Parallel multi-objective optimization method and system for engineering product CAE simulation

Abstract

The application relates to a parallel multi-objective optimization method and system for engineering product CAE simulation, and belongs to the technical field of simulation optimization. The method solves the problems that the simulation-driven design cycle is long and it is difficult to obtain a high-quality multi-objective trade-off optimization scheme. The method comprises the following steps: based on multiple objective functions and constraint conditions, initial sample data is obtained through two-stage collaborative optimization and is put into a sample library; a joint surrogate model is constructed and trained, and a hierarchical error compensation mechanism is initialized; multiple rounds of iterative optimization are performed until a preset optimization termination condition is met; each round of iterative optimization comprises the following steps: based on the current joint surrogate model and the hierarchical error compensation mechanism, multiple candidate design points are generated in parallel, and then the multiple candidate design points are distributed to multiple computing nodes for parallel simulation calculation to obtain new sample data which is put into the sample library; the joint surrogate model and the hierarchical error compensation mechanism are updated; and a multi-objective optimization design scheme set of a product to be optimized is obtained from the final sample library. The optimization efficiency is improved.

Description

Technical Field

[0001] This invention relates to the field of simulation optimization technology, and in particular to a parallel multi-objective optimization method and system for CAE simulation of engineering products. Background Technology

[0002] With the increasing complexity of multiphysics coupled CAE simulation optimization problems in fields such as aerospace and automotive engineering, engineering designs often need to simultaneously optimize 5-20 design objectives and satisfy 10-50 nonlinear constraints, forming complex high-dimensional multi-objective optimization problems. These problems typically require the use of computationally expensive simulation programs, with a single simulation taking anywhere from several minutes to several hours, posing a significant computational challenge to traditional optimization methods.

[0003] In the history of technological development, multi-objective optimization methods have evolved from traditional mathematical programming to intelligent optimization algorithms. Early methods such as Sequential Quadratic Programming (SQP) performed well on small-scale problems, but faced computational inefficiencies when dealing with high-dimensional problems, especially in parallel computing environments. Even when deployed on a 100-core cluster, these serial computation-based algorithms typically achieved a parallel speedup of less than 30%, resulting in significant waste of computational resources. Subsequent evolutionary algorithms, such as NSGA-II, made progress in population optimization, but their requirement for extensive function evaluation still presents efficiency bottlenecks in computationally intensive problems. To reduce computational costs, surrogate model techniques were introduced into the optimization field, replacing expensive real simulations by constructing approximate models of the objective function and constraints. Surrogate models can reduce the number of simulation calls to some extent, accelerating the optimization process.

[0004] However, existing multi-objective optimization techniques based on surrogate models still have significant shortcomings: First, these models need to be completely retrained after each sampling, and a single model update can take several hours on about 10 objective problems, which seriously affects optimization efficiency; Second, fixed batch processing strategies cannot adapt to the computational needs of different stages of the optimization process, resulting in a computational resource idle rate of up to about half; In addition, existing methods are inefficient when dealing with expensive constraints and it is difficult to achieve an effective balance between objective optimization and constraint satisfaction. Summary of the Invention

[0005] Based on the above analysis, the embodiments of the present invention aim to provide a multi-objective optimization method and system for CAE simulation of engineering products, in order to solve the problems of low utilization of computing resources and efficiency of proxy model updates, as well as inflexible task allocation strategies in the existing high-dimensional multi-objective optimization, which leads to a long cycle of CAE simulation-driven design of engineering products and makes it difficult to obtain high-quality design solutions that meet multiple performance requirements within limited resources.

[0006] On one hand, embodiments of the present invention provide a parallel multi-objective optimization method for CAE simulation of engineering products, comprising the following steps:

[0007] Based on the CAE simulation objectives of the product to be optimized, design variables, multiple objective functions, and constraints are determined. Initial sample data is obtained through two-stage collaborative optimization and placed into a sample library. A joint agent model is constructed based on multiple objective functions and constraints, and the joint agent model is trained using a sample library to initialize a hierarchical error compensation mechanism. Multiple rounds of iterative optimization are performed until a preset optimization termination condition is met, resulting in the final sample library. Each round of iterative optimization includes: generating multiple candidate design points in parallel based on the current joint surrogate model and hierarchical error compensation mechanism; distributing the multiple candidate design points to multiple computing nodes for parallel CAE simulation calculations to obtain the simulation response value corresponding to each candidate design point; adding the candidate design points and their simulation response values ​​to the sample library; and updating the joint surrogate model and hierarchical error compensation mechanism using the updated sample library for the next round of iterative optimization. Obtain a set of multi-objective optimization design schemes for the product to be optimized from the final sample library.

[0008] Based on further improvements to the above method, a two-stage collaborative optimization includes: In the first stage, multiple objective functions are solved in parallel as sub-problems. The overall objective function is constructed by weighted summation of each objective function and the introduction of penalty terms for constraints, resulting in multiple sets of design variables that constitute the preliminary design point set. In the second stage, the initial design point set is merged with the design points obtained through Latin hypercube sampling to form the initial population; the initial population is optimized using a non-dominated sorting genetic algorithm accelerated by GPU parallelism, and the output non-dominated solution set is used as the initial sample data.

[0009] Based on further improvements to the above method, the overall objective function is expressed by the following formula: , in, Design points The total objective function value; Indicates the number of objective functions. Indicates the number of constraints; Design points The corresponding number The objective function value is the actual value output by the simulation model; Indicates the first The weights of the objective functions are set as follows: ; Indicates the penalty coefficient. Design points The corresponding number The value of each constraint condition.

[0010] Further improvements to the above method involve constructing a joint surrogate model based on multiple objective functions and constraints. This includes: using a Gaussian regression model to independently model each objective function and a neural network model to independently model each constraint, and then combining them to obtain the joint surrogate model.

[0011] Based on the above method, a further improvement is made to the initialization of the hierarchical error compensation mechanism, including: Based on the output of the joint agent model to the initial sample data, the initial target confidence weight and initial constraint penalty weight are obtained, and then the total predicted compensation value of each design point in the sample library is calculated.

