Trend-guided dynamic multi-objective optimization evolution method

Abstract

The invention belongs to the technical field of multi-objective optimization, and particularly relates to a trend guide type dynamic multi-objective optimization evolution method, which comprises the steps of S1, trend modeling and direction construction in an intelligent scene; s2, constructing a disturbance and search mechanism under trend guidance; s3, a multi-target knee point recognition and feedback enhancement mechanism; s4, performing evolutionary calculation on a parameter regulation and control mechanism; s5, elite sparse resampling and trend collaborative scheduling optimization; the method has the advantages that a closed-loop optimization system integrating trend prediction, knee point strengthening, disturbance generation and self-adaptive feedback regulation is constructed, the convergence, directivity, diversity and stability of a solution set are comprehensively improved in a dynamic environment, the search directivity and the global convergence speed are remarkably enhanced, and the method is suitable for the dynamic environment. The problem of low efficiency caused by dependence on random disturbance is avoided, and rapid positioning of a high-quality optimal solution set is facilitated.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of multi-objective optimization, and particularly relates to a trend guiding type multi-objective optimization method for intelligent energy management, and is particularly suitable for application scenarios such as load scheduling under new energy output uncertainty, power market transaction optimization, carbon emission collaborative control and energy system operation state adaptive prediction. BACKGROUND

[0002] Intelligent scheduling and carbon emission optimization of energy systems have become the current key research direction. In order to achieve a collaborative balance between economy, environmental protection and system stability and other multiple objectives, many researchers have constructed energy management models based on multi-objective optimization theory, and the models have been widely applied in typical scenarios such as regional energy systems, power trading platforms and multi-energy complementary scheduling.

[0003] In the prior art, some methods use a strategy optimization mechanism based on reinforcement learning, which realizes low-carbon scheduling of cold, heat and electricity in an energy system through continuous interaction between a Deep Reinforcement Learning (DRL) model and the environment. However, such methods have the following disadvantages: first, the model needs a large number of training samples, and it is difficult to accurately describe the evolution trend between optimization variables, lacking active perception of the change direction of the non-dominated front; second, the strategy learning process has a "black box" characteristic, lacking explainability and credibility, resulting in great difficulty in practical application and deployment. Another type of method focuses on improving the application of evolutionary algorithms in multi-objective optimization, typical examples being the Non-dominated Sorting Genetic Algorithm (NSGA-II) or its variants. These methods construct an approximate Pareto optimal solution set through population evolution, but generally have the following problems: on the one hand, the evolution process lacks intelligent guidance based on historical evolution trends, and usually relies on random disturbance for searching, resulting in slow convergence speed and easy falling into local optimal solutions; on the other hand, the existing optimization framework mostly does not integrate knee point identification and feedback mechanisms, and it is difficult to identify key solutions with the maximum target revenue inflection point in the optimization process, so it cannot effectively guarantee the diversity and balance of the solution set.

[0004] In addition, the current mainstream optimization methods lack a unified modeling mechanism for the trend, disturbance strength and feedback repair in the evolution process when dealing with high-dimensional and dynamically changing energy scheduling problems, and cannot meet the complex requirements of dynamic fusion of multi-source information and hierarchical adjustment of solution sets in actual scenarios.

[0005] The existing methods mainly have the following four problems: First, the existing methods lack environmental adaptability and have weak response to dynamic changes, In practical multi-objective optimization applications, the objective function, constraint condition and Pareto front often change nonlinearly and complexly drift over time. However, existing optimization algorithms, such as Chinese patent 202510623228.4, disclose a micro-grid multi-objective optimization method and system based on improved SABO algorithm, which mainly relies on static or linear adjustment parameters based on the strategy of disturbance and reverse solution injection, and fails to design a trend modeling or dynamic regulation mechanism facing time series evolution, resulting in the algorithm's inability to identify the magnitude and direction of environmental changes in real time, lack of sensitivity to rapid dynamic fluctuations, and significant decline in optimization performance, with the population easily falling into lag or degradation. In addition, traditional methods mostly rely on fixed disturbance proportion and local search, which can maintain solution set diversity to some extent, but lack monitoring mechanisms for overall shift trends and prediction reliability of solution sets in a dynamic multi-objective environment, resulting in the algorithm having no way to adjust when the target space changes dramatically, and poor adaptability.

