A trend-guided dynamic multi-objective optimization evolutionary method

Abstract

This invention belongs to the field of multi-objective optimization technology, specifically involving a trend-guided dynamic multi-objective optimization evolutionary method, including: S1. Trend modeling and direction construction in intelligent scenarios; S2. Construction of perturbation and search mechanisms under trend guidance; S3. Multi-objective knee point identification and feedback reinforcement mechanism; S4. Evolutionary computation parameter control mechanism; S5. Elite sparse resampling and trend collaborative scheduling optimization. The advantages of this invention are: it constructs a closed-loop optimization system that integrates trend prediction, knee point reinforcement, perturbation generation, and adaptive feedback control, and achieves a comprehensive improvement in the convergence, directionality, diversity, and stability of the solution set in a dynamic environment, significantly enhancing the search directionality and global convergence speed, avoiding the inefficiency problem caused by relying on random perturbations, and helping to quickly locate high-quality optimal solution sets.

Description

Technical Field

[0001] This invention belongs to the field of multi-objective optimization technology, specifically involving a trend-guided multi-objective optimization method for smart energy management, which is particularly suitable for application scenarios such as load dispatching under uncertainty of new energy output, power market transaction optimization, carbon emission coordinated control and adaptive prediction of energy system operation status. Background Technology

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

[0003] In existing technologies, some methods employ reinforcement learning-based policy optimization mechanisms, using deep reinforcement learning (DRL) models to continuously interact with the environment to achieve low-carbon scheduling of cooling, heating, and power in energy systems. However, these methods have the following drawbacks: First, the models require a large number of training samples and struggle to accurately describe the evolutionary trends among optimization variables, lacking proactive awareness of the direction of changes in the non-dominated frontier; second, the policy learning process is a "black box," lacking interpretability and credibility, leading to significant difficulties in practical application and deployment. Another type of method focuses on improving the application of evolutionary algorithms in multi-objective optimization, typically including the Non-Dominated Sorting Genetic Algorithm (NSGA-II) or its variants. These methods construct approximate Pareto optimal solution sets through population evolution, but they generally suffer from the following problems: On the one hand, the evolutionary process lacks intelligent guidance based on historical evolutionary trends and usually relies on random perturbations for searching, resulting in slow convergence speed and easy getting trapped in local optima; on the other hand, most existing optimization frameworks do not integrate knee point identification and feedback mechanisms, making it difficult to identify key solutions with the inflection point of maximum objective benefit during the optimization process, thus failing to effectively guarantee the diversity and balance of the solution set.

[0004] Furthermore, current mainstream optimization methods lack a unified modeling mechanism for trends, disturbance intensity, and feedback repair during the evolution process when dealing with high-dimensional and dynamically changing energy scheduling problems. This makes it impossible to meet the complex needs of dynamic fusion of multi-source information and adjustment of solution set levels in real-world scenarios.

[0005] The existing methods mainly have the following four problems:

[0006] I. Existing methods lack environmental adaptability and have a weak ability to respond to dynamic changes.

[0007] In practical multi-objective optimization applications, the objective function, constraints, and Pareto front often undergo nonlinear changes and complex drifts over time. However, existing optimization algorithms, such as Chinese Patent 202510623228.4, which discloses a microgrid multi-objective optimization method and system based on an improved SABO algorithm, rely primarily on static or linear adjustment parameters for their perturbation and reverse solution injection strategies. They fail to design trend modeling or dynamic control mechanisms oriented towards time-series evolution, resulting in the algorithm's inability to identify the magnitude and direction of environmental changes in real time, a lack of sensitivity to rapid dynamic fluctuations, a significant decline in optimization performance, and a tendency for the population to lag or degenerate. Furthermore, traditional methods mostly rely on fixed perturbation ratios and local searches. While this can maintain solution set diversity to some extent, in multi-objective dynamic environments, the lack of a monitoring mechanism for the overall shift trend of the solution set and prediction reliability means the algorithm cannot adjust when the objective space changes drastically, resulting in poor adaptability.

[0008] Second, the lack of an effective knee point identification and feedback control mechanism makes it difficult to highlight the key compromise solution zone.

