A multi-objective simulation optimization method and system based on a proxy model for a complex system

Abstract

The present application relates to the technical field of simulation optimization, and more particularly to a complex system multi-objective simulation optimization method and system based on a proxy model. The method comprises the following steps: obtaining complex system task data; constructing a sampling topology according to the complex system task data to obtain sample space data; performing deterministic simulation sensing on the sample space data to obtain initial simulation data; training the initial simulation data using a deep kernel Gaussian process to obtain a proxy model; performing real simulation verification according to the proxy model to obtain simulation verification data; and iteratively optimizing the proxy model according to the simulation verification data to obtain a proxy optimization model. By constructing a variable coupling and target conflict driven sampling topology structure, the sample space can focus on covering key coupling areas and multi-objective conflict areas. Combined with deep kernel Gaussian process proxy modeling and real simulation verification iteration, the number of high-cost real simulations is reduced, and the prediction accuracy is improved.

Description

Technical Field

[0001] This invention relates to the field of simulation optimization technology, and in particular to a multi-objective simulation optimization method and system for complex systems based on a surrogate model. Background Technology

[0002] In fields such as engineering design, system scheduling, and complex process optimization, many practical problems involve high-dimensional design variables, complex constraints, and multiple conflicting optimization objectives. For example, in energy system design, supply chain scheduling, structural design optimization, and complex production system configuration, extensive simulation calculations are needed to evaluate system performance under different combinations of variables. However, traditional direct simulation optimization methods typically rely on high-fidelity simulation models, which are computationally expensive and often fail to meet computational efficiency requirements when conducting large-scale searches in high-dimensional parameter spaces. To reduce computational overhead, existing research often uses surrogate models to approximate the input-output relationships of complex systems. For example, Gaussian process models, radial basis function models, or neural network models are used to predict system responses, and these predictions are used to guide the optimization search process. However, in multi-objective complex system scenarios, existing methods still have the following problems: On the one hand, traditional sampling methods often use random or uniform sampling strategies, which are difficult to fully reflect the coupling relationships between variables and the conflicting structures between objective functions, resulting in low sampling efficiency; on the other hand, during the training of surrogate models, if the training samples are insufficiently distributed in key regions, prediction errors can easily accumulate. Summary of the Invention

[0003] To address the aforementioned technical problems, this invention proposes a multi-objective simulation optimization method and system for complex systems based on a proxy model, thereby solving at least one of the aforementioned technical problems.

[0004] This application provides a multi-objective simulation optimization method for complex systems based on a surrogate model, comprising the following steps: S1: Acquire complex system task data; construct a sampling topology based on the complex system task data to obtain sample space data; S2: Perform deterministic simulation sensing on the sample space data to obtain initial simulation data; S3: Train the surrogate model using a deep kernel Gaussian process on the initial simulation data; S4: Perform real-world simulation verification based on the proxy model to obtain simulation verification data; iteratively optimize the proxy model based on the simulation verification data to obtain the optimized proxy model.

[0005] This invention utilizes sampling topology construction to perceive variable coupling relationships and constraint boundary structures, enabling the sample space to more effectively cover potential critical regions. It combines deterministic simulation to obtain highly reliable initial data and employs a deep kernel Gaussian process to establish a surrogate model with nonlinear expressive power and uncertainty assessment capabilities. Model biases are continuously corrected through real simulation verification and an error-driven iterative optimization mechanism. This reduces the number of real simulation calculations while improving the efficiency and prediction accuracy of multi-objective optimization search, thereby enhancing the overall stability and solution efficiency of the complex system simulation optimization process.

[0006] Preferably, the sampling topology construction specifically involves: Task variable data is obtained by performing heterogeneous task interpretation based on complex system task data. Variable coupling weaving is performed based on task variable data to obtain variable coupling graph data; Coupled cluster compression is performed on the variable coupling graph data to obtain sampled cell data; Constraint boundary attachment mapping is performed on the sampled unit data to obtain boundary layer data; Target conflict ridges are extracted from the boundary layered data to obtain conflict ridge data; Multi-density sampling skeletons are generated based on conflict ridge data to obtain sample space data.

[0007] This invention employs heterogeneous interpretation and variable coupling weaving to construct structural relationships between variables in complex system task data. Representative sampling units are formed through coupling cluster compression, thereby reducing the sampling complexity of the high-dimensional variable space. By identifying the feasible region boundary structure through constraint boundary attachment mapping and extracting and locating potential conflict regions in multi-objective optimization using target conflict ridge lines, the system generates a multi-density sampling skeleton, enabling higher sampling density in key areas. This approach improves sampling efficiency in key areas while ensuring sample space coverage, thus providing more representative training data for surrogate model training.

[0008] Preferably, the coupling cluster compression specifically involves: Based on the variable coupling graph data, coupling edge filtering is performed to obtain cluster filtering data; Cluster boundary correction was performed on the cluster screening data to obtain stable cluster data; Based on stable cluster data, dominant variables within the clusters are extracted to obtain compressed mapping data; The compressed mapping data is reconstructed by inter-cluster connections to obtain the sampled skeleton data; The sampling unit output is obtained by analyzing the sampling skeleton data.

[0009] In this invention, by filtering coupling edges and correcting cluster boundaries in the variable coupling graph, stable coupling structures between variables can be identified and interference caused by accidental associations can be eliminated, making variable grouping more reliable. By extracting dominant variables within clusters and establishing compressed mapping relationships, the influence of key variables is maintained while reducing the participation of redundant variables in sampling, thereby reducing the complexity of high-dimensional space search. The system reconstructs connections between clusters and generates a sampling skeleton, which can maintain the structural association between different variable clusters, making the formed sampling units both representative and structurally consistent.

[0010] Preferably, the target conflict ridge extraction specifically involves: Boundary sample neighborhoods are constructed based on boundary hierarchical data to obtain boundary neighborhood data; Calculate the target gradient by performing target change gradient calculation on the boundary neighborhood data to obtain target gradient data; Target conflict data is obtained by performing target conflict determination on the target gradient data; Based on the target conflict data, conflict paths are connected to obtain initial ridge data; The initial ridge data is stabilized to obtain conflict ridge data.

[0011] This invention constructs a boundary sample neighborhood and calculates the target change gradient to represent the local change direction of multi-objective responses near the feasible region boundary, thereby identifying potential conflict relationships between different objectives. The system performs conflict determination and path connection, extracting conflict ridge structures reflecting multi-objective trade-offs, and eliminates the impact of local noise on path continuity through ridge stabilization. This enables the location of the most significant multi-objective conflict regions in a complex variable space, providing clear structural guidance for sampling and optimization searches, thus improving the search efficiency and solution quality of multi-objective simulation optimization.

[0012] Preferably, the multi-density sampling skeleton generation specifically involves: Ridge segment decomposition is performed based on conflict ridge data to obtain ridge segment data; Based on the ridge segmentation data, sampling density mapping is performed to obtain density stratification data; Based on the density stratification data, ridge center sampling nodes are generated to obtain the central skeleton data; Based on the central skeleton data, a horizontally extended sampling band is constructed to obtain the skeleton network data; Interlayer coherence processing is performed on the skeleton network data to obtain sample space data.

[0013] In this invention, by segmenting the conflict ridges and establishing a sampling density mapping, the sampling intensity can be configured differently according to the degree of target conflict in different regions, so that key conflict areas can obtain higher sampling density. By generating ridge center nodes and constructing lateral expansion sampling bands, the adjacent transition areas can be covered while maintaining the continuity of the ridge structure, thus forming a hierarchical sampling skeleton network. Combined with inter-layer coherence processing, spatial breaks caused by abrupt changes in sampling density can be avoided, so that the sample space maintains overall coverage while highlighting key areas, providing a more balanced and high-value sample distribution for surrogate model training.

[0014] Preferably, S2 specifically comprises: Sample node data is obtained by parsing the sample space data. Simulation input parameter data is obtained by constructing a simulation input mapping based on the simulation node data. Deterministic simulation is performed based on the simulated input parameter data to obtain the original simulation data; The original simulation data is subjected to multi-objective simulation extraction processing to obtain the target simulation data; The simulation results are verified based on the target simulation data to obtain the initial simulation data.

[0015] This invention utilizes structured parsing of nodes in the sample space and constructs simulated input mappings to effectively convert sampled variables into parameter combinations that meet the requirements of the simulation model, thereby ensuring the consistency and computability of the simulated input. By obtaining stable raw response data through deterministic simulation execution and performing multi-objective index extraction and verification on the results, abnormal or unsatisfactory samples can be eliminated. This results in a reliable initial simulation dataset, providing accurate and representative foundational data for surrogate model training, thus improving the stability and prediction accuracy of the simulation optimization process.

[0016] Preferably, S3 specifically comprises: Input and output samples are decoupled from the initial simulation data to obtain training sample data; A deep kernel mapping network is constructed based on the training sample data to obtain latent space mapping data; The deep kernel function is generated based on the latent space mapping data to obtain the kernel representation data; Gaussian process prior modeling is performed based on kernel representation data to obtain prior surrogate data; The process parameter data is obtained by performing joint marginal likelihood optimization on the prior proxy data; Multi-objective result fitting is performed on the process parameter data to obtain multi-objective prediction data; Quantify the prediction uncertainty of multi-objective prediction data to obtain confidence assessment data; The proxy output is processed based on the confidence assessment data to obtain the proxy model.