[0006] Secondly, there is a lack of effective knee point identification and feedback regulation mechanism, and it is difficult to highlight the key trade-off solution area, The knee point area in multi-objective optimization usually represents the optimal trade-off solution and is the most valuable decision-making area in engineering practice. However, existing methods, such as Chinese patent 202510572214.4, disclose an intelligent job scheduling system and method for multi-objective optimization, which only relies on random disturbance and non-dominated sorting mechanism based on simulated annealing neighborhood disturbance method, and fails to identify, track and search the knee point area in real time, resulting in sparse distribution of solution sets in the key trade-off area, and inability to meet the high-density coverage and accurate positioning of trade-off solutions in actual engineering requirements. Moreover, the knee point area is not modeled or prioritized, resulting in a lack of targeted trade-off of solution sets, and a lack of reliable support for users in selecting balanced solutions, limiting the multi-objective performance of the algorithm.

[0007] Thirdly, there is a lack of unified closed-loop mechanism of trend-disturbance-feedback, and the convergence stability is insufficient, Existing methods generally design trend prediction, disturbance generation and feedback regulation modules separately, lacking a closed-loop optimization architecture for overall linkage. For example, Chinese patent 202510623228.4 discloses a micro-grid multi-objective optimization method and system based on improved SABO algorithm, which only relies on fixed disturbance proportion and random solution injection to maintain diversity, lacks integration of trend evolution and feedback evaluation, resulting in poor convergence of the algorithm in long-term operation, large fluctuations in search results, and unstable solution set quality. Moreover, most evolutionary algorithms only perform disturbance, local search or resampling at fixed steps, lacking closed-loop regulation based on trend evaluation, and the overall stability and convergence efficiency of the algorithm are limited.

[0008] Fourthly, there is a lack of system integration of multi-source trend information, and the search direction is insufficient, In most existing methods, for example, Chinese patent 202510572214.4 discloses a multi-objective optimization intelligent job scheduling system and its scheduling method. The search disturbance described in the patent mainly relies on randomness or single direction strategy, and fails to systematically integrate multi-source trend information such as center deviation, knee point deviation and principal component direction, resulting in insufficient search orientation, slow convergence speed of solution set and limited optimization efficiency. In addition, existing strategies in trend utilization mostly stop at simple estimation of overall drift of solution set, lacking multi-dimensional trend fusion and direction strengthening mechanism, and the search path is blind, which cannot fully utilize historical evolution information.

[0009] In summary, the existing multi-objective optimization method still has technical gaps in trend identification, feedback regulation, disturbance guidance and key solution extraction. Therefore, a new optimization framework for energy scheduling scenarios is urgently needed, which can have trend guiding ability, feedback mechanism and multi-layer disturbance structure to improve search efficiency, enhance convergence stability, and improve controllability and interpretability of solution set structure. SUMMARY

[0010] In view of the above problems, the purpose of the present application is to provide a trend-guided dynamic multi-objective optimization evolution method for constructing a closed-loop optimization system that integrates trend prediction, knee point reinforcement, disturbance generation and adaptive feedback regulation, and to realize comprehensive improvement of solution set convergence, directionality, diversity and stability in dynamic environment.