[0012] Based on further improvements to the above method, the hierarchical error compensation mechanism calculates the total prediction compensation value using the following formula: , in, Design points Total predicted compensation value, Indicates the number of objective functions. Indicates the number of constraints. In the joint agency model, the first... The target confidence weights of the model with each objective function. ∈[0,1]; In the joint agency model, the first... The model of the objective function for the design point The standard deviation of the output prediction; In the joint agency model, the first... The maximum predicted standard deviation of the model with each objective function for the design point of the current batch is used for normalization. This indicates a violation of the weight constraint. ∈[0.1,1]; In the joint agency model, the first... The model with several constraints is for the design point. Output of constrained predicted values, Indicates the first The upper limit of a constraint condition; Indicates the first The constraint tolerance range of each constraint condition is used for normalization; This indicates taking the maximum value.

[0013] Based on further improvements to the above method, multiple candidate design points are generated in parallel using an improved Chebyshev scalarization method, including: The ideal reference point for the current iteration is obtained from the optimal solution of several iterations based on a sliding window. Based on an ideal reference point, multiple improved Chebyshev scalar quantum problems are constructed by sampling from the Dirichlet distribution to generate multiple weight vectors, and by introducing the total predicted compensation value and balance coefficient obtained by the current hierarchical error compensation mechanism. Multiple candidate design points are generated by solving the improved Chebyshev scalar quantum problem in parallel.

[0014] Based on the above method, the improved Chebyshev scalar quantum problem is expressed by the following formula: , in, Indicates the first One candidate design point, Indicates the number of objective functions. This indicates the use of the first agent in the joint agent model. The model of the objective function for the design point Output target prediction value, Indicates the first An ideal reference point for each objective function; Indicates the first The range of variation of the target predicted value of each objective function; This indicates the current hierarchical error compensation mechanism for the design point. The total predicted compensation value is calculated. Indicates the balance coefficient; Indicates the generation of the first When selecting the candidate design point, the weight vector from the generated weight vector is used. The weight components of each objective function.

[0015] Based on the further improvement of the above method, multiple candidate design points are assigned to multiple computation nodes, including: Based on the target prediction value output by the joint agent model for each candidate design point, calculate the target spatial distance between any two candidate design points; based on the target spatial distance, use a clustering algorithm to divide multiple candidate design points into multiple groups; Based on the number of multiple candidate design points and the current number of CPU cores, obtain the number of compute nodes; assign each group to a compute node.

[0016] On the other hand, embodiments of the present invention provide a parallel multi-objective optimization system for CAE simulation of engineering products, comprising: The initial sample generation module is used to determine design variables, multiple objective functions, and constraints based on the CAE simulation objectives of the product to be optimized, and to obtain initial sample data through two-stage collaborative optimization and put it into the sample library; The joint agent model construction module is used to construct a joint agent model based on multiple objective functions and constraints, train the joint agent model using a sample library, and initialize the hierarchical error compensation mechanism. The candidate design point generation module is used to perform multiple rounds of iterative optimization until a preset optimization termination condition is met, resulting in the final sample library. Each round of iterative optimization includes: generating multiple candidate design points in parallel based on the current joint surrogate model and hierarchical error compensation mechanism; distributing the multiple candidate design points to multiple computing nodes for parallel CAE simulation calculations to obtain the simulation response value corresponding to each candidate design point; adding the candidate design points and their simulation response values ​​to the sample library; and updating the joint surrogate model and hierarchical error compensation mechanism using the updated sample library for the next round of iteration. The optimization scheme acquisition module is used to obtain a set of multi-objective optimization design schemes for the product to be optimized from the final sample library.

[0017] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects: 1. By constructing a complete technical closed loop of "intelligent initialization - iterative proxy model optimization - dynamic resource allocation", the system systematically solves the long-standing problems of high computational cost, low resource utilization and slow convergence speed in the field of computationally intensive multi-objective optimization. It deeply integrates the powerful fitting ability of deep learning, the global search ability of multi-objective evolutionary algorithms and the efficient execution ability of high-performance parallel computing, and improves optimization efficiency while ensuring the convergence and diversity of Pareto fronts. It provides a practical and feasible automated and intelligent solution for simulation-driven design of complex engineering products.

[0018] 2. A two-stage collaborative optimization initial solution set generation mechanism is proposed. By using GPU parallel acceleration to solve multiple sub-problems and combining it with the accelerated NSGA-II refining strategy, the generation efficiency and quality of the initial solution set are significantly improved, thereby enhancing the efficiency and stability of the overall optimization process from the source.

[0019] 3. A joint surrogate model with decoupled modeling of objectives and constraints is adopted, and combined with a hierarchical error compensation mechanism, the confidence weight of the objective and the penalty weight of the constraint are adaptively adjusted, which effectively balances the relationship between objective optimization and constraint satisfaction, and realizes intelligent perception of the local prediction accuracy of the model and dynamic guidance on the feasibility of the optimization process.

[0020] 4. Based on the improved Chebyshev scalarization method, high-quality candidate design points are generated, achieving a dynamic and intelligent balance between "utilizing the currently known optimal information" and "exploring unknown high-potential areas". Through intelligent clustering based on target space prediction, similar candidate points are grouped, and parallel computing is performed using a dynamic load balancing strategy, realizing intelligent allocation and efficient utilization of computing resources.

[0021] In this invention, the above-described technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of this invention will be set forth in the following description, and some advantages may become apparent from the description or be learned by practicing the invention. The objects and other advantages of this invention can be realized and obtained from what is particularly pointed out in the description and drawings. Attached Figure Description

[0022] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts. Figure 1 This is a flowchart of a parallel multi-objective optimization method for CAE simulation of engineering products in Embodiment 1 of the present invention. Detailed Implementation

[0023] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0024] Example 1 A specific embodiment of the present invention discloses a parallel multi-objective optimization method for CAE simulation of engineering products, such as... Figure 1 As shown, it includes steps S1-S4.

[0025] S1. Based on the CAE simulation objectives of the product to be optimized, design variables, multiple objective functions, and constraints are determined. Initial sample data is obtained through two-stage collaborative optimization and placed into the sample library.