[0017] In this invention, by decoupling the input and output of the initial simulation data and constructing a deep kernel mapping network, complex nonlinear variable relationships can be mapped to a more expressive latent space, thereby enhancing the surrogate model's ability to represent the response characteristics of complex systems. The system combines deep kernel functions with Gaussian process prior modeling, and achieves adaptive adjustment of model parameters through marginal likelihood joint optimization. It also fits and quantifies the uncertainty of multi-objective results, enabling the surrogate model to maintain prediction accuracy while possessing reliable confidence assessment capabilities, thus providing stable and efficient prediction support for real simulation verification and optimization decision-making.

[0018] Preferably, the real-world simulation verification specifically includes: The sample prediction evaluation is performed based on the surrogate model to obtain sample prediction data; The predicted sample data is used to screen validation samples to obtain validation sample data. The original validation data is obtained by performing a realistic simulation based on the validation sample data. The prediction error is evaluated on the original validation data to obtain simulated validation data.

[0019] This invention utilizes a surrogate model to predict and evaluate candidate samples, enabling the early identification of potential optimal solution regions without performing numerous real simulations. By selecting representative samples for real simulation through validation sample screening, unnecessary simulation computation overhead is reduced. Error evaluation between the real simulation results and the predicted results quantifies the prediction deviation of the surrogate model in different regions, providing a basis for model correction. Therefore, while ensuring validation accuracy, the number of real simulations is reduced, improving the overall efficiency and reliability of the multi-objective simulation optimization process for complex systems.

[0020] Preferably, the iterative optimization specifically involves: Based on the simulation verification data, the prediction residuals are analyzed to obtain the residual evaluation data; The residual evaluation data is augmented with training samples to obtain updated sample data. The kernel mapping structure is adjusted based on the updated sample data to obtain optimized structure data. The Gaussian process parameters are updated on the structural optimization data to obtain the updated model data; The updated model data is integrated with the model output to obtain the surrogate optimization model.

[0021] This invention analyzes the prediction residuals of simulated validation data to identify prediction biases of the surrogate model in different regions, and accordingly expands the training samples to enhance data support in key areas. Through kernel mapping structure adjustment and Gaussian process parameter updates, the model's expressive power and parameter configuration are adaptively optimized, enabling the model to more accurately represent the multi-objective response characteristics of complex systems. The system integrates model outputs to form a surrogate optimization model, which improves overall fitting accuracy while maintaining prediction stability, thereby enhancing the reliability and computational efficiency of the simulation optimization process.

[0022] Preferably, the present invention also provides a multi-objective simulation optimization system for complex systems based on a surrogate model, used to execute the multi-objective simulation optimization method for complex systems based on a surrogate model as described above, the multi-objective simulation optimization system for complex systems based on a surrogate model includes: The sampling topology construction module is used to acquire complex system task data; based on the complex system task data, a sampling topology is constructed to obtain sample space data. The deterministic simulation sensing module is used to perform deterministic simulation sensing on sample space data to obtain initial simulation data; The Deep Kernel Gaussian Process (DKG) training module is used to train the surrogate model using a deep kernel Gaussian process on the initial simulation data. The proxy model optimization module is used to perform real-world simulation verification based on the proxy model to obtain simulation verification data; and to iteratively optimize the proxy model based on the simulation verification data to obtain the optimized proxy model.

[0023] The beneficial effects of this invention are as follows: By constructing a sampling topology, complex system task data is structurally analyzed. A hierarchical sample space is generated using variable coupling relationships, constraint boundary distribution, and target conflict structure. This allows the sampling process to prioritize areas with strong variable coupling, significant target conflict, and sensitive boundaries, thereby improving the representativeness of the sample data. Stable and reliable multi-target response data is obtained through deterministic simulation perception, providing high-quality training samples for surrogate model training. Deep kernel Gaussian processes are used to model the simulation data, enhancing the expressive power of complex nonlinear relationships through deep kernel mapping. Combined with Gaussian processes, prediction uncertainty is quantified, thus constructing a surrogate model with predictive and confidence assessment capabilities. The surrogate model guides real simulation verification and error evaluation, enabling the model to supplement samples and correct parameters for areas of prediction deviation, continuously improving model accuracy through iterative optimization. Through the aforementioned progressive structured sampling, surrogate modeling, and error-driven update process, the search efficiency and prediction reliability of multi-target simulation optimization are improved while reducing the number of real simulation calculations. Attached Figure Description

[0024] Other features, objects, and advantages of this application will become more apparent from the following detailed description of the non-limiting embodiments, taken with reference to the accompanying drawings: Figure 1 A flowchart illustrating the steps of a multi-objective simulation optimization method for complex systems based on a proxy model is shown in one embodiment. Figure 2 A flowchart illustrating the steps of a sampling topology construction method according to an embodiment is shown; Figure 3 A flowchart illustrating the steps of a deterministic simulation sensing method according to one embodiment is shown. Figure 4 A flowchart illustrating the steps of a deep kernel Gaussian process training method according to an embodiment is shown. Figure 5 A flowchart illustrating the steps of a real-world simulation verification method according to one embodiment is shown. Detailed Implementation

[0025] The technical method of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0026] Furthermore, the accompanying drawings are merely illustrative of the invention and are not necessarily drawn to scale. Functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor methods and / or microcontroller methods.

[0027] It should be understood that although the terms "first," "second," etc., may be used herein to describe various units, these units should not be limited by these terms. These terms are used merely to distinguish one unit from another. For example, without departing from the scope of the exemplary embodiments, a first unit may be referred to as a second unit, and similarly, a second unit may be referred to as a first unit. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0028] This method is applied to a class of complex intelligent supply chain fulfillment scheduling systems. The task data of these complex systems includes 18 design variables, such as supplier selection, warehouse replenishment cycle, vehicle delivery batches, route allocation, inventory safety margin coefficient, and order priority rules. The objective function includes the average order delivery delay. Inventory safety level deviation rate Unit order transportation energy consumption and order fulfillment volatility The constraints include supplier supply capacity, warehouse capacity, vehicle load capacity, delivery time window, and order demand satisfaction. The system constructs a sampling topology based on variable coupling relationships, compressing 18 variables into 4 sampling units, and generating 96 sampling nodes in the constraint boundaries and target conflict areas to obtain sample space data.

[0029] The system selects 36 feasible but unevaluated sampling nodes and calls a deterministic simulation program to obtain initial simulation data. For example, for a given sampling point... The simulation results represent the average order delivery delay. Hourly inventory safety level deviation rate Unit order transportation energy consumption kWh / unit, order fulfillment volatility The system trains a deep kernel Gaussian process surrogate model based on the initial simulation data, enabling the surrogate model to output the predicted target response and prediction uncertainty for each candidate sampling point.

[0030] In the real-world simulation validation phase, the system selected 12 sampling points from the remaining unevaluated nodes that were in the prediction non-dominated region or had high prediction uncertainty for real-world simulation validation. After validation, it was found that the initial average relative error of the surrogate model was 8.7%, with the target error for average order delivery delay at 8.9%, inventory safety level deviation at 7.4%, unit order transportation energy consumption at 8.1%, and order fulfillment volatility at 10.3%. The system incorporated these real-world simulation validation results into the training samples and iteratively optimized the surrogate model, reducing the average relative error to 3.8% and the maximum single-objective error from 12.6% to 5.2%.

[0031] Through this embodiment, the specific technical effects of this method are as follows: With a total simulation budget of 120 simulations, a stable surrogate optimization model can be obtained using only 48 deterministic simulations and real simulations for verification. Compared to directly simulating all candidate solutions one by one, the number of simulation calls is reduced by approximately 60%. Simultaneously, because sampling nodes are preferentially deployed near constraint boundaries and target conflict ridges, the surrogate model fits the conflict areas between delivery delays, inventory deviations, transportation energy consumption, and fulfillment fluctuations more accurately. The optimized scheme obtained by the system reduces the average order delivery delay from 10.8 hours to 8.9 hours, the inventory safety level deviation rate from 9.5% to 6.8%, the unit order transportation energy consumption from 3.12 kWh / order to 2.74 kWh / order, and the order fulfillment fluctuation rate from 5.6% to 3.9%. This demonstrates that this method can improve the search efficiency, prediction reliability, and scheduling scheme stability of multi-objective optimization in complex systems under limited simulation budgets.