[0009] In multi-objective optimization, the knee point typically represents the optimal compromise solution and is the most valuable decision region in engineering practice. However, existing methods, such as Chinese Patent 202510572214.4, disclose an intelligent job scheduling system and method for multi-objective optimization. The simulated annealing neighborhood perturbation method described in this patent relies solely on random perturbation and non-dominated sorting mechanisms, failing to identify, track, and prioritize the knee point in real time. This results in a sparse distribution of the solution set generated by the algorithm within the key compromise region, failing to meet the high-density coverage and accurate location of compromise solutions required in practical engineering. Furthermore, the lack of modeling or prioritization of the knee point region leads to a lack of targeted compromise in the solution set, providing users with unreliable support when selecting balanced solutions, thus limiting the multi-objective performance of the algorithm.

[0010] Third, the lack of a unified closed-loop mechanism for trend-perturbation-feedback results in insufficient convergence stability.

[0011] Existing methods generally design trend prediction, disturbance generation, and feedback regulation modules separately, lacking an overall interconnected closed-loop optimization architecture. For example, Chinese Patent 202510623228.4 discloses a microgrid multi-objective optimization method and system based on an improved SABO algorithm. This method relies solely on a fixed disturbance ratio and random solution injection to maintain diversity, lacking integration of trend evolution and feedback evaluation. This results in poor convergence, large fluctuations in search results, and unstable solution set quality during long-term operation. Furthermore, most evolutionary algorithms only perform disturbances, local searches, or resampling at fixed steps, lacking closed-loop regulation based on trend evaluation, thus limiting the overall stability and convergence efficiency of the algorithms.

[0012] Fourth, there is a lack of systematic integration of multi-source trend information, resulting in insufficient search guidance.

[0013] Most existing methods, such as Chinese Patent 202510572214.4, disclose a multi-objective optimization intelligent job scheduling system and its scheduling method. The search perturbation described in this patent mainly relies on randomness or a single-directional strategy, failing to systematically integrate multi-source trend information such as center offset, knee offset, and principal component direction. This results in insufficient search guidance, slow solution set convergence speed, and limited optimization efficiency. In addition, existing strategies mostly rely on simple estimation of the overall drift of the solution set in terms of trend utilization, lacking multi-dimensional trend fusion and directional reinforcement mechanisms. The search path is blind and cannot fully utilize historical evolution information.

[0014] In summary, existing multi-objective optimization methods still have technical gaps in trend identification, feedback adjustment, perturbation guidance, and key solution extraction. Therefore, there is an urgent need for a novel optimization framework for energy dispatching scenarios, which can possess trend guidance capabilities, feedback mechanisms, and multi-layer perturbation structures to improve search efficiency, enhance convergence stability, and improve the controllability and interpretability of the solution set structure. Summary of the Invention

[0015] In view of the above problems, the purpose of this invention is to provide a trend-guided dynamic multi-objective optimization evolution method to construct a closed-loop optimization system that integrates trend prediction, knee point reinforcement, perturbation generation and adaptive feedback control, and to achieve a comprehensive improvement in solution set convergence, directionality, diversity and stability in a dynamic environment.

[0016] This invention provides a trend-guided dynamic multi-objective optimization evolution method, comprising the following steps:

[0017] S1. Trend Modeling and Direction Construction in Intelligent Scenarios

[0018] By modeling the historical multi-objective solution set, the system identifies and extracts the dynamic migration pattern and distribution pattern of the solution set in the target space. Specifically, this includes normalization to eliminate the influence of dimensions, using the group centroid to estimate the global drift trend, identifying the knee point and its migration trajectory through a compromise distance metric, extracting the principal component direction to characterize the group's extensibility, and finally fusing global, local and morphological multi-components to construct a comprehensive trend vector.

[0019] S2. Construction of Trend-Guided Disturbance and Search Mechanisms

[0020] By translating individuals along the predicted trend direction, while simultaneously superimposing global Gaussian perturbations and local random perturbations;

[0021] S3. Multi-target knee point recognition and feedback reinforcement mechanism

[0022] By generating high-potential solutions near the knee point and combining convergence and diversity indices to calculate individual feedback weights, the migration probability is adjusted based on the rate of environmental change and trend prediction error.

[0023] S4. Evolutionary computational parameter regulation mechanism,

[0024] 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, and key search parameters that are dynamically adjusted include mutation probability and migration probability.