[0011] The trend-guided dynamic multi-objective optimization evolution method provided by the present application comprises the following steps: S1. Trend modeling and direction construction in intelligent scenarios, By modeling the historical multi-objective solution set, the system identifies and extracts the dynamic migration law and distribution form of the solution set in the target space, including normalization to eliminate dimensional influence, using group centroid to estimate global drift trend, identifying knee point and its migration trajectory by compromise distance measurement, extracting principal component direction to represent group expansion, and finally integrating global, local and morphological multi-components to construct comprehensive trend vector; S2. Disturbance and search mechanism construction under trend guidance, By translating the individual along the predicted trend direction, while superimposing global Gaussian disturbance and local random disturbance; S3. Multi-objective knee point identification and feedback reinforcement mechanism, By generating high-potential solutions near the knee point, and combining convergence and diversity index to calculate individual feedback weight, and then adjusting migration probability according to environmental change rate and trend prediction error; S4. Evolution calculation parameter regulation mechanism, By calculating the degree of environmental drift and trend prediction error in real time, a quantitative relationship between exploration intensity and environmental uncertainty is established. Key search parameters that are dynamically adjusted include mutation probability and migration probability. S5. Elite sparse resampling and trend coordinated scheduling optimization, Redundant solutions are eliminated through high-dimensional Mahalanobis distance to enhance the sparsity and coverage of the solution set. The candidate solutions generated by trend prediction are weighted and fused with the candidate solutions obtained by evolutionary search according to their credibility to form a final solution set with both diversity and convergence.

[0012] As a preferred embodiment of the present invention, step S1 further includes the following steps: A1. Perform normalization on each target dimension and map all solutions to the [0,1] interval. ; Indicates that the solution The normalized value on the target dimension, Indicates the The original fitness vector of each individual in the multi-objective space, represents the ideal point, that is, the optimal value of each target dimension, represents the anti-ideal point, i.e., the worst value of each target dimension; A2. Extract the global movement trend of the population, Center offset, ; ; Indicates the number of solutions participating in the statistics; Indicates the A solution at the moment The target vector of represents the multi-objective average value of all solutions in the current generation, that is, the group center of mass at the current moment, is the difference between the centroid positions of the current and previous generations, indicating the overall movement direction of the population, i.e., the global drift vector, which is one of the global components of the trend direction; A3. The compromise of the measurement solution. The larger the distance, the stronger the compromise. Knee point identification, ; Indicates the The perpendicular distances of each solution to the ideal and anti-ideal lines, express The value of a solution in two target dimensions; Represent the two coordinates of the ideal point. For the minimization problem, take the minimum value of each objective; Represent the two coordinates of the anti-ideal point; for the minimization problem, take the maximum value of each objective; A4. Capturing the migration of key trade-off areas over time. Knee offset, ; represents the knee point displacement vector, that is, the migration direction and amplitude of the knee point detected twice in the target space, represents the main knee point vector identified in the target space at the current moment; Indicates the last moment The corresponding principal knee vector, Indicates the current moment; ; Represents the principal component analysis operation: calculate the covariance matrix of the input data and then perform eigenvalue decomposition; express The direction of the first principal component obtained, that is, the direction in which the data variance is the largest, and the first principal component of the solution covariance matrix represents the main expansion direction of the population distribution.

[0013] As a preference of the present invention, step S2 further includes the following steps: B1. Drive the search towards the estimated direction, Trend disturbance, ; represents the newly generated candidate solution after trend disturbance, represents the coordinates of the original individual in the decision space, Indicates control along the trend direction The average amplitude, represents the trend direction in the decision space, represents the proportional coefficient of global random perturbation, represents independent zero-mean Gaussian noise in each dimension; By translating along the trend direction and superimposing Gaussian noise, it adds guidance and diversity; B2. Local disturbance, ; represents the candidate solution generated after local perturbation, represents the local noise weight, represents the Gaussian noise vector, Local perturbations can further refine the search near the identified trend direction.