[0032] Please see Figures 1 to 5 This application provides a multi-objective simulation optimization method for complex systems based on a surrogate model, comprising the following steps: S1: Acquire complex system task data; construct a sampling topology based on the complex system task data to obtain sample space data; In one embodiment, the system acquires complex system task data. The complex system task data includes design variable data. ( Design variables for the i-th complex system task, where i takes values ​​from 1 to n, and variable boundary data. ( Let be the lower limit of the value of the i-th design variable. (the upper limit of the value of the i-th design variable), objective function data ( Optimize the objective function for the i-th task, where i takes values ​​from 1 to n, and consider the constraint data. ( (This refers to the constraint decision function for the i-th task, where i takes values ​​from 1 to n), and simulation interface data. And calculate budget data B. The system first converts all constraints into a unified form. The system adopts a standard form and performs interval normalization on continuous variables based on variable type, establishes legal value numbers for discrete variables, and establishes difference marking rules for enumerated variables. Legal value numbers refer to the system assigning a unique number to each allowed value of a discrete variable. Difference marking rules refer to the system marking differences in the values ​​of enumerated variables; for example, if two sampling points have the same supplier type, path mode, or equipment mode, it is recorded as 0, and if they are different, it is recorded as 1. The system converts upper limit constraints, lower limit constraints, interval constraints, equality constraints, and business rule constraints in the constraint data into a unified feasibility determination form. Where x represents a candidate sampling point, This represents the constraint violation amount of the j-th constraint at that sampling point; when When, it means that the candidate sampling point satisfies the constraint, when When this occurs, it indicates that the candidate sampling point violates the constraint.

[0033] Subsequently in the variable space (include as well as Within the sample point set, stratified sampling or equal-interval sampling is used to generate the sample point set. ,in , To calculate the budget data, which is the total number of times high-cost simulations, experimental evaluations, or objective function calculations are allowed during this complex system optimization process, the system performs constraint verification at each sampling point, retaining those that satisfy all constraints. The sampling points are taken as the node set V. for The Middle One sampling point, The values ​​are 1…n, and a set of node attributes is generated based on the variable values, constraint verification results, simulation call status, and interface matching results for each sampling point. Node attribute set This is used to record the node number, variable value, feasibility status, whether it has been evaluated, and the corresponding simulation interface identifier for each sampling node. The system calculates the mixing distance between nodes. For each node, select the k (e.g., 5) nearest legal nodes to form an adjacency edge set E, resulting in the sampling topology T=(V,E). The system encapsulates the variable space, sampling nodes, adjacency edges, objective function, constraints, simulation interface, computational budget, and node attributes into sample space data. .

[0034] S2: Perform deterministic simulation sensing on the sample space data to obtain initial simulation data; In one embodiment, the system reads sample space data. Based on the node attribute set A, sample nodes that satisfy the condition of "feasible and unevaluated" are selected from the node set V, i.e., nodes that meet the constraints but have not yet had their simulation interface invoked. The sampling nodes used in the deterministic simulation yield the set of nodes to be simulated. If And satisfy all ,but , indicates feasibility; otherwise , indicating that it is not feasible. The system is in a constrained state. (System reads...) Each node to be simulated corresponding Medium sampling point and verify And satisfy all constraints The system determines the number of simulated calls in this round based on the calculated budget B. ,and ;when The number of nodes exceeds When simulating, nodes with fewer than k / 2 adjacent nodes are prioritized for simulation. The system follows the simulation interface data. sampling points The input vector is converted into an interface vector, and under fixed model version, fixed boundary conditions, and fixed random seeds, a deterministic simulation interface is called to obtain the target response vector. ,in This represents the r-th sampling point. This represents the target response value of the r-th sampling point under the objective function of the a-th task. , This represents the total number of optimization objectives. Target response values ​​can include at least one of the following: computation count response value, time response value, energy consumption response value, efficiency response value, reliability response value, or service level response value. Node Corresponding sampling points The state after calling the simulation interface is considered the interface state, such as call success, call failure, timeout, output exception, etc. This applies to adjacent edges where both ends of the node have completed simulation. Simultaneously, the corresponding nodes are updated to be evaluated, and the system calculates the adjacency response difference. , To and Another sampling point that is adjacent to another point. The system will number the node. Sampling points The initial simulation data consists of the target response, constraint state, number of simulation calls, interface state, adjacency response differences, and the updated set of node attributes. .

[0035] S3: Train the surrogate model using a deep kernel Gaussian process on the initial simulation data; In one embodiment, the system reads initial simulation data. Filter the constraint states Interface status For nodes that were successfully invoked and whose evaluation status is "evaluated", a valid training sample set is formed. The system calculates the intensity of local response changes at nodes based on the differences in adjacent responses. and will The high-variability regions are labeled and written into the training samples. The system will then use these sampling points. As model input, the target response vector The a-th target response value As output, construct a single-objective training set. The system will Inputting into a deep feature mapping network yields feature vectors. , Indicated by network parameters A defined feature mapping function, The deep feature mapping network, including the weights, biases, and activation parameters of each hidden layer, employs a three-layer feedforward network, comprising an input layer, a first hidden layer, a second hidden layer, and a feature output layer. If sampling points... If the variable dimension is n, then the number of neurons in the first hidden layer can be 32, the number of neurons in the second hidden layer can be 16, and the feature output dimension can be 8; the weight matrix of the first hidden layer... It can be initialized with random numbers in the interval [-0.1, 0.1], bias vector. It can be initialized to 0; the weight matrix of the second hidden layer. It can be initialized with random numbers in the interval [-0.08, 0.08], bias vector. Can be initialized to 0; Feature output layer weight matrix It can be initialized with random numbers in the interval [-0.05, 0.05], bias vector. It can be initialized to 0. The activation function can be the LeakyReLU function: ,in The slope parameter for the negative half-axis can be taken as follows: Constructing a deep kernel function based on feature vectors: ,in Let be the kernel length scale corresponding to the a-th target. Let V be the signal variance, representing the magnitude of change in the a-th target response value itself. The noise variance represents the allowable small numerical error or observation noise intensity in the simulation results. For node consistency marking, when r=s, meaning both indices point to the same sampling node, ;when That is, when two indices point to different sampling nodes, The system updates the depth mapping parameters by maximizing the marginal likelihood based on the training samples. And kernel parameters, to obtain the depth kernel Gaussian process sub-model corresponding to the a-th target; for After training them one by one, the surrogate model is obtained. , This represents the target surrogate sub-model for the a-th objective, used to predict its target response value under the objective function of the a-th task based on the sampling point p. , , This represents the total number of optimization targets.

[0036] S4: Perform real-world simulation verification based on the proxy model to obtain simulation verification data; iteratively optimize the proxy model based on the simulation verification data to obtain the optimized proxy model.

[0037] In one embodiment, the system reads the proxy model. and initial simulation data Filter constraint states from the sample space Furthermore, for candidate sampling points whose evaluation status is "unevaluated", a verification candidate set is obtained. The system will select candidate sampling points. Input each target agent sub-model , The ordinal term, with values ​​from 1 to m, yields the predicted target response / predicted response. , For the first target agent sub-model For sampling points The primary target outcome obtained from the forecast, such as the predicted cost response value / predicted delivery delay response value, or other pre-defined primary focus targets, For the second target agent sub-model For sampling points The predicted second objective outcome, such as the predicted time response value or efficiency response value, For the first Target Agent Submodel For sampling points The final target result obtained from the prediction is used to obtain the output prediction mean based on the predicted target response. It also outputs the prediction variance. The prediction uncertainty can be obtained by summing the standard deviations of each target prediction, for example: ,in This indicates that the a-th target surrogate sub-model is related to the sampling points. The standard deviation of the prediction The larger the value, the less certain the surrogate model's prediction for that sampling point is. The system predicts the response vector based on the surrogate of the candidate sampling points. A predicted non-dominated solution set is constructed. If a candidate sampling point belongs to the predicted non-dominated solution set, it is determined to be near the non-dominated boundary. The system prioritizes prediction results that are near the non-dominated boundary and have low prediction uncertainty. Higher than the mean of the candidate set, or the intensity of local response changes in the adjacent region The candidate sampling points located in the top 20% of the candidate set form the set of real simulation verification points. The system calculates the remaining budget. Determine the number of verification calls ,and System call simulation interface right The actual target response is obtained by performing a realistic simulation using mid-sample points. ,in This represents the t-th verification sampling point. Indicates sampling point via simulation interface The actual simulated response value of the a-th objective obtained after performing a realistic simulation is the actual response. , This represents the total number of optimization objectives, and the verification error is calculated. The system encapsulates verification points, predicted responses, actual responses, prediction uncertainty, verification errors, interface status, and cumulative call counts into simulated verification data. .

[0038] The system reads simulation verification data. Filter the verification samples whose API call status is successful to obtain the valid verification sample set: ,in To verify the sampling points, To realistically simulate the response, For proxy response prediction, Let be the verification error for the a-th target. To predict uncertainty, the system will realistically simulate the response. Write the training set corresponding to the a-th target to form the updated training set: ,in For the original training set / single-target training set corresponding to the a-th target, To verify the intensity of local response changes in the adjacent region of the sampling point, the system determines whether the surrogate model needs local correction based on the verification error. If so: Then, the verification sampling point is marked as an error correction sample, where The error threshold for the a-th target can be taken as 5% of the training response range of that target, i.e.: , For the maximum true response value of the a-th objective, To determine the minimum true response value for target a, the system uses the original depth mapping parameters. Using kernel parameters as initial parameters, based on updating the training set Remaximizing the marginal likelihood for depth mapping parameters and kernel length scale Signal variance and noise variance The update is performed to obtain the updated target agent sub-model of the a-th generation. The system for The above updates are executed one by one, and the prediction-real simulation-error correction-model update process is repeated as long as the remaining computational budget meets the conditions, until the maximum verification error of all targets does not exceed the corresponding threshold, or the cumulative number of simulation calls reaches the computational budget B. The system encapsulates the updated target proxy sub-models into proxy optimization models: ,in This represents the surrogate optimization model obtained after verification through real simulation and error correction.