[0025] S5. Elite sparse resampling and trend-based collaborative scheduling optimization.

[0026] Redundant solutions are eliminated by using high-dimensional Mahalanobis distance to enhance the sparsity and coverage of the solution set. The candidate solutions generated by trend prediction and those obtained by evolutionary search are then fused together according to their credibility to form a final solution set that combines diversity and convergence.

[0027] As a preferred embodiment of the present invention, step S1 further includes the following step:

[0028] A1. Perform normalization on each target dimension, mapping all solutions to the interval [0,1].

[0029] ;

[0030] This indicates that for each solution at the th... Normalized values ​​for each target dimension Indicates the first The original fitness vector of each individual in the multi-object space. This represents the ideal point, that is, the optimal value for each objective dimension. This represents the anti-ideal point, i.e., the worst value of each objective dimension;

[0031] A2. Extract the global movement trend of the population.

[0032] Center offset,

[0033] ;

[0034] ;

[0035] This indicates the number of solutions included in the statistics; Indicates the first The solution is at time... The target vector; This represents the multi-objective average of all solutions in the current generation, i.e., the population centroid at the current moment. The difference between the centroid positions of the current generation and the previous generation represents the overall movement direction of the population, i.e., the global drift vector, and serves as one of the global components of the trend direction.

[0036] A3. Measuring the compromise of the solution; a larger distance indicates a stronger compromise.

[0037] Knee point recognition,

[0038] ;

[0039] Indicates the first Each solution yields the perpendicular distance between the ideal and anti-ideal lines. express The values ​​of each solution in the two objective dimensions; Two coordinates represent the ideal point; for a minimization problem, the minimum value of each objective is taken. These represent the two coordinates of the anti-ideal point; for the minimization problem, the maximum value of each objective is taken;

[0040] A4. Capture the migration of key compromise areas along the timeline.

[0041] Knee point offset,

[0042] ;

[0043] This represents the knee displacement vector, i.e., the direction and magnitude of the knee's migration in the target space during the two detected events. This represents the vector of the principal knee point identified in the target space at the current moment; Indicates the previous moment The corresponding principal knee vector, Indicates the current time;

[0044] ;

[0045] Principal component analysis (PCA) involves calculating the covariance matrix of the input data and then performing eigenvalue decomposition. express The direction of the first principal component obtained is the direction of the largest data variance. The first principal component of the solution set covariance matrix represents the main expansion direction of the population distribution.

[0046] As a preferred embodiment of the present invention, step S2 further includes the following step:

[0047] B1. Drives the search in the direction of estimation.

[0048] Trend disturbance,

[0049] ;

[0050] This represents a newly generated candidate solution after the trend perturbation. This represents the coordinates of the original individual in the decision space. Indicates control along the trend direction average amplitude Indicates the trend direction in the decision space. The proportionality coefficient representing the global random disturbance. This represents zero-mean Gaussian noise that is independent in each dimension;

[0051] By translating along the trend direction and simultaneously superimposing Gaussian noise, it imparts directionality and diversity;

[0052] B2. Local disturbance,

[0053] ;

[0054] This represents the candidate solution generated after local perturbation. Represents local noise weights. Represents a Gaussian noise vector.

[0055] Local perturbations can further refine the search near the established trend direction.

[0056] As a preferred embodiment of the present invention, step S3 further includes the following step:

[0057] C1. Combining the importance of convergence and diversity among individuals, select and retain high-value individuals.

[0058] Lift the knee point convergence,

[0059] ;

[0060] Indicates at the knee point Surrounding, after directional shift The candidate solutions obtained; Indicates the current time The principal knee point vector is the principal knee point vector identified in the target space at the current moment. Scalar coefficient representing the control step size This represents the direction vector of the knee offset. Represents the independent knee noise variance for each dimension;

[0061] Generate new solutions around the knee point, focusing on exploring key compromise regions;

[0062] C2. Dynamic feedback mechanism,

[0063] ;

[0064] Indicates the first The overall feedback weight of each solution; Indicates the weighting coefficient. Indicates the convergence index. This represents a diversity index, which measures the contribution of the solution to the diversity of the overall solution set.

