic multi-objective optimization algorithm CITI with migration and interpolation strategies driven by clustering individual changes in S3 to generate an initial population in the new environment includes: S31. Adopt the prediction strategy CIF guided by the changing trend of clustering individual targets to predict new individuals and generate a new initial population X CIF ; S32. Generate a new initial population X CIF according to the new initial population X NNI ; S33. Generate a new initial population X CIF according to the new initial population X DDA ; S34. According to the new initial population X CIF The new initial population X NNI and the new initial population X DDA , use the environmental selection mechanism of NSGA-II for selection to obtain the initial population of the new environment.

3. The dynamic multi-objective optimization method based on CITI according to claim 2, characterized in that, Using the prediction strategy CIF guided by the change trend of clustered individual targets in S31 to predict new individuals and generate a new initial population X CIF , including: S311. Obtain the population POS of the first two environments t and POS t-1 , and respectively remove the duplicate individuals in the population POS t and the population POS t-1 ; S312. Compare the sizes of the two populations after removing duplicate individuals, and for each non-dominated solution in the larger population, find the corresponding non-dominated solution from the smaller population based on the Euclidean distance to form a sample pair; S313. Calculate the Euclidean distance ED of the sample pairs i and the angular distance AD i , and construct the feature matrix of each individual according to the Euclidean distance ED i and the angular distance AD i ; S314. Use the Kmeans method to cluster the feature matrix; S315. Divide the subpopulations according to the clustering results, and calculate the cluster center C of each subpopulation respectively i =[mED i , mAD i (i = 1, 2, 3), and construct a cluster center matrix C based on the cluster centers of all subpopulations; S316. Remove duplicate individuals in the sub-population; S317. Design a prediction mechanism based on the cluster center matrix, and predict new individuals according to the sub-population after removing duplicate individuals and the prediction mechanism to form a population P1; S318. Perform non-dominated sorting on the new individuals in population P1, and save the non-dominated individuals to the new initial population X CIF ; S319. Determine whether the number of non-dominated solutions in population P1 is less than a preset threshold; if so, select N / 2 individuals from the dominated individuals for update according to the rank of non-dominated sorting and the crowding distance, and perform non-dominated sorting on the updated individuals and the individuals in the new initial population X CIF and put the non-dominated individuals into the new initial population X CIF .

4. The dynamic multi-objective optimization method based on CITI according to claim 3, wherein The prediction mechanism includes: When the parameters mED i and mAD i of the cluster center of the sub-population are both the minimum values of each column in the cluster center matrix C, a new individual is predicted using the following formula (1): In the formula, represents a new individual, represents the individual within the \(i\)-th cluster at time \(t\), represents the centroid of represents the set of all solutions of the subpopulation subp within the \(i\)-th cluster i at time \(t\), represents the centroid of represents the set of all solutions of the subpopulation subp within the \(i\)-th cluster i at time \(t - 1\), \(N(0,\sigma 2 )\) represents a random number that follows a normal distribution with a mean of 0 and a variance of \(\sigma 2 ; When the parameter mED of the cluster center of the sub-population i is the second minimum value of the first column in the cluster center matrix C or mAD i is the second minimum value of the second column in C, and mAD i is the minimum value or mED of the second column in C i is the second minimum value of the first column in C, and, mAD i is the maximum value of the second column in C and mED i is the minimum value or the second minimum value of the first column in C, use the following formulas (2) and (3) to predict a new individual: where σ represents the crossover coefficient, represents the individual in the population at time t - 1 that has the nearest Euclidean distance to, r represents a random number between [0, 1], n t represents the change intensity of the environment, τ t represents the change frequency of the environment, and β represents the mutation coefficient; When the parameter mED of the cluster center of the sub-population i is the maximum value of the first column in the cluster center matrix C, a new individual is predicted using the following formula (4): In the formula, part represents that each non-dominated solution at time t within a cluster samples L promising small regions at intervals of part within the search range.