[0026] Based on the specific engineering simulation optimization objectives, a complete optimization problem is defined, and then a batch of initial sample data with good diversity and convergence and its true performance data (i.e. response values) are efficiently obtained through a two-stage collaborative optimization method.

[0027] In CAE simulation, design variables include, but are not limited to: geometrical parameters, material property parameters, load condition parameters, and boundary condition parameters. Response values ​​obtained from CAE simulation calculations are scalar or field variables used to evaluate product performance, including but not limited to: structural mass properties, mechanical response, thermal response, fluid dynamics response, or multi-physics coupled response. For example, response values ​​include: structural mass, moment of inertia; structural stress values, strain values; deformation displacement; vibration frequency, mode shape; temperature field distribution values; flow field characteristic parameters; or multi-physics coupled response parameters.

[0028] This embodiment takes the lightweight design scenario of the B-pillar of a car body as an example. In this scenario, it is first necessary to determine the design variables, multiple objective functions and constraints in the multi-objective optimization problem according to the simulation objectives.

[0029] The design variables are selected based on design experience and process requirements, focusing on parameters that are critical to performance and are manufacturable. These include the thickness of the sheet metal in the upper, middle, and lower regions of the B-pillar, and the height and width of the internal reinforcing ribs. The design space is composed of all possible combinations of design variables within their value ranges. A set of specific assigned design variables in the design space is a specific instance within the design space, corresponding to a design point.

[0030] The objective functions and constraints are quantified into data functions and constraints based on the simulation objectives of side-impact safety, lightweighting, and cost control. There are three objective functions: minimizing the weight of the B-pillar, minimizing its maximum intrusion in the side-impact simulation, and minimizing cost. The constraints include: the maximum stress does not exceed the material yield strength and the displacement of key points does not exceed the safety threshold.

[0031] Furthermore, the two-stage collaborative optimization includes: ① In the first stage, multiple objective functions are solved in parallel as sub-problems. The overall objective function is constructed by weighted summation of each objective function and the introduction of penalty terms for constraints, thus obtaining the preliminary design point set.

[0032] It should be noted that the parallel computing capabilities of the GPU are used to solve each sub-problem in parallel, including: A unified CUDA kernel function is written for each subproblem. This kernel function encapsulates the mathematical definition of the subproblem and its gradient calculation. At runtime, multiple kernel function instances are dynamically mapped and allocated to multiple streaming multiprocessors (SMs) on the GPU for concurrent execution by calling the CUDA runtime library. Each SM is independently responsible for solving a subproblem, and intermediate data is exchanged and synchronized through the GPU's global memory.

[0033] The candidate solutions obtained need to satisfy the constructed overall objective function, expressed by the following formula: , in, Design points The total objective function value; Indicates the number of objective functions. Indicates the number of constraints; Design points The corresponding number The objective function value is the actual value output by the simulation model; Indicates the first The weights of the objective function are typically set as follows: To ensure balanced optimization of all objectives; Indicates the penalty coefficient. Design points The corresponding number The value of each constraint condition.

[0034] It should be noted that the penalty coefficient An adaptive adjustment mechanism is employed, the logic of which is encoded in the host-side control program. This program monitors constraint violations in all subproblems and dynamically adjusts accordingly. The numerical values ​​are used to intelligently balance the relationship between "objective function optimization" and "constraint satisfaction" during the optimization process, and parameters are passed between the GPU global memory and the kernel functions of each subproblem.

[0035] During implementation, in each solution process, the violation rate and average violation intensity are calculated based on the total constraint violations for each candidate solution, and then normalized; where the violation rate... It is the proportion of candidate solutions with a total constraint violation greater than 0 out of all candidate solutions; average violation intensity. It is the average of the total number of constraint violations in the candidate solutions that violate the constraints.

[0036] When there are many candidate solutions that violate the constraints and the degree of violation is severe, the penalty coefficient should be increased significantly. To strengthen the penalty, the search direction is forced to quickly return to the feasible region; when the violation is minor or most candidate solutions are feasible, the penalty is appropriately reduced. This is to avoid excessively strong penalty terms distorting the optimization of the original objective function, thus allowing more focus on optimizing the objective.

[0037] The penalty coefficient is calculated using the following formula. Make dynamic adjustments: , in, and These represent the penalty coefficients before and after the adjustment, respectively; and These represent the lower and upper limits of the adjusted penalty coefficient, respectively. They are usually determined based on the magnitude relationship between the objective function and the constraint violation, to ensure that the two have comparable influence in the optimization process and to avoid one of them dominating the overall objective function. This indicates the adjustment strength coefficient, which is usually set to [0.5, 2.0] based on engineering practice and numerical stability considerations, in order to control the sensitivity of the penalty coefficient to constraint violations.

[0038] Ultimately, multiple optimal solutions that minimize the overall objective function are obtained, resulting in a preliminary, diverse set of design points. For example, to increase the diversity of solutions, several representative solutions are selected from the multiple elite solutions saved during the optimization process to obtain the preliminary set of design points.

[0039] This stage fully leverages the parallel computing capabilities of GPUs, distributing multiple subproblems across different streaming multiprocessors (SMs) for simultaneous solution. Each SM unit independently processes the optimization computation of one subproblem, sharing intermediate results via global memory. This parallel architecture offers a 5-10 times improvement in solution efficiency compared to traditional CPU serial computation, making it particularly suitable for engineering optimization problems with high objective dimensions.

[0040] ② In the second stage, the preliminary design point set is merged with the design points obtained through Latin hypercube sampling to form the initial population; the initial population is optimized by a non-dominated sorting genetic algorithm accelerated by GPU parallelism, and the output non-dominated solution set is used as the initial sample data.

[0041] The initial design point set obtained in the first stage is merged with the additional design points generated through Latin hypercube sampling to form a large-scale initial population. The objective vector data (i.e., objective function value) of each individual in the initial population is transferred in batches to GPU memory, and the NSGA-II algorithm (non-dominated sorting genetic algorithm) with deep acceleration via CUDA is used to perform evolutionary optimization on this population. The computationally intensive non-dominated sorting and crowding distance calculations are ported to the GPU for execution, and the optimization process is significantly accelerated by comparing the dominance relationships between individuals in parallel using thousands of threads. After several generations of evolution, the algorithm selects several of the most representative non-dominated solutions as the initial anchor point set based on the non-dominated level and crowding distance.