[0065] C3. Adaptability Enhancement

[0066] migration probability,

[0067] ;

[0068] Indicates the migration probability. Represents the basic transfer probability. Indicates the environmental sensitivity coefficient. This represents the rate of environmental change, specifically the relative magnitude of the centroid shift between two generations. Indicates the prediction error coefficient. Indicates the error in trend prediction;

[0069] By combining the importance of convergence and diversity of individuals, high-value individuals are selected and retained.

[0070] As a preferred embodiment of the present invention, step S4 further includes the following step:

[0071] D1. Based on the rate of environmental change Dynamically adjust mutation probability and the weight parameters of the comprehensive trend vector;

[0072] Environmental change rate

[0073] ;

[0074] This represents the group's center of mass at the current moment. This indicates the center of mass at the previous moment. Represents the global drift vector.

[0075] Environmental change rate Quantifying the degree of centroid drift between two consecutive generations of a population. The larger the value, the more drastic the changes in the Pareto frontier, providing real-time feedback and indicating whether the exploration intensity needs to be increased;

[0076] D2. Prediction error, participating in adaptive control.

[0077] ;

[0078] This indicates the number of solutions included in the statistics. Represents the predicted target vector. Represents the target vector obtained from the actual assessment; trend prediction error This represents the average deviation between the trend forecasting model and the true Pareto frontier, when... If the threshold is exceeded, the system will automatically increase the proportion of random exploration or decrease the weight of trend guidance.

[0079] D3. Enhance global exploration capabilities and improve the algorithm's adaptability to uncertainty.

[0080] Mutation probability,

[0081] ;

[0082] Mutation probability The forecast is dynamically adjusted based on the current rate of environmental change and prediction errors. Represents the basic mutation probability. This indicates that drastic environmental changes increase the probability of mutation. This indicates that when the prediction is unreliable, the probability of mutation is increased.

[0083] As a preferred embodiment of the present invention, step S5 further includes the following step:

[0084] E1. Mahalanobis distance eliminates redundancy, sparsifies elites, and reduces repetition.

[0085] ;

[0086] Represents an individual With individuals Mahalanobis distance in high-dimensional space Indicates the first The eigenvectors of each solution Indicates the first The eigenvectors of each solution This is the matrix transpose. Let the covariance matrix of the solution set be denoted as , when If the threshold is exceeded, two solutions are determined to be highly redundant, and one is discarded.

[0087] E2. Solution set fusion ensures that the solution sets are both directional and diverse.

[0088] ;

[0089] This indicates that the trend prediction generates a solution set. This represents the candidate solution set generated by the trend prediction module. This indicates that evolutionary search generates a solution set, which is then fused with weights. Trend forecasting error Reverse adjustment, when Low, At high times, the system adopts ;when high, At low speeds, the system adopts .

[0090] The beneficial effects of this invention are as follows:

[0091] 1. This invention constructs a multidimensional trend modeling method based on the center offset vector, knee offset vector, and principal component direction vector. By calculating in real time the centroid migration amplitude of the solution set and the trend prediction deviation, it drives the dynamic adjustment of the mutation probability, local perturbation step size, and solution set update strategy, thereby realizing the algorithm's real-time perception and adaptive optimization of the dynamic environment.

[0092] 2. This invention proposes a geometric analysis method based on the ideal-anti-ideal line distance to dynamically identify the position and offset trend of the knee point solution, and uses the knee point offset to generate candidate solutions, constructing a high-potential search region around the knee point. By fusing convergence index (CV) and diversity index (Div) to calculate the comprehensive feedback weight, the selection and strengthening probability of the knee point solution are dynamically adjusted, enabling the algorithm to continuously track and intelligently strengthen key compromise regions.

[0093] 3. This invention can significantly improve the solution set coverage density and quality in the knee region, enhance the ability to interpret compromises in multi-objective optimization results, and improve the engineering applicability of the optimization solution.

[0094] 4. This invention constructs a closed-loop optimization system integrating trend modeling, perturbation generation, feedback control, and sparse fusion. By real-time monitoring of environmental change rates and prediction errors, it drives dynamic adjustments to search parameters; by combining trend direction guidance with local perturbations, it achieves a balance between guidance and diversity; and by Mahalanobis distance sparsification and multi-strategy solution set fusion, it enhances the stability and diversity of the solution set. Furthermore, this closed-loop mechanism achieves organic linkage between trend prediction, perturbation execution, and feedback control, enabling it to maintain the diversity and stability of the solution set distribution in complex dynamic environments over the long term, thus improving the global optimization performance of the algorithm under dynamic multi-objective problems.