5. The dynamic multi-objective optimization method based on CITI according to claim 2, wherein The X of the new initial population in S32 CIF and the nearest neighbor interpolation method NNI are used to generate a new initial population X NNI , including: S321. Generate the objective vector f for each individual in the new initial population X CIF ; the objective vectors of all individuals form F i ; the number of objectives is m CIF ; S322. Quantize the target vector f i to obtain the quantized target vector f i ′ ; S323. Calculate the cosine distance disf between two target points ij ; S324. For the 2-target problem when disf ij <10 -10 and for the 3-target problem when disf ij <10 -4 remove duplicate target points f i ′ ; S325. For the target points after rejection, calculate the adjacent points of each target point in quadrant Q2 to quadrant Q 2m above; S326. Determine the interpolation region according to the cosine distance between the target point and the adjacent points; S327. Determine the number of target points to be inserted according to the cosine distance between the target point and the adjacent points; S328. Determine whether there are other neighbor points of the target point after removal except the endpoints; If so, insert new target points; If not, update the vector and insert new target points; S329. Update the boundary points, establish a linear inverse inference model, and map the new target points to the decision space according to the linear inverse inference model to obtain a new initial population X NNI .

6. The dynamic multi-objective optimization method based on CITI according to claim 5, characterized in that The interpolation region to be determined according to the cosine distance between the target point and the adjacent points is given by the following formula (5): where disf i,k represents the cosine distance between the target point and the adjacent point; The number of target points to be inserted is determined according to the cosine distance between the target point and the adjacent points by the following formula (6): In the formula, Num represents the number of target points to be inserted; New target points are inserted by the following formula (7): where f new represents the new target point, f i represents the target end point of the i-th area to be interpolated, f j represents the other target end point of the i-th area to be interpolated, λ represents the equal division coefficient, which is used to determine the concave and convex position of the target point, represents the cross product enhancement term.

7. The dynamic multi-objective optimization method based on CITI according to claim 2, characterized in that The new initial population X in S33 CIF and the prediction strategy DDA for dual-source domain adaptation are used to generate a new initial population X DDA , including: S331. Take the new initial population X CIF as the target domain D T ; S332. Determine whether the number of environment changes is greater than 3 or equal to 3; If it is equal to 3, then select N T = min(|POS1|, |POS2|) individuals from population POS1 and population POS2 respectively according to the crowding distance to obtain the dual source domain D Si (i = 1, 2); If it is greater than 3, calculate the centroid of the historical environmental population and the centroid of the target domain to calculate the Euclidean distance; select two populations POS n1 and POS n2 from the historical environmental population according to the Euclidean distance; select N n1 individuals from population POS n2 and population POS T = min(|POS n1 |, |POS n2 |) to obtain the dual-source domain D Si (i = 1, 2); S333. Transfer the individuals in the dual source domain D Si to the target domain D Ti to obtain a new initial population X DDA .

8. A CITI-based dynamic multi-objective optimization device, which is used to implement the CITI-based dynamic multi-objective optimization method according to any one of claims 1-7, characterized in that, The device includes: A construction module for constructing a dynamic multi-objective optimization problem of the control system; An optimization module for randomly generating an initial population for the dynamic multi-objective optimization problem and using a base algorithm to optimize the initial population to obtain an optimized initial population; A generation module for using the evaluation mechanism of the population to detect whether the environment has changed; If the environment has changed, use the dynamic multi-objective optimization algorithm CITI with migration and interpolation strategies driven by clustering individual changes to generate an initial population in the new environment, and then obtain a control strategy; If the environment remains unchanged, the base algorithm is used to optimize the population, and then the control strategy is obtained. A control module, configured to complete control tasks according to the control strategy.

9. A dynamic multi-objective optimization device, characterized in that, The dynamic multi-objective optimization device includes: A processor; A memory, on which computer-readable instructions are stored. When the computer-readable instructions are executed by the processor, the method described in any one of claims 1 to 7 is implemented.

10. A computer-readable storage medium, characterized in that, Program code is stored in the computer-readable storage medium, and the program code can be called by the processor to execute the method described in any one of claims 1 to 7.

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