[0042] Specifically, GPU-accelerated threads are coded using PyTorch's Tensor operations or directly in CUDA C++ and encapsulated into easily callable functions. Finally, a specified number of individuals with the best non-dominated level and maximum crowding distance are selected from the optimized population to form the final high-quality initial solution set. Its size is determined to be 1.5 times the number of multi-objective optimization problems K, rounded up; this is the initial solution set size. One, to ensure that the number of solution sets matches the dimensions of the problem.

[0043] Finally, in the finite element simulation software, the design points in the initial solution set are evaluated in parallel to obtain the corresponding true objective function values ​​and constraint values, such as precise weight, intrusion amount, cost, stress and displacement data. These are stored as initial sample data in a centralized sample library in the form of "design variable-actual performance" data pairs.

[0044] S2. Construct a joint agent model based on multiple objective functions and constraints, train the joint agent model using a sample library, and initialize the hierarchical error compensation mechanism.

[0045] This embodiment employs a hybrid modeling strategy to construct a joint objective-constraint surrogate model. This involves modeling the objective function and constraints using different machine learning methods and then combining them into a unified prediction model, as shown in the following expression: , in, This represents a goal-constraint joint agent model. Indicates the first A proxy model for a single objective function. Indicates the first A neural network model with several constraints. Indicates combination, This indicates the transpose operation.

[0046] Specifically, a Gaussian regression model is used to independently model each objective function, and a neural network model is used to independently model each constraint condition. These are then combined to obtain a joint objective-constraint surrogate model.

[0047] It should be noted that the objective function is modeled using a Gaussian regression model (Kriging), which not only predicts the target value but also provides prediction uncertainty to guide subsequent sampling. The kernel function in the model uses the Matern 5 / 2 kernel, suitable for high-dimensional nonlinear optimization problems. Constraints are modeled using neural network models, such as radial basis function neural networks or fully connected neural networks with multiple hidden layers, to enhance the fitting ability to complex constraints. Compared to traditional polynomial response surfaces, neural networks can better capture nonlinear constraint relationships, such as engineering constraints like strength and deformation. The various models are decoupled during training.

[0048] When training the joint surrogate model using a sample library, the hyperparameters of each objective function model are optimized using methods such as maximum likelihood estimation to ensure its ability to fit high-dimensional nonlinear problems.

[0049] Taking the modeling of the objective function "minimizing the weight of column B" as an example, the training process is based on multiple sample data (design variables, actual weights). First, the design variables are preprocessed by normalization. Then, by maximizing the marginal likelihood function of the Gaussian process, the optimal hyperparameters of the model are automatically learned using the L-BFGS-B optimizer, including the feature length scale of the kernel function, signal variance, and noise variance. After training, the model not only provides a predicted weight for the new design point but also simultaneously calculates the prediction standard deviation to reflect the prediction uncertainty.

[0050] The structural parameters of the neural network corresponding to each constraint, such as the number of hidden layers and the number of neurons, are configurable options that can be set by the user according to the complexity of the problem. During training, mean squared error is used as the loss function, and iterative training is performed using optimizers such as Adam to capture the complex nonlinear relationship between the constraints and the design variables.

[0051] For example, in the lightweight design scenario of the B-pillar of a car body, there are two constraints: a maximum stress constraint model is established to ensure that the maximum stress does not exceed the material yield limit; and a key point displacement constraint model is established to ensure that the key point displacement does not exceed the safety threshold. The two constraint models share the same input layer (design variables) but have independent output layers and network parameters.

[0052] The maximum stress constraint model is trained using design variables from multiple samples in the sample library and the actual maximum stress. This trains the model to learn the nonlinear mapping relationship between plate thickness, stiffener size, and the maximum structural stress in each region, outputting the predicted maximum stress of the B-pillar in a side-impact simulation. The connection point between the upper part of the B-pillar and the roof beam is selected as a key point. The displacement constraint model for this key point is trained using design variables from multiple samples in the sample library, learning the mapping relationship between the design variables and the displacement response generated by the key point, outputting the predicted displacement of the key point. If multiple key points are considered, a structurally similar but parameter-independent model is built for each key point.

[0053] Furthermore, after all models are trained, a unified joint prediction interface is set up for the obtained objective-constraint joint surrogate model. As an intelligent surrogate model that quickly approximates the input-output relationship, it receives a design variable vector as input, and then synchronously calls all trained objective function models and constraint models. Finally, it summarizes and outputs the combined prediction vector, including: all objective prediction values ​​and prediction standard deviations (prediction uncertainty), as well as all constraint prediction values, laying the foundation for subsequent efficient iterative optimization.

[0054] It should be noted that due to the prediction error inherent in the surrogate model, direct use may cause the optimization to deviate from the true Pareto front. Therefore, to further improve the reliability and efficiency of the optimization process, this embodiment introduces a hierarchical error compensation mechanism. This mechanism dynamically adjusts the target confidence weights and constraint violation weights of each objective function model to calculate the total prediction compensation value at the design point, which consists of two parts: the target prediction error compensation value and the constraint violation penalty value, as shown in the following formula: , in, Design points Total predicted compensation value, Indicates the first The target confidence weights of the surrogate model for each objective function. ∈[0,1]; In the joint agency model, the first... The model of the objective function for the design point The standard deviation of the output prediction; In the joint agency model, the first... The maximum predicted standard deviation of the model with each objective function for the design point of the current batch is used for normalization. This indicates a violation of the weight constraint. ∈[0.1,1]; In the joint agency model, the first... The model with several constraints is for the design point. Output of constrained predicted values, Indicates the first The upper limit of a constraint condition; Indicates the first The constraint tolerance range of each constraint condition is used for normalization; This indicates taking the maximum value.