[0014] As a preferred embodiment of the present application, the following step is further included in step S3: C1. Screening and retaining high-value individuals in combination with the importance of convergence and diversity of individuals, Enhancing knee point convergence, ; Indicates the knee point around the knee point , through the direction offset of the candidate solution obtained; Indicates the main knee point vector at the current time, i.e. the main knee point vector identified in the target space at the current time; Indicates the scalar coefficient of the control step length, Indicates the knee point offset direction vector; Indicates the knee point noise variance of each dimension independently; Generate new solutions around the knee point, and focus on exploring key compromise regions; C2. Dynamic feedback mechanism, ; Indicates the comprehensive feedback weight of the th solution; Indicates the weighting coefficient, Indicates the convergence index, Indicates the diversity index, i.e. measures the diversity contribution of the solution to the overall solution set; C3. Adaptive promotion, Migration probability, ; Indicates the migration probability, Indicates the basic migration probability, Indicates the environment sensitive coefficient, Indicates the environment change rate, i.e. the relative amplitude of the centroid offset of two generations, Indicates the prediction error coefficient, Indicates the trend prediction error; Screening and retaining high-value individuals in combination with the importance of convergence and diversity of individuals.

[0015] As a preferred embodiment of the present application, the following step is further included in step S4: D1. According to the environment change rate Dynamic adjustment of mutation probability and weight parameters of comprehensive trend vector; Environment change rate, ; ​the centroid of the population at the current time, the centroid at the previous time, the global drift vector, the rate of environmental change quantify the degree of drift of the population centroid between two consecutive generations, the larger the value, the more drastic the change of the current Pareto front, providing real-time feedback on whether to increase the exploration intensity; D2. prediction error, participating in adaptive control, ; the number of solutions participating in statistics, the predicted target vector, the target vector obtained by real evaluation; trend prediction error the average deviation between the trend prediction model and the real Pareto front, when when the threshold is exceeded, the system automatically increases the proportion of random exploration or reduces the trend guidance weight; D3. Enhance global exploration, improve algorithm adaptability to uncertainty, mutation probability, ; mutation probability dynamically adjusted according to the current rate of environmental change and the prediction error, the basic mutation probability, indicates that when the environment changes drastically, the mutation probability is increased, indicates that when the prediction is unreliable, the mutation probability is increased.

[0016] As a preferred embodiment of the present application, the following steps are further included in step S5: E1. Mahalanobis distance eliminates redundancy, elite sparsification, and reduces duplication, ; the individual and the individual the Mahalanobis distance in high-dimensional space, the feature vector of the th solution, the feature vector of the th solution, is the matrix transpose; the covariance matrix of the solution set, when < threshold, determine that two solutions are highly redundant, and eliminate one; E2. Solution set fusion makes the solution set both guiding and diverse, ; representing trend prediction generating solution set, representing candidate solution set generated by trend prediction module, representing evolutionary search generating solution set, fusion weight with trend prediction error counter-regulation, when low, high, the system adopts ; when high, low, the system adopts .

[0017] The beneficial effects of the present application are as follows: 1. The present application constructs a multi-dimensional trend modeling method based on center offset vector, knee point offset vector and principal component direction vector. Through real-time calculation of solution set centroid migration amplitude, trend prediction deviation and other indicators, the dynamic adjustment of mutation probability, local disturbance step and solution set update strategy is driven, realizing real-time perception and adaptive optimization of the algorithm to dynamic environment.

[0018] 2. The present application proposes a geometric analysis method based on ideal-anti-ideal line distance, dynamically identifies the position and offset trend of knee point solution, and generates candidate solutions using knee point offset to construct a high-potential search area around the knee point. By fusing convergence index (CV) and diversity index (Div) to calculate comprehensive counterweight, the selection and reinforcement probability of knee point solution is dynamically adjusted, so that the algorithm can realize continuous tracking and intelligent reinforcement in key compromise area.

[0019] 3. The present application can significantly improve the solution set coverage density and quality of the knee point area, enhance the compromise explanation ability of multi-objective optimization results, and improve the engineering applicability of optimization solutions.

[0020] 4. The present application constructs a closed-loop optimization system integrating trend modeling-perturbation generation-feedback regulation-sparse fusion. Through real-time monitoring of environmental change rate and prediction error, the dynamic adjustment of search parameters is driven; through the combination of trend direction guidance and local disturbance, the balance of guidance and diversity is realized; and through Mahalanobis distance sparsification and multi-strategy solution set fusion, the stability and diversity of solution set are improved. Moreover, the closed-loop mechanism realizes the organic linkage of trend prediction, perturbation execution and feedback regulation, which can maintain the diversity and stability of solution set distribution in complex dynamic environment for a long time, and improve the global optimization performance of the algorithm in dynamic multi-objective problems.