[0095] 5. This invention significantly enhances search directionality and global convergence speed, avoids the inefficiency caused by relying on random perturbations, and helps to quickly locate high-quality optimal solution sets. Detailed Implementation

[0096] This embodiment provides a trend-guided dynamic multi-objective optimization evolution method, including the following steps:

[0097] S1. Trend Modeling and Direction Construction in Intelligent Scenarios

[0098] By modeling historical multi-objective solution sets, the system identifies and extracts the dynamic migration patterns and distribution patterns of the solution sets in the target space. Specifically, this includes normalization to eliminate the influence of dimensions, using the population centroid to estimate the global drift trend, identifying the knee point and its migration trajectory through a compromise distance metric, extracting the principal component direction to characterize the population extensibility, and finally fusing global, local, and morphological multi-components to construct a comprehensive trend vector. This provides sufficient directional information for subsequent searches and enhances the adaptability to dynamic environments.

[0099] A1. Perform normalization on each target dimension, mapping all solutions to the interval [0,1].

[0100] ;

[0101] This indicates that for each solution at the th... Normalized values ​​for each target dimension Indicates the first The original fitness vector of each individual in the multi-object space. This represents the ideal point, that is, the optimal value for each objective dimension. This represents the anti-ideal point, i.e., the worst value of each objective dimension;

[0102] This normalization formula eliminates scale differences across different objective dimensions, ensuring dimensional consistency in subsequent calculations and providing a consistent data foundation for trend modeling. In multi-objective optimization, differences in the dimensions and scales of different objectives can lead to distortions in distance, variance, and orientation estimations. Without normalization, some dimensions have larger numerical ranges, dominating PCA and distance calculations; trend orientation tends to favor objectives with larger dimensions. Therefore, this normalization formula is introduced to ensure that: ;

[0103] A2. Extract the global movement trend of the population.

[0104] Center offset,

[0105] ;

[0106] ;

[0107] This indicates the number of solutions included in the statistics; Indicates the first The solution is at time... The target vector; This represents the multi-objective average of all solutions in the current generation, i.e., the population centroid at the current moment. The difference between the centroid positions of the current generation and the previous generation represents the overall movement direction of the population, i.e., the global drift vector, and serves as one of the global components of the trend direction.

[0108] A3. Measuring the compromise of the solution: the larger the distance, the stronger the compromise (knee point).

[0109] Knee point recognition,

[0110] ;

[0111] Indicates the first Each solution yields the perpendicular distance between the ideal and anti-ideal lines. express The values ​​of each solution in the two objective dimensions; The two coordinates represent the ideal point. For a minimization problem, the minimum value of each objective is taken. Represents the two coordinates of the inverse ideal point (Nadirpoint); for the minimization problem, the maximum value of each objective is taken;

[0112] A4. Capture the migration of key compromise areas along the timeline.

[0113] Knee point offset,

[0114] ;

[0115] This represents the knee displacement vector, i.e., the direction and magnitude of the knee's migration in the target space during the two detected events. This represents the vector of the principal knee point identified in the target space at the current moment; Indicates the previous moment The corresponding principal knee vector, Indicates the current time;

[0116] ;

[0117] Principal component analysis (PCA) involves calculating the covariance matrix of the input data and then performing eigenvalue decomposition. express The direction of the first principal component obtained is the direction of the largest data variance. The first principal component of the solution set covariance matrix represents the main expansion direction of the population distribution.

[0118] S2. Construction of Trend-Guided Disturbance and Search Mechanisms

[0119] This step is based on trend vector-driven search operation. It mainly involves translating individuals along the predicted trend direction, while superimposing global Gaussian perturbation and local random perturbation. This makes the search both highly directional to accelerate convergence to the optimal region and maintains local diversity to prevent getting trapped in local optima. Thus, it effectively achieves a balance between global exploration and local development in complex dynamic multi-objective environments.

[0120] B1. Drives the search in the direction of estimation.