[0055] It should be noted that the dynamic adjustment strategy for the target confidence weight is as follows: if the prediction accuracy of a target is high (small error), then the weight is increased. This gives it a higher weight in the optimization; if the prediction of a certain objective is unstable (large error), then its weight is reduced. This reduces its impact on the optimization direction. The dynamic adjustment strategy for constraint violation weights is: if the current Pareto solution set is highly feasible (constraints are well satisfied), then reduce the weights. Reduce the penalty intensity; if the current solution set constraint is severely violated, increase the penalty intensity. The forced optimization converges to the feasible region.

[0056] Initialize the hierarchical error compensation mechanism, including: Based on the output of the joint agent model to the initial sample data, the initial target confidence weight and initial constraint penalty weight are obtained, and then the total predicted compensation value of each design point in the sample library is calculated.

[0057] The initial target confidence weights are obtained by evaluating the prediction accuracy of the initial sample data using the models of each objective function. For example, the reciprocal of each prediction accuracy is calculated and normalized to serve as the target confidence weight for the corresponding model. The prediction accuracy is obtained by calculating the mean absolute percentage error (MAPE) or normalized mean square error (NMSE) between the predicted values ​​and the actual simulation values ​​at each design point in the initial sample library.

[0058] The initial constraint violation weight is obtained by using the model of each constraint condition to evaluate the feasibility ratio of the initial sample data.

[0059] For example, the proportion of design points that satisfy all constraints in the initial sample data is compared with the highest and lowest thresholds. If it is less than or equal to the lowest threshold, such as 0.3, it is set to a higher value, such as 0.8; if it is greater than the highest threshold, such as 0.7, it is set to a lower value, such as 0.2; if it is between the lowest and highest thresholds, the corresponding value is obtained by linear interpolation.

[0060] It should be noted that this embodiment does not limit the specific adjustment method of the target confidence weight and constraint violation weight, as long as it conforms to the dynamic adjustment strategy. In the initialization phase, due to the lack of historical data, the target confidence weight and constraint violation coefficient are set once based on the overall statistical characteristics of a limited initial sample, aiming to establish a reasonable starting point for optimization. In the subsequent iterative optimization step S3, the continuously accumulated sample data and optimization status feedback will be used to dynamically update the target confidence weight and constraint violation weight using a more refined adaptive strategy, thereby achieving intelligent guidance for the entire optimization process.

[0061] The joint prediction interface is called for each design point in the sample library to obtain the corresponding combined prediction vector. Then, based on the initial target confidence weight and the initial constraint violation weight, the corresponding initial total prediction compensation value is calculated.

[0062] S3. Perform multiple rounds of iterative optimization until the preset optimization termination condition is met to obtain the final sample library. Each round of iterative optimization includes: generating multiple candidate design points in parallel based on the current joint agent model and hierarchical error compensation mechanism; distributing the multiple candidate design points to multiple computing nodes for parallel CAE simulation calculations to obtain the simulation response value corresponding to each candidate design point; adding the candidate design points and their simulation response values ​​to the sample library; and updating the joint agent model and hierarchical error compensation mechanism using the updated sample library for the next round of iterative optimization.

[0063] Each round of iterative optimization includes steps S31-S34.

[0064] S31. Based on the current joint agent model and hierarchical error compensation mechanism, multiple candidate design points are generated in parallel.

[0065] This step employs an improved Chebyshev scalarization method, which samples a diversity weight vector, dynamically estimates an ideal reference point, and introduces a hierarchical error compensation mechanism to calculate the total prediction compensation term and balance coefficient. Multiple scalarization sub-problems are solved in parallel to generate candidate points.

[0066] Specifically, it includes: ① Obtain the ideal reference point for the current iteration from the optimal solution of several iterations based on a sliding window; Using a sliding window containing the non-dominated solutions of the most recent several generations, the ideal reference point vector for the current iteration is dynamically calculated based on the minimum value of each objective function within the window. It facilitates dynamic tracking of the optimization process and more accurately reflects the current Pareto front position compared to a fixed ideal point.

[0067] ②Based on an ideal reference point, multiple improved Chebyshev scalar quantum problems are constructed by sampling from the Dirichlet distribution to generate multiple weight vectors, and by introducing the total predicted compensation value and balance coefficient obtained by the current hierarchical error compensation mechanism.

[0068] It should be noted that sampling from the Dirichlet distribution generates dynamic weight vectors, ensuring the diversity of weight vectors and avoiding the search process from getting trapped in local optima.

[0069] Furthermore, an improved Chebyshev scalar optimization subproblem is constructed for each sampled weight vector. Each subproblem aims to find a candidate design point that minimizes the weighted maximum distance between the objective function values ​​predicted by the joint surrogate model and the ideal reference point. In this process, the system also introduces a balancing coefficient to adjust the trade-off between exploration and development. This coefficient controls the weight of the uncertainty term predicted by the surrogate model, thereby achieving a balance between fully utilizing current known information and exploring unknown regions.

[0070] The improved Chebyshev scalar quantum problem is expressed by the following formula: , in, Indicates the first One candidate design point, This indicates the use of the first agent in the joint agent model. The model of the objective function for the design point Output target prediction value, Indicates the first An ideal reference point for each objective function; Indicates the first The range of variation of the target predicted value of an objective function, that is, the difference between the maximum and minimum values; This indicates the current hierarchical error compensation mechanism for the design point. The total predicted compensation value is calculated. Indicates the balance coefficient; Indicates the generation of the first When selecting the candidate design point, the weight vector from the generated weight vector is used. The weight components of each objective function.

[0071] It should be noted that the balance coefficient An adaptive strategy is employed to control the intensity of the total predicted compensation value; a smaller value favors development, while a larger value favors exploration. This adaptive mechanism ensures that the search process maintains an efficient balance between exploration and development at different stages.

[0072] Preferably, the balance coefficient can be dynamically adjusted according to a preset decay rule; alternatively, it can be dynamically adjusted based on the progress of the optimization iteration and the diversity of the current solution set distribution. In the early stages of optimization or when the diversity of the solution set decreases, the balance coefficient is automatically increased to strengthen global exploration; in the later stages of optimization or when the solution set distribution is good, the balance coefficient is automatically decreased to focus on local development. The ratio of the current iteration round to the total number of iteration rounds is used to represent the progress of the iterative optimization; based on the solution set obtained after the previous iteration, the mean or standard deviation of the crowding distance of the available solution sets is calculated to measure the diversity of the solution set distribution.