[0039] Preferably, the sampling topology construction specifically involves: S11: Perform heterogeneous task interpretation based on complex system task data to obtain task variable data; In one embodiment, the system reads complex system task data. The design variables, boundaries, objectives, constraints, simulation interfaces, and budgets are parsed according to field type to obtain the design variables. Variable value boundary data , set of objective functions Constraint function set Simulation interface data And calculate budget data B. The continuous variable subspace is... , representing the upper and lower limits of the value, where the discrete or enumerated variable subspace is . , representing discrete variables or enumerated variables All valid values ​​can be selected. The system establishes a variable-target dependency table. and variable-constraint dependency table ,in Indicates increase The system determines the direction of improvement, irrelevance, or degradation of the a-th objective based on the direction of the partial derivatives of the variables in the objective function expression, the business rule table, or the trial calculation results of small disturbances. When increase To achieve the goal A value of 1 is assigned when there is improvement, 0 when there is no significant impact, and -1 when the target is deteriorated. This yields the task variable data. .

[0040] S12: Perform variable coupling weaving based on task variable data to obtain variable coupling graph data; In one embodiment, the system uses each design variable as a variable node , forming a set of nodes If two variables Simultaneously appearing in the same objective function Dependency table In, or simultaneously appear in the same constraint function Dependency table In the middle, then at the corresponding node Establish coupling edges between The set of variable coupling edges is obtained. The system records the source of the coupling edge as target coupling, constraint coupling, or target-constraint composite coupling, and records the corresponding... or Numbering. If a variable is not coupled with other variables, it is retained as a single node. The system obtains variable coupling graph data. ,in Set of edge source labels.

[0041] S13: Perform coupled cluster compression on the variable coupling graph data to obtain sampled cell data; In one embodiment, the system couples variable graph data. Connectivity component identification is performed, and variable nodes connected by coupling edges are grouped into the same coupling cluster. If the number of variables in a certain coupled cluster does not exceed a preset upper limit. ,For example If the number of variables exceeds a certain threshold, it is directly compressed into a single sampling unit; if the number of variables exceeds a certain threshold, it is directly compressed into a single sampling unit. Then, priority is given to using the common constraint number. The sample is split such that variables in each split unit still share at least one source of objective or constraint. Each sample unit is represented as follows: ,in For a set of unit variables, , Represents the set of variables for the h-th sampling unit. This represents the i-th design variable in the sampling unit. Represent design variables variable subspace, This represents the joint sampling space formed by all legal combinations of variable values ​​within the sampling unit. and Given the set of objectives and constraints involved in this unit, the sampling unit data is obtained. .

[0042] S14: Perform constraint boundary attachment mapping on the sampled unit data to obtain boundary layer data; In one embodiment, the system reads the sampling unit. Unify the constraints as The system in each variable subspace Candidate anchor points are generated by taking the lower bound, midpoint, and upper bound, and constraint values ​​are calculated for each anchor point b. If there exist constraints that satisfy... If all constraints are satisfied, then mark the anchor point as the constraint boundary attachment point; If it exists, then mark it as an interior point; if it exists If the point is infeasible, it is marked as infeasible and removed. The constraint can be set to 2% of the span at the candidate anchor point. The system outputs boundary layering data. ,in For the set of sampling units, Attach a set of points to the boundary. For the set of interior points, For variables—target dependency table, For the set of objective functions, For the set of constraint functions, To calculate budget data.

[0043] S15: Extract the target conflict ridge line from the boundary layer data to obtain conflict ridge line data; In one embodiment, the system reads boundary layering data. Set of boundary attachment points in and variables—target dependency table For the variables within the sampling unit to which the boundary attachment point c belongs. If there are two targets , making If increasing the same variable produces opposite improvements for two objectives, then the boundary attachment point is marked as a target conflict point. The system connects anchor points within the same sampling unit whose variable values ​​differ by only one offset and are all target conflict points to form ridge lines, thus obtaining conflict ridge line data. ,in For the set of conflict ridge points, This is the set of edges connecting conflict ridges.

[0044] S16: Generate a multi-density sampling skeleton based on the conflict ridge data to obtain sample space data.

[0045] In one embodiment, the system reads conflict ridge data. And allocate the number of samples to each sampling unit according to the calculated budget B. , Let h be the set of variables for the h-th sampling unit. The system is at the conflict ridge point. The area uses a fine sampling interval At the boundary attachment point The area uses a medium sampling interval , inside point The area uses the basic sampling interval ,in , Let i be the upper limit of the value of the i-th continuous variable. This represents the lower bound of the values ​​of the i-th continuous variable. The number of samples for the h-th sampling unit; when When the variable is discrete or enumerated, the system selects from its set of legal values. Values ​​are extracted without considering consecutive intervals. The system excludes values ​​that do not meet the criteria. The sampling points are selected, and the retained points are constructed as sampling nodes V. Adjacent edges E are established based on the k nearest nodes within the same sampling unit to obtain the sample space data. ,in Represents the sample variable space. Represents the set of sampling nodes. Represents the set of adjacent edges sampled. Represents the set of objective functions. Represents the set of constraint functions. This represents simulation interface data. This indicates the calculation of budget data. For node attribute collection ,in , Number the nodes. Bind sampling points to nodes. For the constrained state, For region type labeling, Number the sampling unit to which it belongs.

[0046] Preferably, the coupling cluster compression specifically involves: Based on the variable coupling graph data, coupling edge filtering is performed to obtain cluster filtering data; In one embodiment, the system reads variable coupling graph data. ,in For a set of variable nodes, For the set of variable coupling edges, This is the set of tags for the sources of coupled edges. For any coupled edge... If its source tag contains a common objective function number ,and , Or, the source tag contains the common constraint function number. If the condition is met, the coupled edge is retained; otherwise, it is discarded. The system denotes the set of retained coupled edges as follows: Cluster screening data were obtained. ,in To preserve the source markers corresponding to the coupling edges.

[0047] Cluster boundary correction was performed on the cluster screening data to obtain stable cluster data; In one embodiment, the system reads cluster screening data. According to the preservation of coupling edges Partitioning the variable nodes into connected components yields an initial set of clusters. For each variable node The system counts the number of edges it has within the current cluster. and the number of edges connecting it to other clusters in the original variable coupling graph. .like If so, then the node is corrected to an independent cluster; if If the node is not found to have a shared objective or constraint number, it will be merged into the neighboring cluster with the highest number of shared objectives or constraints. This process yields stable cluster data. , For stable cluster assemblies.

[0048] Based on stable cluster data, dominant variables within the clusters are extracted to obtain compressed mapping data; In one embodiment, the system reads stable cluster data. For any stable cluster The system calculates each variable node within the cluster. Cluster intranode degree And count the number of constraints that the variable participates in. The system prioritizes... The variable with the largest degree is chosen as the dominant variable; if multiple variables have the same degree, then the dominant variable is selected. Larger variables are designated as dominant variables. The system then maps non-dominant variables to the dominant variables based on the objective or constraint numbers they share, resulting in compressed mapping data. ,in for, As the dominant variable, This is a mapping table from variables within a cluster to the dominant variable.

[0049] The compressed mapping data is reconstructed by inter-cluster connections to obtain the sampled skeleton data; In one embodiment, the system reads compressed mapping data. and original variable coupling graph data For any two stable clusters and If the original set of coupled edges There are edges in ,and , Then, a cluster connection edge is established between the two clusters. The target number or constraint number corresponding to the original coupling edge is written into the connection source marker. The system uses the dominant variables of each cluster as skeleton nodes and the cluster connection edges as skeleton edges to obtain sampled skeleton data. ,in For the set of cluster skeleton nodes, For the set of inter-cluster connecting edges, For the set of source tags for inter-cluster connections, inheriting , To compress the mapped data.

[0050] The sampling unit output is obtained by analyzing the sampling skeleton data.

[0051] In one embodiment, the system reads the sampled skeleton data. and task variable data For each stable cluster The system extracts the set of variables it contains. And based on the boundary data of variable values Generate unit variable space The system reads the set of objective functions involved in this cluster. and set of constraint functions and related dominant variables Mapping table Inter-cluster connection edges System output sampling unit And form sampling unit data .