[0021] 5. The present application significantly enhances the search directionality and global convergence speed, avoids the low efficiency problem caused by relying on random disturbance, and helps to quickly locate high-quality optimal solution set. DETAILED DESCRIPTION

[0022] This embodiment provides a trend-guided dynamic multi-objective optimization evolution method, including the following steps: S1. Trend modeling and direction construction in intelligent scenarios, By modeling historical multi-target solution sets, the system identifies and extracts the dynamic migration patterns and distribution patterns of solution sets in the target space. Specifically, this includes normalization to eliminate dimensionality effects, estimation of global drift trends using the group centroid, identification of knee points and their migration trajectories using a compromise distance metric, extraction of principal component directions to characterize group scalability, and finally, fusion of global, local, and morphological components to construct a comprehensive trend vector. This provides fully guiding directional information for subsequent searches and improves the ability to adapt to dynamic environments. A1. Perform normalization on each target dimension and map all solutions to the [0,1] interval. ; Indicates that the solution is The normalized value on the target dimension, Indicates the The original fitness vector of each individual in the multi-objective space, represents the ideal point, that is, the optimal value of each target dimension, represents the anti-ideal point, i.e., the worst value of each target dimension; Eliminate scale differences between different target dimensions to ensure dimensional consistency in subsequent calculations; provide a consistent data foundation for trend modeling. In multi-objective optimization, dimensional and scale differences between different targets can lead to distortions in distance, variance, and direction estimates. Without normalization, some dimensions have larger numerical ranges, dominating PCA and distance calculations, and the trend direction is biased toward targets with larger dimensions. Therefore, this normalization formula is introduced to ensure: ; A2. Extract the global movement trend of the population, Center offset, ; ; Indicates the number of solutions participating in the statistics; Indicates the A solution at the moment The target vector of represents the multi-objective average value of all solutions in the current generation, that is, the group center of mass at the current moment, is the difference between the centroid positions of the current and previous generations, indicating the overall movement direction of the population, i.e., the global drift vector, which is one of the global components of the trend direction; A3. The compromise of the measurement solution. The larger the distance, the stronger the compromise (knee point). Knee point identification, ; Indicates the The perpendicular distances of each solution to the ideal and anti-ideal lines, express The value of a solution in two target dimensions; The two coordinates of the ideal point represent the minimum value of each objective in the minimization problem. Represents the two coordinates of the anti-ideal point (Nadirpoint); for the minimization problem, take the maximum value of each objective; A4. Capturing the migration of key trade-off areas over time. Knee offset, ; represents the knee point displacement vector, that is, the migration direction and amplitude of the knee point detected twice in the target space, represents the main knee point vector identified in the target space at the current moment; Indicates the last moment The corresponding principal knee vector, Indicates the current moment; ; Represents the principal component analysis operation: calculate the covariance matrix of the input data and then perform eigenvalue decomposition; express The direction of the first principal component obtained, that is, the direction in which the data variance is the largest, and the first principal component of the solution covariance matrix represents the main expansion direction of the population distribution.

[0023] S2. Construction of disturbance and search mechanism under trend guidance, This step is based on trend vector-driven search operations. It mainly translates individuals along the predicted trend direction and superimposes global Gaussian perturbations and local random perturbations. This makes the search both highly directional to accelerate convergence to the optimal region and maintain local diversity to prevent falling into local optimality. This effectively achieves a balance between global exploration and local exploitation in a complex dynamic multi-objective environment. B1. Drive the search in the estimated direction, Trend disturbance, ; represents the newly generated candidate solution after trend disturbance, represents the coordinates of the original individual in the decision space, Indicates control along the trend direction The average amplitude, denotes the trend direction in the decision space, denotes the proportional coefficient of global random disturbance, denotes the zero-mean Gaussian noise in each dimension independently; By translating along the trend direction while superimposing Gaussian noise, the guidance and diversity are endowed; B2. Local disturbance, ; denotes the candidate solution generated after local disturbance, denotes the local noise weight, denotes the Gaussian noise vector, Through local disturbance, the search can be further refined near the determined trend direction, improving the local exploration accuracy.