[0121] Trend disturbance,

[0122] ;

[0123] This represents a newly generated candidate solution after the trend perturbation. This represents the coordinates of the original individual in the decision space. Indicates control along the trend direction average amplitude Indicates the trend direction in the decision space. The scaling factor represents the global random disturbance. This represents zero-mean Gaussian noise that is independent in each dimension;

[0124] By translating along the trend direction and simultaneously superimposing Gaussian noise, it imparts directionality and diversity;

[0125] B2. Local disturbance,

[0126] ;

[0127] This represents the candidate solution generated after local perturbation. Represents local noise weights. Represents a Gaussian noise vector.

[0128] Local perturbations can refine the search further near the established trend direction, improving the accuracy of local exploration.

[0129] S3. Multi-target knee point recognition and feedback reinforcement mechanism

[0130] The purpose of this step is to dynamically enhance the search for key compromise regions by generating high-potential solutions near the knee point, calculating individual feedback weights by combining convergence and diversity indices, and adjusting the migration probability based on the rate of environmental change and trend prediction error, thus forming an adaptive feedback mechanism that enables the algorithm to continuously focus on and prioritize the exploration of potential optimal solutions that combine convergence and diversity under dynamic conditions.

[0131] C1. Combining the importance of convergence and diversity among individuals, select and retain high-value individuals.

[0132] Lift the knee point convergence,

[0133] ;

[0134] Indicates at the knee point Surrounding, after directional shift The candidate solutions obtained; Indicates the current time The principal knee point vector is the principal knee point vector identified in the target space at the current moment. Scalar coefficient representing the control step size This represents the direction vector of the knee offset. Represents the independent knee noise variance for each dimension;

[0135] Generate new solutions around the knee point, focusing on exploring key compromise regions;

[0136] C2. Dynamic feedback mechanism,

[0137] ;

[0138] Indicates the first The overall feedback weight of each solution; Indicates the weighting coefficient. Indicates the convergence index. This represents a diversity index, which measures the contribution of the solution to the diversity of the overall solution set.

[0139] C3. Adaptability Enhancement

[0140] migration probability,

[0141] ;

[0142] Indicates the migration probability. Represents the basic transfer probability. Indicates the environmental sensitivity coefficient. This represents the rate of environmental change, specifically the relative magnitude of the centroid shift between two generations. Indicates the prediction error coefficient. Indicates the error in trend prediction;

[0143] By combining the importance of convergence and diversity of individuals, high-value individuals are selected and retained.

[0144] S4. Evolutionary computational parameter regulation mechanism,

[0145] 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. The key search parameters, including mutation probability and migration probability, are dynamically adjusted. This allows the algorithm to adaptively adjust the search strategy according to environmental stability or volatility, thereby improving the flexibility and robustness of the long-term optimization process.

[0146] D1. Based on the rate of environmental change Dynamically adjust mutation probability and the weight parameters of the comprehensive trend vector;

[0147] Environmental change rate

[0148] ;

[0149] This represents the group's center of mass at the current moment. This indicates the center of mass at the previous moment. Represents the global drift vector.

[0150] Environmental change rate Quantify the degree of drift of the centroid (global average position) between two consecutive generations of population. The larger the value, the more drastic the changes in the Pareto frontier, providing real-time feedback and indicating whether the exploration intensity needs to be increased;

[0151] D2. Prediction error, participating in adaptive control.

[0152] ;

[0153] This indicates the number of solutions included in the statistics. Represents the predicted target vector. Represents the target vector obtained from the actual assessment; trend prediction error This represents the average deviation between the trend forecasting model and the true Pareto frontier, when... If the threshold is exceeded, the system (energy system) will automatically increase the random exploration ratio or correspondingly decrease the trend guidance weight.

[0154] D3. Enhance global exploration capabilities and improve the algorithm's adaptability to uncertainty.

[0155] Mutation probability,

[0156] ;

[0157] Mutation probability The forecast is dynamically adjusted based on the current rate of environmental change and prediction errors. This represents the basic mutation probability (used to guarantee the minimum search). This indicates that drastic environmental changes increase the probability of mutation. This indicates that when the prediction is unreliable, the probability of mutation is increased.

[0158] S5. Elite sparse resampling and trend-based collaborative scheduling optimization.