[0052] Preferably, the target conflict ridge extraction specifically involves: Boundary sample neighborhoods are constructed based on boundary hierarchical data to obtain boundary neighborhood data; In one embodiment, the system reads boundary layering data. For the h-th sampling unit The system will form a local sample set by combining the boundary attachment points and internal feasible points belonging to the unit. For any boundary attachment point The system is based on the distance of normalized variables from Select the nearest one Using each sample as a neighborhood point, we obtain the boundary neighborhood data. ,in Let b represent the set of neighborhood samples of the boundary point b. .

[0053] Target gradient data is obtained by calculating the target change gradient on the boundary neighborhood data; In one embodiment, the system reads boundary neighborhood data. and the set of objective functions For boundary point b and its neighboring points The system calculates the target difference. If the variable For continuous variables and That is, neighborhood points If the value of the i-th variable is different from the value of the boundary attachment point b on the i-th variable, then calculate: If multiple neighborhood points exist, the median is taken as the target gradient in the direction of the variable; if no neighborhood points are available, then let... The system obtains the target gradient data. ,in .

[0054] Target conflict data is obtained by performing target conflict determination on the target gradient data; In one embodiment, the system reads target gradient data. For the same boundary point b, the same variable and any two targets The system first normalizes the gradient: ,in If satisfied ,and , If a target conflict exists at that point, a conflict record is generated. ,in , The target conflict intensity value at boundary point b; thus, target conflict data is obtained. .

[0055] Based on the target conflict data, conflict paths are connected to obtain initial ridge data; In one embodiment, the system reads target collision data. and boundary neighborhood data If two targets conflict... and Belonging to the same sampling unit ,and , Ridge point or boundary point The corresponding neighborhood sample set, and the conflict records of the two have the same conflict variable. and the same goal Then the system establishes a conflict connection edge between the two. The system uses all target conflict points as the initial set of ridge points. All conflicting connecting edges are used as the initial ridge edge set. To obtain initial ridge data .

[0056] The initial ridge data is stabilized to obtain conflict ridge data.

[0057] In one embodiment, the system reads initial ridge data. ,right The connected components are then filtered. If the number of nodes in a connected component is less than 3, that component is removed; if multiple conflict records exist for the same ridge point, the conflict strength is retained. The maximum record. The system sets an upper limit on the number of ridge points based on the calculated budget B. When the number of reserved points exceeds At that time, according to Keep the largest from the smallest. Points. The system obtains conflict ridge data. , The set of conflict ridge points represents the set of ridge sampling points that have been identified as target conflict points and retained after stabilization screening. For the set of edges connecting conflict ridges, Data is layered at the boundaries.

[0058] Preferably, the multi-density sampling skeleton generation specifically involves: Ridge segment decomposition is performed based on conflict ridge data to obtain ridge segment data; In one embodiment, the system reads conflict ridge data. Set of conflict ridge points For the set of points, the set of conflict ridges connecting edges Construct a ridge graph for the edge set. The system identifies connected components within the same sampling unit and uses ridge points with a degree not equal to 2 as segment endpoints; if all nodes in a connected component have a degree of 2, then the conflict intensity can be arbitrarily selected. The largest point is taken as the starting point. The system proceeds along... Sequential splitting yields ridge segments ,in , , Number the sampling unit and output the ridge segment data. .

[0059] Based on the ridge segmentation data, sampling density mapping is performed to obtain density stratification data; In one embodiment, the system reads ridge segment data. Calculate the segment conflict intensity for each ridge segment: ,in Let be the conflict intensity at ridge point b. Then set density levels ;like Then set ;like Then set The system determines the number of variables based on the number of sampling units. Determine the number of samples at the center of the ridge segment and output density stratification data. .

[0060] Based on the density stratification data, ridge center sampling nodes are generated to obtain the central skeleton data; In one embodiment, the system reads density stratification data. For each ridge segment The system according to Middle adjacent ridge points Generate center sampling points. For continuous variables, use linear interpolation: , For the first Each ridge center sampling point represents the sampling point between two adjacent ridge points. and The center sampling point obtained by interpolation between them, For the r-th ridge endpoint, For the s-th ridge endpoint, The number of center samples for the l-th ridge segment. The central sampling point number, Using the ridge segment index, for discrete or enumerated variables, the interpolation result is mapped to its set of valid values. The value closest in terms of distance. The system reserves the value that satisfies this condition. And all point, For the first Each sampling unit variable space, For the first The constraint functions at the sampling points The constraint judgment value at the point is used to obtain the set of central sampling nodes. And establish the center edges in ridge order. Obtain the central skeleton data .

[0061] Based on the central skeleton data, a horizontally extended sampling band is constructed to obtain the skeleton network data; In one embodiment, the system reads the central skeleton data. For each central sampling node The system reads its corresponding sampling unit. set of variables For continuous variables Generate horizontal expansion points and Only the i-th variable increases or decreases respectively. , , Let i be the upper limit of the value of the i-th continuous variable. This represents the lower bound of the values ​​of the i-th continuous variable. The number of samples taken from the center of the l-th ridge segment; for discrete or enumerated variables, adjacent values ​​from their valid value set are selected as extended values. System elimination does not satisfy... or The extension point, For the reason , Alternatively, candidate points can be formed by expanding adjacent values ​​of discrete / enumerated variables, and the retained points are connected to the corresponding center nodes to obtain the skeleton network data. , To expand the set of sampling nodes horizontally, This is a set of horizontally expanding connecting edges.

[0062] Interlayer coherence processing is performed on the skeleton network data to obtain sample space data.

[0063] In one embodiment, the system reads skeleton network data. , central sampling node With extended sampling nodes The nodes are merged into a sampling node set V. If two nodes have completely identical variable values, one node is retained and its region type label is merged. The system retains the center edge. Extended edges The system then supplements adjacent edges within the same sampling unit based on the k nearest nodes, resulting in a sampled adjacent edge set E. The system generates attributes for each node. , The node number indicates that the system is a sampling node. The unique identifier assigned, Bind sampling points to nodes to represent sampling nodes. A corresponding set of variable value combinations, The constraint state represents the sampling point. Does it satisfy the variable space and constraint conditions? The region type label indicates which type of sampling region the sampling node originates from, such as the center sampling point. Horizontal expansion points or , Number the sampling unit to which it belongs, indicating the sampling node. Sampling unit The number, The evaluation state of the r-th node indicates whether the sampling node has completed the simulation evaluation, forming a node attribute set A, and outputting sample space data: ,in Represents the sample variable space. Represents the set of sampling nodes. Represents the set of adjacent edges sampled. Represents the set of objective functions. Represents the set of constraint functions. This represents simulation interface data. This indicates the calculation of budget data.

[0064] Preferably, S2 specifically comprises: S21: Perform sample node parsing processing based on the sample space data to obtain simulated node data; In one embodiment, the system reads sample space data. And read the node number of each sampling node from the node attribute set A. Sampling points Constraint state Evaluation status and the sampling unit number The system filters those that meet the requirements. and The sampled nodes (i.e., those that satisfy the constraints but are not evaluated by simulation) are used as the nodes to be simulated, and the node degree is calculated based on the set of adjacent edges E. ,in This represents the r-th sampling node. Indicates sampling node Sampling nodes that are adjacent to each other, where E represents the set of adjacent edges. This indicates that there is an adjacent edge between the two sampling nodes. Indicates sampling node The number of adjacent nodes; the system obtains simulated node data. .

[0065] S22: Construct the simulation input mapping based on the simulation node data to obtain the simulation input parameter data; In one embodiment, the system reads simulated node data. and simulation interface data The system follows The interface input field table, field order, and unit rules will be used to select sampling points. ( Let be the value of the first design variable in the r-th sampling point. Let be the value of the second design variable in the r-th sampling point. Mapping the variable values ​​(for the value of the nth design variable at the rth sampling point) to the interface input vector If the unit of the interface field differs from the unit of the variable, then follow the unit of the interface field. The system will convert the units according to the unit conversion rules. Encapsulated as analog input parameter data .

[0066] S23: Perform deterministic simulation based on the simulated input parameter data to obtain the original simulation data; In one embodiment, the system reads simulated input parameter data. The number of simulated calls in this round is determined based on the calculated budget B. ,and B represents the maximum number of times the simulation interface can be called. The system counts the number of simulation calls that have been used so far. And obtain the remaining calculation budget. The system is based on the set of nodes to be simulated. The number of nodes and the remaining computing budget determine the number of simulation calls in this round: ,in Indicates the number of nodes to be simulated. This indicates the proportion of budget used in this round, which can be taken as 0.2 to 0.5. Non-empty and calculated At that time, the system will Set to 1; when When this happens, the system stops the current round of deterministic simulation calls. The number of nodes to be simulated exceeds When, the system prioritizes The input vector corresponding to the smaller node Perform the simulation. The system calls the simulation interface. ,Will Input a deterministic simulation program and obtain the raw output of the interface. And record the interface status. and simulation time That is, the deterministic simulation program is simulation interface data. The target evaluation procedure is used to evaluate the target based on the interface input vector. For sampling points Perform deterministic target calculations or simulation evaluations. The simulation interface data... At a minimum, it should include the interface address of the deterministic simulation program, input fields, output fields, field units, model version, and calling rules; the system will sample points Mapped to interface input vector Then, the deterministic simulation program is called to obtain the raw output of the interface. And extract to form the target response vector. The system obtains the raw simulation data. .