[0024] S3. Multi-objective knee point identification and feedback reinforcement mechanism, The purpose of this step is to dynamically reinforce the search of key compromise areas by generating high-potential solutions near the knee point, calculating individual feedback weights based on convergence and diversity indicators, adjusting migration probabilities according to environmental change rate and trend prediction error, forming an adaptive feedback mechanism, so that the algorithm can continuously focus and preferentially explore potential optimal solutions with convergence and diversity under dynamic conditions; C1. Individual importance combined with convergence and diversity, screening and retaining high-value individuals, improve knee point convergence, ; denotes the candidate solution obtained by direction offsetting around the knee point ; denotes the current main knee point vector, i.e. the main knee point vector identified in the target space at the current time; denotes the scalar coefficient controlling the step size, denotes the knee point offset direction vector; denotes the knee point noise variance in each dimension independently; Generate new solutions around the knee point, focusing on exploring key compromise areas; C2. Dynamic feedback mechanism, ; ; denotes the comprehensive feedback weight of the th solution; denotes the weighting coefficient, denotes the convergence index, denotes the diversity index, i.e. measures the diversity contribution of the solution to the overall solution set;​ C3. Adaptively promoting, Migration probability, ; Migration probability, Base migration probability, Environment-sensitive coefficient, Environment change rate, i.e., the relative amplitude of the two-generation centroid shift, Prediction error coefficient, Trend prediction error; Screen and retain high-value individuals in combination with convergence and diversity of individual importance.

[0025] S4. Evolutionary calculation parameter regulation mechanism, By calculating the environmental drift degree and trend prediction error in real time, the quantitative relationship between exploration intensity and environmental uncertainty is established, and the key search parameters including mutation probability and migration probability are dynamically adjusted, that is, the key search parameters including mutation probability and migration probability are dynamically adjusted, so that the algorithm can adaptively adjust the search strategy according to the stability or volatility of the environment, thereby improving the flexibility and robustness in the long-term optimization process; D1. According to the environment change rate Dynamic adjustment of mutation probability And the weight parameter of the comprehensive trend vector; Environment change rate, ; Current centroid of the population, Last time centroid, Global drift vector, Environment change rate Quantify the drift degree of the centroid of the population of the two consecutive generations (global average position), The greater the value, the more dramatic the change in the current Pareto front, providing real-time feedback to indicate whether the exploration intensity needs to be increased; D2. Prediction error, involved in adaptive control, ; The number of solutions involved in statistics, Predicted target vector, Real target vector obtained by real evaluation; trend prediction error The average deviation between the trend prediction model and the real Pareto front, when Exceeding the preset threshold, the system (energy system) automatically increases the proportion of random exploration or correspondingly reduces the trend guiding weight; D3. Enhance global exploration, improve algorithm adaptability to uncertainty, Mutation probability, ; Mutation probability Adjust dynamically according to current environment change rate and prediction error, Represents the basic mutation probability (to ensure the minimum search), Represents when the environment changes dramatically, increase the mutation probability, Represents when the prediction is unreliable, increase the mutation probability.

[0026] S5. Elite sparse resampling and trend collaborative scheduling optimization, The core purpose of this step is to remove redundant solutions by high-dimensional Mahalanobis distance to enhance the sparsity and coverage of the solution set, and to weight the candidate solutions generated by trend prediction and evolutionary search according to the credibility, form the final solution set with diversity and convergence, so as to realize the collaborative scheduling of trend-driven and evolutionary-driven, and improve the global stability and performance of dynamic multi-objective optimization.