[0073] ③ By solving the improved Chebyshev scalar quantum problem in parallel, multiple candidate design points are generated, forming a set of candidate design points with high quality and diversity.

[0074] On the GPU, multiple parallel optimization threads are launched, each responsible for solving an improved Chebyshev scalar subproblem. Within the optimization algorithm for solving each subproblem, when it is necessary to evaluate the scalar function values ​​of a batch of experimental design points, a batch calculation method is adopted: multiple experimental points are composed into a matrix, and the scalar function values ​​of all points are obtained at once through a joint surrogate model and a hierarchical error compensation mechanism. This enables efficient exploration of different regions of the target space in one iteration, while maintaining the diversity of the solution set.

[0075] S32. Assign multiple candidate design points to multiple computing nodes for parallel CAE simulation calculations to obtain the simulation response value corresponding to each candidate design point; add the candidate design points and their simulation response values ​​to the sample library.

[0076] After obtaining candidate points, this step intelligently groups and efficiently evaluates them using a dynamic load balancing strategy, including: ① Calculate the target spatial distance between any two candidate design points based on the target prediction value output by the joint agent model for each candidate design point; and divide the multiple candidate design points into multiple groups based on the target spatial distance using a clustering algorithm.

[0077] Specifically, the formula for calculating the spatial distance to the target is as follows: , in, Indicates candidate design points and The target spatial distance between them.

[0078] Furthermore, clustering algorithms, such as the K-means++ algorithm, are used to group candidate design points based on the target spatial distance.

[0079] Compared to existing technologies, this distance metric operates within the target space and considers the different dimensions of each objective function. Normalization ensures that each objective contributes equally to the overall distance. Clustering groups candidate design points with similar characteristics together, making subsequent simulation evaluation tasks more targeted.

[0080] ② Based on the number of multiple candidate design points and the current number of CPU cores, obtain the number of computing nodes; assign each group to a computing node.

[0081] It should be noted that the number of nodes is calculated using the following formula: , in, Indicates the number of nodes. Indicates the number of candidate design points. This indicates the current number of CPU cores.

[0082] This approach automatically adjusts the number of computing nodes based on the number of candidate points, while reserving 50% of computing resources for other processing, ensuring overall load balancing.

[0083] Each computing node independently calls the finite element analysis software to perform parallel CAE simulation calculations on a set of assigned candidate design points, obtaining the simulation response value (i.e., the real high-fidelity performance data) corresponding to each candidate design point. Each candidate design point and its corresponding simulation response value together constitute a new sample, and these new samples are added to the sample library.

[0084] This step, based on intelligent grouping and dynamic resource allocation mechanisms using target space similarity, greatly improves the utilization efficiency of computing resources and the throughput of the overall optimization process.

[0085] S33. Update the joint agent model and hierarchical error compensation mechanism using the updated sample library.

[0086] By using the updated sample library, incremental updates are performed on the Gaussian regression models of each objective function and the neural network models of each constraint in the joint surrogate model, thereby improving the overall prediction accuracy of the model.

[0087] For example, the new sample data is merged with the initial sample data to re-optimize the hyperparameters in the Gaussian regression model; the learning rate is reduced by using the new sample data and some historical sample data, and a small number of rounds of fine-tuning training are performed on the existing neural network model to achieve incremental learning of the neural network model.

[0088] The updated hierarchical error compensation mechanism dynamically adjusts its parameters—target confidence weight and constraint violation weight—based on the latest prediction error trends of multiple samples and changes in the feasibility of the candidate solution set. Specifically, the target confidence weight is positively correlated with model prediction accuracy and negatively correlated with error; the constraint violation weight is negatively correlated with the feasibility ratio.

[0089] Preferably, retrieve the nearest One (e.g.) Design points that have been verified by simulation This yields the true simulation values ​​for each design point for each objective optimization problem. And use a joint agent model to obtain the target prediction value of each objective function. .

[0090] Furthermore, the new target confidence weights are obtained using the following formula: , in, and These represent the target confidence weights before and after the update, respectively. Indicates the first The normalized mean square error of each objective function This represents the adjustment coefficient, used to control the strength of the impact of prediction error on the update of target confidence weights. The grid search is used to select values ​​that perform stably on typical test problems.

[0091] For constraint violation weights, the current joint agent model is used to predict multiple recently generated candidate solutions. The proportion of solutions whose predicted constraint values ​​do not exceed the upper limit of the corresponding constraint conditions is counted to obtain the feasibility ratio. If the feasibility ratio is high, the constraint violation weight is reduced, and the penalty is relaxed in the next iteration to encourage target exploration. Conversely, the constraint violation weight is increased to strengthen the penalty and drive the search to converge toward the feasible region.

[0092] Preferably, the new constraint violation weight is obtained using the following formula: , in, This indicates that the new constraint violates the weight. Indicates the base penalty level. ; Indicates the maximum adjustment range. ; Indicates the feasibility ratio.

[0093] It should be noted that the basic penalty level Represents the minimum constraint penalty strength: even if all candidate points are feasible, a small penalty term is retained to prevent the model from taking overly optimistic risks near the feasible region boundary. Its value depends on how strict the problem is regarding constraints and how much it encourages exploration. Maximum adjustment magnitude This determines the range of the penalty coefficient's response to changes in feasibility. The larger the value, the greater the variable range of the constraint violation weight, and the stronger the response to feasibility fluctuations. It is typically set to... .

[0094] Furthermore, by utilizing the target confidence weight and constraint violation weight, the "total predicted compensation value" over the entire design space is recalculated, providing the latest guidance for the generation of candidate points in the next round.

[0095] S34. Iteration termination judgment.

[0096] After completing the model and parameter updates, identify whether the preset optimization termination conditions are met. These conditions include: reaching the maximum number of iterations, the improvement of the Pareto solution set (such as the rate of change of the hypervolume index HV) in multiple consecutive iterations being less than a certain threshold, and reaching the maximum computation time.