[0067] S24: Perform multi-objective simulation extraction processing on the original simulation data to obtain the target simulation data; In one embodiment, the original simulation data is read systematically. , set of objective functions and simulation interface data The system is based on The interface output field table in the document, from the original output Extract the output fields corresponding to each objective; if a certain objective function If multiple fields need to be calculated together, then the calculation should be performed according to the objective function expression. The system encapsulates the responses of each target at the same sampling point into... To obtain target simulation data .

[0068] S25: Verify the simulation results based on the target simulation data to obtain the initial simulation data.

[0069] In one embodiment, the system reads target simulation data. Node attribute set A and adjacent edge set E. System verifies interface status. Check if the call was successful. The system checks whether each target response value is missing, non-numerical, or exceeds the preset physical range; after the verification is passed, the system... Read the constraint state from A. And evaluate the status Update to 1, and obtain the updated set of node attributes. For adjacent edges where both ends of the node have been evaluated and both have a target response. System calculation And encapsulate to obtain initial simulation data. .

[0070] Preferably, S3 specifically comprises: S31: Decouple the input and output samples of the initial simulation data to obtain training sample data; In one embodiment, the system reads initial simulation data. and according to From the updated node attribute set Read the evaluation status The system filters those that meet the requirements. , For the call to be successful and The sample, the sampling points As input, the target response vector The output is broken down into individual target outputs. If a node has evaluated neighboring nodes, the intensity of the node's local response change is calculated. If it does not exist, then let The system obtains training sample data. .

[0071] S32: Construct a deep kernel mapping network based on the training sample data to obtain latent space mapping data; In one embodiment, the system reads training sample data. Each sampling point Input deep kernel mapping network The latent space features are obtained as follows: ,in This represents the parameters of the deep kernel mapping network, including the weight matrix, bias vector, and activation function parameters. The system maintains... The correspondences form latent space mapping data: ,in Used for kernel function calculation Used for training the target output.

[0072] S33: Generate a depth kernel function based on the latent space mapping data to obtain kernel representation data; In one embodiment, the system reads latent space mapping data. For the a-th objective, the system takes... Latent space features of any two samples And based on the initial kernel parameters Construct the initial depth kernel function: ,in For node consistency marking, when r=s, it indicates that the same node in the kernel matrix performs kernel calculations with itself. =1; when r≠s, it indicates that kernel calculation is performed between two different sampling nodes. =0, the system relies on latent space characteristics and the training output vector of the a-th target Initialize the depth kernel function parameters. Let represent the initial kernel length scale for the a-th target, which can be taken as the median of the pairwise distances in the latent space of the training samples. The initial signal variance of target a represents the variance of the target a, which can be determined by the sample standard deviation of the training output values ​​of target a. Let represent the initial noise variance of the a-th target, which can be taken as . The system generates an initial kernel matrix in sample order, using either 1% or a preset stable term. Obtain kernel representation data .

[0073] This invention provides an initial depth kernel function, which is used to generate the initial kernel matrix of the a-th target surrogate sub-model. Its essence is based on latent space features. A Gaussian radial basis function kernel is constructed between the two training samples, and a noise stabilizing term is added to the diagonal of the kernel matrix. The system first obtains the corresponding latent space features through a deep kernel mapping network. , Then, based on the Euclidean distance between the two... To measure sample similarity, the closer two samples are in the latent space, the closer the exponent term is to 1, indicating a stronger correlation between their target responses; the farther apart they are, the closer the exponent term is to 0, indicating a weaker correlation.

[0074] S34: Perform Gaussian process prior modeling based on kernel representation data to obtain prior surrogate data; In one embodiment, the system reads kernel representation data. and mapping data from the latent space Extract the training output vector of the a-th target: ,in Represents the r-th training sampling point The true simulated response value under the a-th objective function, where R represents the number of effective training samples. The system operates with a zero-mean function or Using the mean as the mean function, we establish the Gaussian process prior for the a-th objective: The target index, training input, training output, initial kernel matrix, and initial kernel parameters are encapsulated as prior surrogate data. .

[0075] S35: Perform joint marginal likelihood optimization on the prior proxy data to obtain process parameter data; In one embodiment, the system reads prior agent data. Construct the negative log-marginal likelihood for the a-th objective: The system minimizes To achieve the goal, update the deep kernel mapping parameters. nuclear length scale Signal variance and noise variance The updated deep kernel mapping parameters are obtained. nuclear length scale Signal variance and noise variance After optimization, the system recalculates the kernel matrix based on the updated parameters. and its inverse matrix The process parameter data is obtained as follows: .

[0076] This invention provides a formula for calculating the negative logarithmic marginal likelihood, the first term... This represents the fitting error between the training response value and the current kernel model; the smaller the value, the stronger the model's ability to interpret the existing training data. The second term... Volume constraints, representing model complexity or uncertainty, are used to prevent the model from overfitting the training samples; the third term... Let be a constant term determined by the sample size R. This ensures that the a-th target surrogate sub-model fits the existing real simulation samples while avoiding overfitting to a small number of samples.

[0077] S36: Perform multi-objective result fitting on the process parameter data to obtain multi-objective prediction data; In one embodiment, the system reads process parameter data. For any sampling point p, the system first calculates the latent space features using the optimized deep kernel mapping network. Then calculate the kernel vector between the sampling point and the training sample. The system calculates the predicted mean based on the process parameters of the a-th target: The system Calculate each target individually to obtain the multi-target prediction vector: And generate multi-objective prediction data. .

[0078] This invention provides a formula for calculating the predicted mean, based on the kernel similarity between the point p to be predicted and each training sample. Combining the overall correlation structure between training samples Response to existing real targets A relevance-weighted combination is performed to obtain the surrogate predicted response value for the a-th target. If p is more similar to some training samples in the latent space, then these training samples are more relevant to the target's prediction. The contribution of p is greater; if p is far from the existing training samples, its predicted value is more constrained by the overall kernel structure, and the prediction reliability is relatively reduced.

[0079] S37: Quantify the prediction uncertainty of multi-objective prediction data to obtain confidence assessment data; In one embodiment, the system reads multi-target prediction data. and process parameter data For any sampling point p, the system calculates the prediction variance of the a-th target: ,in This represents the prediction standard deviation for the *a*-th objective. The system aggregates the prediction standard deviations of multiple objectives into the prediction uncertainty: and sampling points Predictive response Standard deviation of each target prediction Overall forecast uncertainty and local response change intensity markers Encapsulated as confidence assessment data: .

[0080] S38: Based on the confidence assessment data, organize the agent output to obtain the agent model.

[0081] This invention provides a method for calculating the prediction variance of the a-th target, which is based on the Gaussian process conditional distribution. Due to the training output... The target response at the point to be predicted, along with the target response at point p, follows a joint Gaussian distribution determined by the kernel function. Therefore, given the training output... Then, the conditional variance of the point to be predicted can be expressed as: The first term represents the prior variance of the point to be predicted, and the second term represents the reduction in uncertainty at that point due to the existing training samples. This prediction variance is used to measure the reliability of the surrogate model at the sampling point p. The larger the prediction variance, the more insufficient the training samples near that point or the higher the model uncertainty.

[0082] In one embodiment, the system reads confidence assessment data. Process parameter data and training sample data According to target number Encapsulate each target agent sub-model Each target agent sub-model Including deep kernel mapping parameters nuclear length scale Signal variance Noise variance Training input, training output Optimize kernel matrix Kernel inverse matrix Rules for calculating the predicted mean and predicted variance. The system summarizes these rules to obtain the surrogate model: ,in Let a represent the target agent sub-model of the a-th target.

[0083] Preferably, the real-world simulation verification specifically includes: S41: Evaluate the sample prediction based on the surrogate model to obtain the sample prediction data; In one embodiment, the system reads the proxy model. Sample space data and initial simulation data The system filters constraint states from the node attribute set A. Evaluation status The nodes are used to obtain candidate nodes. and read its bound sampling points The system will Input the target agent sub-model of the a-th target Obtain the agent's predicted response value and the predicted standard deviation The system forms a predicted response vector. And calculate the prediction uncertainty. To obtain sample prediction data .

[0084] S42: Perform validation sample screening on the sample prediction data to obtain validation sample data; In one embodiment, the system reads sample prediction data. And the set of objective functions F. If there is a maximization objective among the objectives, the system first converts it into an equivalent minimization objective, so that all objectives are unified as "the smaller the value, the better". The system then uses the predicted response vector of each candidate sampling point. Constructing predictive nondominated sets If there is no other candidate point Non-inferior in all objectives And at least one objective is superior to ,but The system from Read the initial simulated call count The number of times the call has been used is obtained by combining the historical verification call count. Calculate the remaining budget The system determines the number of verification calls. ,in A value of 0.2 to 0.5 is acceptable, with preference given to values ​​belonging to [specific group / group]. or Samples with values ​​higher than the candidate mean are used to obtain validation sample data. .