[0159] The core objective of this step is to enhance the sparsity and coverage of the solution set by eliminating redundant solutions through high-dimensional Mahalanobis distance, and to fuse the candidate solutions generated by trend prediction with the candidate solutions obtained by evolutionary search according to their credibility weights, forming a final solution set that combines diversity and convergence. This enables coordinated scheduling of trend-driven and evolution-driven approaches, thereby improving the global stability and performance of dynamic multi-objective optimization.

[0160] E1. Mahalanobis distance eliminates redundancy, sparsifies elites, and reduces repetition.

[0161] ;

[0162] Represents an individual With individuals Mahalanobis distance in high-dimensional space Indicates the first The eigenvectors of each solution Indicates the first The eigenvectors of each solution This is the matrix transpose. The Mahalanobis distance represents the covariance matrix of the solution set. Compared to the Euclidean distance, the Mahalanobis distance takes into account the distributional correlation of the solutions. If the threshold is exceeded, two solutions are determined to be highly redundant, and one is discarded.

[0163] E2. Solution set fusion ensures that the solution sets are both directional and diverse.

[0164] ;

[0165] This indicates that the trend prediction generates a solution set. This represents the candidate solution set generated by the trend prediction module. This indicates that evolutionary search generates a solution set, which is then fused with weights. Trend forecasting error Reverse adjustment, when Low, At high times, the system adopts ;when high, At low speeds, the system adopts .

[0166] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A trend-guided dynamic multi-objective optimization evolutionary method, characterized in that, Includes 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 pattern and distribution pattern of the solution set in the target space. Specifically, this includes normalization to eliminate the influence of dimensions, using the group centroid to estimate the global drift trend, identifying the knee point and its migration trajectory through a compromise distance metric, extracting the principal component direction to characterize the group's extensibility, and finally fusing global, local and morphological multi-components to construct a comprehensive trend vector. S2. Construction of Trend-Guided Disturbance and Search Mechanisms By translating individuals along the predicted trend direction, while simultaneously superimposing global Gaussian perturbations and local random perturbations; S3. Multi-target knee point recognition and feedback reinforcement mechanism By generating high-potential solutions near the knee point and combining convergence and diversity indices to calculate individual feedback weights, the migration probability is adjusted based on the rate of environmental change and trend prediction error. S4. Evolutionary computational 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, and key search parameters that are dynamically adjusted include mutation probability and migration probability. S5. Elite sparse resampling and trend-based collaborative scheduling optimization. Redundant solutions are eliminated by using high-dimensional Mahalanobis distance to enhance the sparsity and coverage of the solution set. The candidate solutions generated by trend prediction and those obtained by evolutionary search are then fused together according to their credibility to form a final solution set that combines diversity and convergence.

2. The trend-guided dynamic multi-objective optimization evolution method according to claim 1, characterized in that, Step S1 also includes the following steps: A1. Perform normalization on each target dimension, mapping all solutions to the interval [0,1]. ； This indicates that for each solution at the th... Normalized values ​​for each target dimension Indicates the first The original fitness vector of each individual in the multi-object space. This represents the ideal point, that is, the optimal value for each objective dimension. This represents the anti-ideal point, i.e., the worst value of each objective dimension; A2. Extract the global movement trend of the population. Center offset, ； ； This indicates the number of solutions included in the statistics; Indicates the first The solution is at time... The target vector; This represents the multi-objective average of all solutions in the current generation, i.e., the population centroid at the current moment. The difference between the centroid positions of the current generation and the previous generation represents the overall movement direction of the population, i.e., the global drift vector, and serves as one of the global components of the trend direction. A3. Measuring the compromise of the solution; a larger distance indicates a stronger compromise. Knee point recognition, ； Indicates the first Each solution yields the perpendicular distance between the ideal and anti-ideal lines. express The values ​​of each solution in the two objective dimensions; Two coordinates represent the ideal point; for a minimization problem, the minimum value of each objective is taken. These represent the two coordinates of the anti-ideal point; for the minimization problem, the maximum value of each objective is taken; A4. Capture the migration of key compromise areas along the timeline. Knee point offset, ； This represents the knee displacement vector, i.e., the direction and magnitude of the knee's migration in the target space during the two detected events. This represents the vector of the principal knee point identified in the target space at the current moment; Indicates the previous moment The corresponding principal knee vector, Indicates the current moment; ； Principal component analysis (PCA) involves calculating the covariance matrix of the input data and then performing eigenvalue decomposition. express The direction of the first principal component obtained is the direction of the largest data variance. The first principal component of the solution set covariance matrix represents the main expansion direction of the population distribution.