[0097] If no optimization termination condition is met, the loop continues, and the process jumps to S31 to start a new round of iteration. If any termination condition is met, the iteration loop ends, the loop exits, and the process proceeds to step S4.

[0098] S4. Obtain a set of multi-objective optimization design schemes for the product to be optimized from the final sample library.

[0099] After the iterative optimization is completed, the final sample library is obtained, which contains all the sample data accumulated during the entire optimization process and evaluated by real simulation. All feasible solutions (satisfying all constraints) and mutually non-dominated are extracted from it (and sorted by non-dominance) to obtain the multi-objective Pareto optimal solution set. Each solution is a design variable vector (i.e. a set of design variable values ​​at a design point), corresponding to an optimization design scheme of the product to be optimized.

[0100] For example, in the application scenario of lightweight design for automotive B-pillars, the NSGA-II algorithm is used to obtain the Pareto optimal solution set. One design point = [thickness A = 2.1mm, thickness B = 1.8mm, thickness C = 1.6mm, stiffener height = 30mm, stiffener width = 18mm] represents a specific B-pillar structural parameter scheme. This scheme satisfies all safety constraints such as strength and stiffness, and achieves Pareto optimality in multiple objectives such as "weight", "collision intrusion", and "cost".

[0101] From multiple optimized design options, one or more options are selected based on actual engineering preferences (such as a greater emphasis on lightweighting or safety) for subsequent detailed design, manufacturing, or as input for other analyses. Therefore, this invention does not provide an abstract mathematical solution, but rather a directly applicable parametric design scheme that drives product design iteration through intelligent optimization.

[0102] Preferably, the optimized design scheme set (multi-objective Pareto optimal solution set) is output in the form of visualized and structured data, including: generating a three-dimensional Pareto front plot of "weight-intrusion-cost", and a detailed data table. The table lists the specific design variable values ​​(such as the thickness of the sheet metal in each region, the height and width of the internal stiffeners), the predicted and verified performance indicators, and the constraint satisfaction status of each optimized scheme, providing automotive engineers with a clear and quantitative basis for making the final lightweight design decision of the B-pillar.

[0103] Compared with existing technologies, this embodiment provides a parallel multi-objective optimization method for CAE simulation of engineering products. By constructing a complete technical closed loop of "intelligent initialization - iterative proxy model optimization - dynamic resource allocation," it systematically solves the long-standing problems of high computational cost, low resource utilization, and slow convergence speed in the field of computationally intensive multi-objective optimization. It deeply integrates the powerful fitting ability of deep learning, the global search capability of multi-objective evolutionary algorithms, and the efficient execution capability of high-performance parallel computing. This achieves improved optimization efficiency while ensuring Pareto front convergence and diversity, providing a practical automated and intelligent solution for simulation-driven design of complex engineering products. A two-stage collaborative optimization initial solution set generation mechanism is proposed. By accelerating the solution of multiple sub-problems through GPU parallel acceleration and combining it with the accelerated NSGA-II refining strategy, the generation efficiency and quality of the initial solution set are significantly improved, thereby enhancing the efficiency and stability of the overall optimization process from the source. A joint surrogate model employing decoupled modeling of objectives and constraints, combined with a hierarchical error compensation mechanism, adaptively adjusts the objective confidence weight and constraint penalty weight, effectively balancing the relationship between objective optimization and constraint satisfaction. This achieves intelligent perception of the model's local prediction accuracy and dynamic guidance of the optimization process's feasibility. High-quality candidate design points are generated based on an improved Chebyshev scalarization method, achieving a dynamic and intelligent balance between "utilizing currently known optimal information" and "exploring unknown high-potential regions." Intelligent clustering based on objective space prediction groups similar candidate points, and parallel computation is performed using a dynamic load balancing strategy, achieving intelligent allocation and efficient utilization of computing resources.

[0104] Example 2 Another embodiment of the present invention discloses a parallel multi-objective optimization system for CAE simulation of engineering products, thereby implementing the parallel multi-objective optimization method for CAE simulation of engineering products in Embodiment 1. The specific implementation of each module is described in the corresponding description in Embodiment 1. The system includes: The initial sample generation module is used to determine design variables, multiple objective functions, and constraints based on the CAE simulation objectives of the product to be optimized, and to obtain initial sample data through two-stage collaborative optimization and put it into the sample library; The joint agent model construction module is used to construct a joint agent model based on multiple objective functions and constraints, train the joint agent model using a sample library, and initialize the hierarchical error compensation mechanism. The candidate design point generation module is used to perform multiple rounds of iterative optimization until a preset optimization termination condition is met, resulting in the final sample library. Each round of iterative optimization includes: generating multiple candidate design points in parallel based on the current joint surrogate model and hierarchical error compensation mechanism; distributing the multiple candidate design points to multiple computing nodes for parallel CAE simulation calculations to obtain the simulation response value corresponding to each candidate design point; adding the candidate design points and their simulation response values ​​to the sample library; and updating the joint surrogate model and hierarchical error compensation mechanism using the updated sample library for the next round of iteration. The optimization scheme acquisition module is used to obtain a set of multi-objective optimization design schemes for the product to be optimized from the final sample library.

[0105] Since the parallel multi-objective optimization system for CAE simulation of engineering products in this embodiment and the aforementioned parallel multi-objective optimization method for CAE simulation of engineering products can be mutually referenced, this description is redundant and will not be repeated here. Because this system embodiment shares the same principle as the above method embodiment, it also possesses the corresponding technical effects of the above method embodiment.

[0106] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware, and the program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.