[0027] E1. Remove redundancy by Mahalanobis distance, elite sparsification, and reduce duplication, ; Represents the individual And the individual Mahalanobis distance in high-dimensional space, Represents the feature vector of the th solution, Represents the feature vector of the th solution, The matrix transpose; Represents the covariance matrix of the solution set. Compared with the Euclidean distance, the Mahalanobis distance considers the correlation of the distribution of the solution, and when <Threshold, determine that two solutions are highly redundant, and remove one; E2. Solution set fusion, make the solution set both guiding and diverse, ; Represents the solution set generated by trend prediction, Represents the candidate solution set generated by the trend prediction module, Represents the solution set generated by evolutionary search, and the fusion weight Adjusts inversely with the trend prediction error When Low, High, the system adopts ; When High, Low, the system adopts .

[0028] The above merely illustrates the specific embodiments of the present application, but the protection scope of the present application is not limited thereto, any person skilled in the art can easily think of the changes or replacements within the technical range disclosed by the present application, which should be covered in the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A trend-guided dynamic multi-objective optimization evolutionary method, characterized in that: The following steps are involved: S1. Trend modeling and direction construction in intelligent scenarios, By modeling the historical multi-target solution set, the system identifies and extracts the dynamic migration patterns and distribution patterns of the solution set in the target space. Specifically, this includes normalization to eliminate dimensionality effects, estimation of global drift trends using the group centroid, identification of knee points and their migration trajectories using a compromise distance metric, extraction of principal component directions to characterize group scalability, and finally, fusion of global, local, and morphological components to construct a comprehensive trend vector. S2. Construction of disturbance and search mechanism under trend guidance, By translating the individual along the predicted trend direction, and superimposing global Gaussian perturbations and local random perturbations; S3. Multi-target knee point identification and feedback reinforcement mechanism, By generating high-potential solutions near the knee point, and combining convergence and diversity indicators to calculate individual feedback weights, the migration probability is adjusted according to the environmental change rate and trend prediction error; S4. Evolutionary computing parameter control mechanism, By calculating the degree of environmental drift and trend prediction error in real time, a quantitative relationship between exploration intensity and environmental uncertainty is established. Key search parameters that are dynamically adjusted include mutation probability and migration probability. S5. Elite sparse resampling and trend coordinated scheduling optimization, Redundant solutions are eliminated through high-dimensional Mahalanobis distance to enhance the sparsity and coverage of the solution set. The candidate solutions generated by trend prediction are weighted and fused with the candidate solutions obtained by evolutionary search according to their credibility to form a final solution set with both diversity and convergence.

2. A trend-guided dynamic multi-objective optimization evolutionary method according to claim 1, characterized in that: Step S1 also includes the following steps: A1. Perform normalization on each target dimension and map all solutions to the [0,1] interval. ； Indicates that the solution is The normalized value on the target dimension, Indicates the The original fitness vector of each individual in the multi-objective space, represents the ideal point, that is, the optimal value of each target dimension, represents the anti-ideal point, i.e., the worst value of each target dimension; A2. Extract the global movement trend of the population, Center offset, ； ； Indicates the number of solutions participating in the statistics; Indicates the A solution at the moment The target vector of represents the multi-objective average value of all solutions in the current generation, that is, the group center of mass at the current moment, is the difference between the centroid positions of the current and previous generations, indicating the overall movement direction of the population, i.e., the global drift vector, which is one of the global components of the trend direction; A3. The compromise of the measurement solution. The larger the distance, the stronger the compromise. Knee point identification, ； Indicates the The perpendicular distances of each solution to the ideal and anti-ideal lines, express The value of a solution in two target dimensions; Represent the two coordinates of the ideal point. For the minimization problem, take the minimum value of each objective; Represent the two coordinates of the anti-ideal point; for the minimization problem, take the maximum value of each objective; A4. Capturing the migration of key trade-off areas over time. Knee offset, ； represents the knee point displacement vector, that is, the migration direction and amplitude of the knee point detected twice in the target space, represents the main knee point vector identified in the target space at the current moment; Indicates the last moment The corresponding principal knee vector, Indicates the current moment; ； Represents the principal component analysis operation: calculate the covariance matrix of the input data and then perform eigenvalue decomposition; express The direction of the first principal component obtained, that is, the direction in which the data variance is the largest, and the first principal component of the solution covariance matrix represents the main expansion direction of the population distribution.