3. The trend-guided dynamic multi-objective optimization evolution method according to claim 1, characterized in that, Step S2 also includes the following steps: B1. Drives the search in the direction of estimation. Trend disturbance, ； This represents a newly generated candidate solution after the trend perturbation. This represents the coordinates of the original individual in the decision space. Indicates control along the trend direction average amplitude Indicates the trend direction in the decision space. The scaling factor represents the global random disturbance. This represents zero-mean Gaussian noise that is independent in each dimension; By translating along the trend direction and simultaneously superimposing Gaussian noise, it imparts directionality and diversity; B2. Local disturbance, ； This represents the candidate solution generated after local perturbation. Represents local noise weights. Represents a Gaussian noise vector. Local perturbations can further refine the search near the established trend direction.

4. The trend-guided dynamic multi-objective optimization evolution method according to claim 1, characterized in that, Step S3 also includes the following steps: C1. Combining the importance of convergence and diversity among individuals, select and retain high-value individuals. Lift the knee point convergence, ； Indicates at the knee point Surrounding, after directional shift The candidate solutions obtained; Indicates the current time The principal knee point vector is the principal knee point vector identified in the target space at the current moment. Scalar coefficient representing the control step size This represents the direction vector of the knee offset. Represents the independent knee noise variance for each dimension; Generate new solutions around the knee point, focusing on exploring key compromise regions; C2. Dynamic feedback mechanism, ； Indicates the first The overall feedback weight of each solution; Indicates the weighting coefficient. Indicates the convergence index. Indicators representing diversity; C3. Adaptability Enhancement migration probability, ； Indicates the migration probability. Represents the basic transfer probability. Indicates the environmental sensitivity coefficient. This represents the rate of environmental change, specifically the relative magnitude of the centroid shift between two generations. Indicates the prediction error coefficient. Indicates the error in trend prediction; By combining the importance of convergence and diversity of individuals, high-value individuals are selected and retained.

5. The trend-guided dynamic multi-objective optimization evolution method according to claim 1, characterized in that, Step S4 also includes the following steps: D1. Based on the rate of environmental change Dynamically adjust mutation probability and the weight parameters of the comprehensive trend vector; Environmental change rate ； This represents the group's center of mass at the current moment. This indicates the center of mass at the previous moment. Represents the global drift vector. Environmental change rate Quantifying the degree of centroid drift between two consecutive generations of a population. The larger the value, the more drastic the changes in the Pareto frontier, providing real-time feedback and indicating whether the exploration intensity needs to be increased; D2. Prediction error, participating in adaptive control. ； This indicates the number of solutions included in the statistics. Represents the predicted target vector. Represents the target vector obtained from the actual assessment; trend prediction error This represents the average deviation between the trend forecasting model and the true Pareto frontier, when... If the threshold is exceeded, the system will automatically increase the proportion of random exploration or decrease the weight of trend guidance. D3. Enhance global exploration capabilities. Mutation probability, ； Mutation probability The forecast is dynamically adjusted based on the current rate of environmental change and prediction errors. Represents the basic mutation probability. This indicates that when the environment changes drastically, This indicates that the prediction is unreliable.

6. The trend-guided dynamic multi-objective optimization evolution method according to claim 1, characterized in that, Step S5 also includes the following steps: E1. Mahalanobis distance eliminates redundancy, sparsifies elites, and reduces repetition. ； Represents an individual With individuals Mahalanobis distance in high-dimensional space Indicates the first The eigenvectors of each solution Indicates the first The eigenvectors of each solution This is the matrix transpose. Let the covariance matrix of the solution set be denoted as , when If the threshold is less than 1, determine that the two solutions are highly redundant and discard one. E2. Solution set fusion ensures that the solution sets are both directional and diverse. ； This indicates that the trend prediction generates a solution set. This represents the candidate solution set generated by the trend prediction module. Evolutionary search generates a solution set, which incorporates weights. Trend forecasting error Reverse adjustment, when Low, At high times, the system adopts ;when high, At low speeds, the system adopts .

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