[0107] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A parallel multi-objective optimization method for CAE simulation of engineering products, characterized in that, Includes the following steps: Based on the CAE simulation objectives of the product to be optimized, design variables, multiple objective functions, and constraints are determined. Initial sample data is obtained through two-stage collaborative optimization and placed into a sample library. A joint agent model is constructed based on multiple objective functions and constraints, and the joint agent model is trained using the sample library to initialize the hierarchical error compensation mechanism. Multiple rounds of iterative optimization are performed until a preset optimization termination condition is met, resulting in the final sample library. Each round of iterative optimization includes: generating multiple candidate design points in parallel based on the current joint agent model and hierarchical error compensation mechanism; distributing the multiple candidate design points to multiple computing nodes for parallel CAE simulation calculations to obtain the simulation response value corresponding to each candidate design point; adding the candidate design points and their simulation response values ​​to the sample library; and updating the joint agent model and the hierarchical error compensation mechanism using the updated sample library for the next round of iterative optimization. Obtain a set of multi-objective optimization design schemes for the product to be optimized from the final sample library.

2. The parallel multi-objective optimization method for CAE simulation of engineering products according to claim 1, characterized in that, The two-stage collaborative optimization includes: In the first stage, multiple objective functions are solved in parallel as sub-problems. The overall objective function is constructed by weighted summation of each objective function and the introduction of penalty terms for constraints, resulting in multiple sets of design variables that constitute the preliminary design point set. In the second stage, the preliminary design point set is merged with the design points obtained through Latin hypercube sampling to form the initial population; the initial population is optimized using a non-dominated sorting genetic algorithm accelerated by GPU parallelism, and the output non-dominated solution set is used as the initial sample data.

3. The parallel multi-objective optimization method for CAE simulation of engineering products according to claim 2, characterized in that, The overall objective function is expressed by the following formula: ， in, Design points The total objective function value; Indicates the number of objective functions. Indicates the number of constraints; Design points The corresponding number The objective function value is the actual value output by the simulation model; Indicates the first The weights of each objective function are set as follows: ; Indicates the penalty coefficient. Design points The corresponding number The value of each constraint condition.

4. The parallel multi-objective optimization method for CAE simulation of engineering products according to claim 1, characterized in that, The construction of a joint agent model based on multiple objective functions and constraints includes: using a Gaussian regression model to independently model each objective function and using a neural network model to independently model each constraint, and then combining them to obtain a joint agent model.

5. The parallel multi-objective optimization method for CAE simulation of engineering products according to claim 1, characterized in that, The initialization hierarchical error compensation mechanism includes: Based on the output of the joint agent model to the initial sample data, the initial target confidence weight and the initial constraint penalty weight are obtained, and then the total predicted compensation value of each design point in the sample library is calculated.

6. The parallel multi-objective optimization method for CAE simulation of engineering products according to claim 5, characterized in that, The hierarchical error compensation mechanism calculates the total prediction compensation value using the following formula: ， in, Design points Total predicted compensation value, Indicates the number of objective functions. Indicates the number of constraints. In the joint agency model, the first... The target confidence weights of the model with each objective function. ∈[0,1]; In the joint agency model, the first... The model of the objective function for the design point The standard deviation of the output prediction; In the joint agency model, the first... The maximum predicted standard deviation of the model with each objective function for the design point of the current batch is used for normalization. This indicates a violation of the weight constraint. ∈[0.1,1]; In the joint agency model, the first... The model with several constraints is for the design point. Output of constrained predicted values, Indicates the first The upper limit of a constraint condition; Indicates the first The constraint tolerance range of each constraint condition is used for normalization; This indicates taking the maximum value.

7. The parallel multi-objective optimization method for CAE simulation of engineering products according to claim 1, characterized in that, The parallel generation of multiple candidate design points is achieved by employing an improved Chebyshev scalarization method, including: The ideal reference point for the current iteration is obtained from the optimal solution of several iterations based on a sliding window. Based on an ideal reference point, multiple improved Chebyshev scalar quantum problems are constructed by sampling from the Dirichlet distribution to generate multiple weight vectors, and by introducing the total predicted compensation value and balance coefficient obtained by the current hierarchical error compensation mechanism. Multiple candidate design points are generated by solving the improved Chebyshev scalar quantum problem in parallel.

8. The parallel multi-objective optimization method for CAE simulation of engineering products according to claim 7, characterized in that, The improved Chebyshev scalar quantum problem is expressed by the following formula: ， in, Indicates the first One candidate design point, Indicates the number of objective functions. This indicates the use of the first agent in the joint agent model. The model of the objective function for the design point Output target prediction value, Indicates the first An ideal reference point for each objective function; Indicates the first The range of variation of the target predicted value of each objective function; This indicates the current hierarchical error compensation mechanism for the design point. The total predicted compensation value is calculated. Indicates the balance coefficient; Indicates the generation of the first When selecting the candidate design point, the weight vector from the generated weight vector is used. The weight components of each objective function.

9. The parallel multi-objective optimization method for CAE simulation of engineering products according to claim 1, characterized in that, Assigning the multiple candidate design points to multiple computing nodes includes: Based on the target prediction value output by the joint agent model for each candidate design point, the target spatial distance between any two candidate design points is calculated; based on the target spatial distance, a clustering algorithm is used to divide the multiple candidate design points into multiple groups. Based on the number of candidate design points and the current number of CPU cores, the number of computing nodes is obtained; each group is then assigned to a computing node.

10. A parallel multi-objective optimization system for CAE simulation of engineering products, characterized in that, include: The initial sample generation module is used to determine design variables, multiple objective functions, and constraints based on the CAE simulation objectives of the product to be optimized, and to obtain initial sample data through two-stage collaborative optimization and put it into the sample library; The joint agent model construction module is used to construct a joint agent model based on multiple objective functions and constraints, train the joint agent model using the sample library, and initialize the hierarchical error compensation mechanism. The candidate design point generation module is used to perform multiple rounds of iterative optimization until a preset optimization termination condition is met, resulting in a final sample library. Each round of iterative optimization includes: generating multiple candidate design points in parallel based on the current joint surrogate model and hierarchical error compensation mechanism; distributing the multiple candidate design points to multiple computing nodes for parallel CAE simulation calculations to obtain the simulation response value corresponding to each candidate design point; adding the candidate design points and their simulation response values ​​to the sample library; and updating the joint surrogate model and the hierarchical error compensation mechanism using the updated sample library for the next round of iteration. The optimization scheme acquisition module is used to obtain a set of multi-objective optimization design schemes for the product to be optimized from the final sample library.

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