3. A trend-guided dynamic multi-objective optimization evolutionary method according to claim 1, characterized in that: Step S2 also includes the following steps: B1. Drive the search towards the estimated direction, Trend disturbance, ； represents the newly generated candidate solution after trend disturbance, represents the coordinates of the original individual in the decision space, Indicates control along the trend direction The average amplitude, represents the trend direction in the decision space, represents the proportional coefficient of global random perturbation, represents independent zero-mean Gaussian noise in each dimension; By translating along the trend direction and superimposing Gaussian noise, it adds guidance and diversity; B2. Local disturbance, ； represents the candidate solution generated after local perturbation, represents the local noise weight, represents the Gaussian noise vector, Local perturbations can further refine the search near the identified trend direction.

4. A trend-guided dynamic multi-objective optimization evolutionary method according to claim 1, characterized in that: Step S3 also includes the following steps: C1. Combine the individual importance of convergence and diversity to screen and retain high-value individuals. Improve knee convergence, ； Indicates at the knee point Around, after the direction offset The candidate solutions obtained; Indicates the current time The main knee point vector of is the main knee point vector identified in the target space at the current moment; represents the scalar coefficient controlling the step size, represents the knee point offset direction vector; represents the independent knee noise variance in each dimension; Generate new solutions around the knee point, focusing on exploring key trade-off areas; C2. Dynamic feedback mechanism, ； Indicates the The comprehensive feedback weight of each solution; represents the weighting coefficient, represents the convergence index, represents the diversity index; C3. Improved adaptability, Migration probability, ； represents the migration probability, represents the basic migration probability, represents the environmental sensitivity coefficient, represents the rate of environmental change, that is, the relative magnitude of the center of mass shift between the two generations, represents the prediction error coefficient, represents the trend forecast error; Combining the individual importance of convergence and diversity, high-value individuals are screened and retained.

5. A trend-guided dynamic multi-objective optimization evolutionary method according to claim 1, characterized in that: Step S4 also includes the following steps: D1. According to the rate of change of environment Dynamically adjust mutation probability and weight parameters of the integrated trend vector; Environmental change rate, ； represents the group center of mass at the current moment, represents the center of mass at the previous moment, represents the global drift vector, Environmental change rate Quantify the degree of drift of the population centroid between two consecutive generations, The larger the value, the more dramatic the change in the current Pareto front, providing real-time feedback and indicating whether the exploration intensity needs to be increased; D2. Prediction error, involved in adaptive control, ； represents the number of solutions involved in the statistics, represents the predicted target vector, represents the target vector obtained by the true evaluation; the trend prediction error represents the average deviation between the trend forecast model and the true Pareto front. If the preset threshold is exceeded, the system will automatically increase the random exploration ratio or reduce the trend guidance weight; D3. Enhance global exploration, Mutation probability, ； Mutation probability Dynamically adjust according to the current environmental change rate and prediction error, represents the basic mutation probability, When the environment changes drastically, Indicates when the forecast is unreliable.

6. A trend-guided dynamic multi-objective optimization evolutionary method according to claim 1, characterized in that: Step S5 also includes the following steps: E1. Mahalanobis distance eliminates redundancy, elite sparseness, and reduces duplication. ； Represents an individual With individuals In high-dimensional space, the Mahalanobis distance Indicates the The eigenvectors of the solutions, Indicates the The eigenvectors of the solutions, is the matrix transpose; represents the covariance matrix of the solution set, when < threshold, the two solutions are considered highly redundant and one is eliminated; E2. The solution set is integrated to make the solution set both directional and diverse. ； represents the solution set generated by trend prediction, represents the candidate solution set generated by the trend prediction module, Indicates that the solution set generated by evolutionary search is integrated with weights Trend forecast error Reverse regulation, when Low, When high, the system uses ;when high, When low, the system uses .

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