[0085] S43: Perform a real simulation based on the verification sample data to obtain the original verification data; In one embodiment, the system reads verification sample data. and simulation interface data The system follows The input field table, field order, and unit rules will be used to verify the sampling points. Mapped to validation input vector System call The program refers to a realistic simulation program or a high-fidelity evaluation program, which will After input, the original verification output of the interface is obtained. The system records the interface status. Simulation time and verify the number of calls If the interface status is failure, timeout, or missing output fields, it is marked as an invalid verification sample; otherwise, it is retained, and the original verification data is obtained. .

[0086] S44: Evaluate the prediction error of the original validation data to obtain simulated validation data.

[0087] In one embodiment, the system reads the original verification data. , set of objective functions Simulation interface data And the set of node attributes A. The system based on Output field rules from the original validation output Extract or calculate the true simulated response value of the a-th target To form the true response vector System calculation verification error And calculate the maximum verification error. For valid verification nodes with valid interface status, the system updates the evaluation status in the node attributes to "evaluated," forming an updated node attribute set. The system encapsulation yielded simulation verification data. .

[0088] Preferably, the iterative optimization specifically involves: Based on the simulation verification data, the prediction residuals are analyzed to obtain the residual evaluation data; In one embodiment, the system reads simulation verification data. Filter interface status This is a verification sample for a successful call. The system reads the proxy model from the previous round. training output set And will add real responses Combined calculation of target response span: The system calculates the normalized residual: ,in The system obtains the maximum normalized residual. Output residual evaluation numbers .

[0089] The residual evaluation data is augmented with training samples to obtain updated sample data. In one embodiment, the system reads residual evaluation data. And the previous proxy model Training sample sets for each target For each verification sampling point The system will realistically simulate the response. Write it into the a-th target training set; if The same sampling points already exist in the middle. Then use Cover the original target response. System formation: Simultaneously, a sample residual label table is generated: Get updated sample data .

[0090] The kernel mapping structure is adjusted based on the updated sample data to obtain optimized structure data. In one embodiment, the system reads updated sample data. And the parameters of the previous deep mapping round The system statistics satisfy... Validation sample ratio .like Then the output dimension of the latent space will be changed from Adjusted to The weights for newly added dimensions are randomly initialized in the range of [-0.05, 0.05], while the weights for existing dimensions are inherited. .like Then, keep the network structure unchanged and only use Used as initial values ​​for continued training. The system outputs structure-optimized data: ,in This represents the initial parameters of the mapping network in this round.

[0091] The Gaussian process parameters are updated on the structural optimization data to obtain the updated model data; In one embodiment, the system reads structural optimization data. For the a-th objective, the system will The sampling points are input into the adjusted mapping network to obtain latent space features: The system according to Reconstruct the kernel matrix And with the objective of minimizing the negative log marginal likelihood, update After training is complete, the system calculates... And output updated model data: .

[0092] The updated model data is integrated with the model output to obtain the surrogate optimization model.

[0093] In one embodiment, the system reads updated model data. and residual assessment data The system is based on the target sequence number. Encapsulate the agent sub-model for optimizing objective a. This includes updated deep mapping parameters, kernel parameters, training sample set, kernel matrix, kernel inverse matrix, prediction mean calculation rules, and prediction variance calculation rules. The system calculates the average maximum residual for this round: This is then written into the model iteration record to obtain the proxy optimization model: .

[0094] Preferably, the present invention also provides a multi-objective simulation optimization system for complex systems based on a surrogate model, used to execute the multi-objective simulation optimization method for complex systems based on a surrogate model as described above, the multi-objective simulation optimization system for complex systems based on a surrogate model comprising: The sampling topology construction module is used to acquire complex system task data; based on the complex system task data, a sampling topology is constructed to obtain sample space data. The deterministic simulation sensing module is used to perform deterministic simulation sensing on sample space data to obtain initial simulation data; The Deep Kernel Gaussian Process (DKG) training module is used to train the surrogate model using a deep kernel Gaussian process on the initial simulation data. The proxy model optimization module is used to perform real-world simulation verification based on the proxy model to obtain simulation verification data; and to iteratively optimize the proxy model based on the simulation verification data to obtain the optimized proxy model.

Claims

1. A multi-objective simulation optimization method for complex systems based on a surrogate model, characterized in that, Includes the following steps: S1: Acquire complex system task data; construct a sampling topology based on the complex system task data to obtain sample space data: The system acquires complex system task data. The complex system task data includes design variable data. , Design variables for the i-th complex system task, where i takes values ​​from 1 to n, and variable boundary data. , Let be the lower limit of the value of the i-th design variable. The upper limit of the value of the i-th design variable, and the objective function data. , Optimize the objective function for the i-th task, and define the constraint data. , For the i-th task constraint decision function, simulation interface data To calculate budget data B, the system first converts all constraints into a unified form. The system adopts a standard form and performs interval normalization on continuous variables based on variable type, establishes legal value numbers for discrete variables, and establishes difference marking rules for enumerated variables. The legal value number refers to the unique number assigned to each allowed value of a discrete variable by the system. The system converts upper limit constraints, lower limit constraints, interval constraints, equality constraints, and business rule constraints in the constraint data into a unified feasibility determination form. ,when When, it means that the candidate sampling point satisfies the constraint, when When this occurs, it indicates that the candidate sampling point violates the constraint in the variable space. The internal sampling point set is generated using stratified sampling or equal-interval sampling. ,in , include as well as The system performs constraint verification on each sampling point, retaining those that satisfy all constraints. The sampling points are taken as the node set V. for The Middle Each sampling point generates a node attribute set based on its variable value, constraint verification result, simulation call status, and interface matching result. Node attribute set This is used to record the node number, variable value, feasibility status, whether it has been evaluated, and the corresponding simulation interface identifier for each sampling node. The system is based on the mixing distance between nodes. The system selects the five nearest legal nodes to each node to form an adjacency edge set E, resulting in a sampling topology T=(V,E). The system encapsulates the variable space, sampling nodes, adjacency edges, objective function, constraints, simulation interface, computational budget, and node attributes into sample space data. ； S2: Perform deterministic simulation sensing on the sample space data to obtain initial simulation data: the system reads the sample space data. Based on the node attribute set A, sample nodes that meet the feasibility requirements but have not yet been evaluated are selected from the node set V, i.e., those that meet the constraints but have not yet had their simulation interface invoked. The sampling nodes used in the deterministic simulation yield the set of nodes to be simulated. If And satisfy all ,but , indicates feasibility; otherwise , indicating that it is not feasible. For the constrained state, the system reads Each node to be simulated corresponding Medium sampling point and verify And satisfy all constraints The system determines the number of simulated calls in this round based on the calculated budget B. ,and ;when The number of nodes exceeds When simulating, nodes with fewer than k / 2 adjacent nodes are selected first, and the system follows the simulation interface data. sampling points The input vector is converted into an interface vector, and under fixed model version, fixed boundary conditions, and fixed random seeds, a deterministic simulation interface is called to obtain the target response vector. ,in This represents the r-th sampling point. This represents the target response value of the r-th sampling point under the objective function of the a-th task. , This represents the total number of optimization objectives. The objective response value includes at least one of the following: computation count response value, time response value, energy consumption response value, efficiency response value, reliability response value, or service level response value. (Node) Corresponding sampling points The state after calling the simulation interface is considered the interface state, including call success, call failure, timeout, and output exception. This applies to adjacent edges where both ends of the node have completed simulation. Simultaneously, the corresponding nodes are updated to be evaluated, and the system calculates the adjacency response difference. , To and For another sampling point that is adjacent to it, the system will number the node. Sampling points The initial simulation data consists of the target response, constraint state, number of simulation calls, interface state, adjacency response differences, and the updated set of node attributes. ； S3: Train the surrogate model using a deep kernel Gaussian process on the initial simulation data: The system reads the initial simulation data. Filter the constraint states Interface status For nodes that were successfully invoked and whose evaluation status is "evaluated", a valid training sample set is formed. The system calculates the intensity of local response changes at nodes based on the differences in adjacent responses. and will As high-variable regions, these are written into the training samples, and the system will use the sampling points... As model input, the target response vector The a-th target response value As output, construct a single-objective training set. The system will Inputting into a deep feature mapping network yields feature vectors. , Indicated by network parameters A defined feature mapping function, Including the weights, biases, and activation parameters of each hidden layer, the deep feature mapping network employs a three-layer feedforward network, including an input layer, a first hidden layer, a second hidden layer, and a feature output layer. If the sampling points... If the variable dimension is n, then the number of neurons in the first hidden layer is 32, the number of neurons in the second hidden layer is 16, and the feature output dimension is 8; the weight matrix of the first hidden layer... Initialize to random numbers in the interval [-0.1, 0.1], bias vector Initialized to 0; second hidden layer weight matrix Initialize to random numbers within the interval [-0.08, 0.08], bias vector Initialized to 0; Feature output layer weight matrix Initialize to random numbers within the interval [-0.05, 0.05], bias vector Initialize to 0, and the activation function can be the LeakyReLU function: ,in The slope parameter of the negative half-axis is taken as... Construct a deep kernel function based on feature vectors: ,in Let be the kernel length scale corresponding to the a-th target. Let V be the signal variance, representing the magnitude of change in the a-th target response value itself. The noise variance represents the allowable small numerical error or observation noise intensity in the simulation results. For node consistency marking, when r=s, meaning both indices point to the same sampling node, ;when That is, when two indices point to different sampling nodes, ; The system updates the depth mapping parameters by maximizing the marginal likelihood based on the training samples. And kernel parameters, to obtain the depth kernel Gaussian process sub-model corresponding to the a-th target; for After training them one by one, the surrogate model is obtained. , This represents the target surrogate sub-model for the a-th objective, used to predict its target response value under the objective function of the a-th task based on the sampling point p. , , Indicates the total number of optimization objectives; S4: Perform real-world simulation verification based on the proxy model to obtain simulation verification data; iteratively optimize the proxy model based on the simulation verification data to obtain the optimized proxy model; the system reads the proxy model. and initial simulation data Filter constraint states from the sample space Furthermore, for candidate sampling points whose evaluation status is "unevaluated", a verification candidate set is obtained. The system will select candidate sampling points Input each target agent sub-model , The ordinal term, with values ​​from 1 to m, yields the predicted target response or predicted response. , For the first target agent sub-model For sampling points The primary objective outcome of the forecast includes predicted cost response values, predicted delivery delay response values, or other pre-defined primary concerns. For the second target agent sub-model For sampling points The predicted second objective outcome includes the predicted time response value or efficiency response value. For the first Target Agent Submodel For sampling points The final target result obtained from the prediction is used to obtain the output prediction mean based on the predicted target response. It also outputs the prediction variance. The prediction uncertainty is obtained by summing the standard deviations of each target prediction, specifically: ,in This indicates that the a-th target surrogate sub-model is related to the sampling points. The standard deviation of the prediction The larger the value, the more uncertain the surrogate model's prediction for that sampling point. The system predicts the response vector based on the surrogate of the candidate sampling point. Construct a predicted non-dominated solution set. If a candidate sampling point belongs to the predicted non-dominated solution set, it is determined that it is near the non-dominated boundary. The system prioritizes prediction results that are near the non-dominated boundary and have low prediction uncertainty. Higher than the mean of the candidate set, or the intensity of local response changes in the adjacent region The candidate sampling points located in the top 20% of the candidate set form the set of real simulation verification points. The system calculates the remaining budget. Determine the number of verification calls ,and System call simulation interface right The actual target response is obtained by performing a realistic simulation using mid-sample points. ,in This represents the t-th verification sampling point. Indicates sampling point via simulation interface The actual simulated response value of the a-th objective obtained after performing a realistic simulation is the actual response. , This represents the total number of optimization objectives, and the verification error is calculated. The system encapsulates verification points, predicted responses, actual responses, prediction uncertainty, verification errors, interface status, and cumulative call counts into simulated verification data. The system reads simulation verification data. Filter the verification samples whose API call status is successful to obtain the valid verification sample set: ,in To verify the sampling points, To realistically simulate the response, For proxy response prediction, Let be the verification error for the a-th target. To predict uncertainty, the system will realistically simulate the response. Write the training set corresponding to the a-th target to form the updated training set: ,in For the original training set or single-target training set corresponding to the a-th target, To verify the intensity of local response changes in the adjacent region of the sampling point, the system determines whether the surrogate model needs local correction based on the verification error. If so: Then, the verification sampling point is marked as an error correction sample, where Let be the error threshold for the a-th target. , For the maximum true response value of the a-th objective, To determine the minimum true response value for target a, the system uses the original depth mapping parameters. Using kernel parameters as initial parameters, based on updating the training set Remaximizing the marginal likelihood for depth mapping parameters and kernel length scale Signal variance and noise variance The update is performed to obtain the updated target agent sub-model of the a-th generation. The system The above updates are executed one by one, and the prediction-real simulation-error correction-model update process is repeated as long as the remaining computational budget meets the conditions, until the maximum verification error of all targets does not exceed the corresponding threshold, or the cumulative number of simulation calls reaches the computational budget B. The system then encapsulates the updated target proxy sub-models into proxy optimization models. ,in This represents the surrogate optimization model obtained after verification through real simulation and error correction.

2. The method according to claim 1, characterized in that, The sampling topology construction is specifically as follows: Task variable data is obtained by performing heterogeneous task interpretation based on complex system task data. Variable coupling weaving is performed based on task variable data to obtain variable coupling graph data; Coupled cluster compression is performed on the variable coupling graph data to obtain sampled cell data; Constraint boundary attachment mapping is performed on the sampled unit data to obtain boundary layer data; Target conflict ridges are extracted from the boundary layered data to obtain conflict ridge data; Multi-density sampling skeletons are generated based on conflict ridge data to obtain sample space data.

3. The method according to claim 2, characterized in that, Coupling cluster compression specifically involves: Based on the variable coupling graph data, coupling edge filtering is performed to obtain cluster filtering data; Cluster boundary correction was performed on the cluster screening data to obtain stable cluster data; Based on stable cluster data, dominant variables within the clusters are extracted to obtain compressed mapping data; The compressed mapping data is reconstructed by inter-cluster connections to obtain the sampled skeleton data; The sampling unit output is obtained by analyzing the sampling skeleton data.

4. The method according to claim 2, characterized in that, The specific steps for extracting the target conflict ridge are as follows: Boundary sample neighborhoods are constructed based on boundary hierarchical data to obtain boundary neighborhood data; Calculate the target gradient by performing target change gradient calculation on the boundary neighborhood data to obtain target gradient data; Target conflict data is obtained by performing target conflict determination on the target gradient data; Based on the target conflict data, conflict paths are connected to obtain initial ridge data; The initial ridge data is stabilized to obtain conflict ridge data.

5. The method according to claim 2, characterized in that, The multi-density sampling skeleton generation is specifically as follows: Ridge segment decomposition is performed based on conflict ridge data to obtain ridge segment data; Based on the ridge segmentation data, sampling density mapping is performed to obtain density stratification data; Based on the density stratification data, ridge center sampling nodes are generated to obtain the central skeleton data; Based on the central skeleton data, a horizontally extended sampling band is constructed to obtain the skeleton network data; Interlayer coherence processing is performed on the skeleton network data to obtain sample space data.

6. The method according to claim 1, characterized in that, S2 specifically refers to: Sample node data is obtained by parsing the sample space data. Simulation input parameter data is obtained by constructing a simulation input mapping based on the simulation node data. Deterministic simulation is performed based on the simulated input parameter data to obtain the original simulation data; The original simulation data is subjected to multi-objective simulation extraction processing to obtain the target simulation data; The simulation results are verified based on the target simulation data to obtain the initial simulation data.

7. The method according to claim 1, characterized in that, S3 specifically refers to: Input and output samples are decoupled from the initial simulation data to obtain training sample data; A deep kernel mapping network is constructed based on the training sample data to obtain latent space mapping data; The deep kernel function is generated based on the latent space mapping data to obtain the kernel representation data; Gaussian process prior modeling is performed based on kernel representation data to obtain prior surrogate data; The process parameter data is obtained by performing joint marginal likelihood optimization on the prior proxy data; Multi-objective result fitting is performed on the process parameter data to obtain multi-objective prediction data; Quantify the prediction uncertainty of multi-objective prediction data to obtain confidence assessment data; The proxy output is processed based on the confidence assessment data to obtain the proxy model.

8. The method according to claim 1, characterized in that, The specific details of the real-world simulation verification are as follows: The sample prediction evaluation is performed based on the surrogate model to obtain sample prediction data; The predicted sample data is used to screen validation samples to obtain validation sample data. The original validation data is obtained by performing a realistic simulation based on the validation sample data. The prediction error is evaluated on the original validation data to obtain simulated validation data.

9. The method according to claim 1, characterized in that, The iterative optimization specifically includes: Based on the simulation verification data, the prediction residuals are analyzed to obtain the residual evaluation data; The residual evaluation data is augmented with training samples to obtain updated sample data. The kernel mapping structure is adjusted based on the updated sample data to obtain optimized structure data. The Gaussian process parameters are updated on the structural optimization data to obtain the updated model data; The updated model data is integrated with the model output to obtain the surrogate optimization model.

10. A multi-objective simulation optimization system for complex systems based on a surrogate model, characterized in that, For executing the surrogate model-based multi-objective simulation optimization method for complex systems as described in claim 1, the surrogate model-based multi-objective simulation optimization system for complex systems comprises: The sampling topology construction module is used to acquire complex system task data; based on the complex system task data, a sampling topology is constructed to obtain sample space data. The deterministic simulation sensing module is used to perform deterministic simulation sensing on sample space data to obtain initial simulation data; The Deep Kernel Gaussian Process (DKG) training module is used to train the surrogate model using a deep kernel Gaussian process on the initial simulation data. The proxy model optimization module is used to perform real-world simulation verification based on the proxy model to obtain simulation verification data; and to iteratively optimize the proxy model based on the simulation verification data to obtain the optimized proxy model.

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