Efficient proxy optimization method for parallel modeling and sub-optimization

Abstract

The invention discloses an efficient proxy optimization method for parallel modeling and sub-optimization. The method comprises the following steps: defining an optimization target and a constraint function and selecting a point adding criterion; initiating a plurality of processes through a message passing interface (MPI); the root process generates an initial sample point set through test design and broadcasts the initial sample point set; sample response values are calculated in parallel in all the processes and summarized through MPI full collection; proxy model modeling tasks are distributed to all processes to be executed in parallel, and model parameters are collected completely after execution is completed; sub-optimization problems of different point adding criteria are distributed to all processes for parallel solving, and new sample points are generated and then summarized; and circularly executing until the convergence standard is met. According to the method, the utilization rate of computing resources is remarkably improved, and the time cost of complex engineering optimization is greatly shortened.

Description

Technical Field

[0001] This application belongs to the field of multidisciplinary optimization design technology, specifically involving an efficient surrogate optimization method for parallel modeling and sub-optimization. Background Technology

[0002] As an important computational optimization strategy, surrogate optimization has received widespread attention and application in the field of multidisciplinary engineering optimization design in recent years. This method significantly reduces the computational burden of complex engineering optimization problems by constructing surrogate models (such as Kriging models and radial basis function models) with lower computational costs to replace the actual high-energy-consuming numerical simulation process. It has shown good applicability, especially in the optimization of complex systems in aerospace, vehicle design, and energy equipment.

[0003] However, with the increasing dimensionality of engineering problems and the growing complexity of constraints, traditional surrogate optimization methods still face significant efficiency bottlenecks when solving high-dimensional, multi-constrained, and strongly nonlinear optimization problems. The surrogate optimization process typically includes three core steps: surrogate model construction, solving sub-optimization problems based on the addition criterion, and sample point simulation computation. Currently, for the sample point computation step, various parallel computing strategies have been developed, such as distributed task scheduling methods based on MPI or Spark, enabling parallel execution of simulation analysis in a cluster environment and effectively shortening the computation time of this step.

[0004] Nevertheless, the surrogate model construction process and the sub-optimization problem solving process are still generally handled sequentially. Specifically, in each iteration, a surrogate model must be built sequentially for the objective function and multiple constraint functions. This process increases in time cost linearly with the number of functions. In addition, for various point-addition criteria (such as expected improvement EI, confidence lower bound LCB, etc.), corresponding sub-optimization problems also need to be solved sequentially, further exacerbating the computational burden. These two stages have become the key bottlenecks restricting the overall efficiency improvement of surrogate optimization.

[0005] While some parallel optimization frameworks have been proposed in existing technologies, their parallel capabilities are mainly concentrated in the sample computation stage, and no systematic parallelization solutions have been proposed for the modeling and sub-optimization stages. Therefore, when facing high-dimensional, multi-constraint optimization problems, traditional serial processing methods cannot fully utilize the parallel computing resources of high-performance computing environments, resulting in increasingly prominent problems such as long optimization cycles and high computational costs. Summary of the Invention

[0006] The purpose of this application is to overcome the problem of low computational efficiency in the modeling and sub-optimization stages of existing surrogate optimization methods, and to provide a surrogate optimization method based on a parallel computing architecture. This method can significantly reduce the time cost of the modeling and sub-optimization processes, effectively overcome the computational bottlenecks faced in high-dimensional complex optimization problems, fully leverage the potential of high-performance computing resources, and improve overall optimization efficiency.

[0007] To achieve the above technical objectives, this application specifically employs the following technical solution: In one aspect of this application, an efficient surrogate optimization method for parallel modeling and sub-optimization is provided, comprising the following steps: Step S1: Define the optimization objective function and constraint functions, and select the set of point-addition criteria, wherein the number of point-addition criteria is... ; Step S2: Start via message passing interface p 1 process, of which p The value of is chosen with the goal of maximizing parallel efficiency; Step S3: The root process extracts an initial sample point set using the experimental design method and broadcasts the sample point set to all processes; Step S4: Distribute the computation task of the initial sample point set evenly to each process. Each process independently calculates the response value of the sample point. After the computation is completed, the response set of the initial sample is obtained through the MPI full collection operation. Step S5: Distribute the modeling tasks for the objective function and constraint function evenly to each process. Each process independently builds a proxy model. After the modeling is completed, the model parameters are sent to the root process. Step S6: Distribute the point-addition criteria equally among the processes. The root process sends the model parameters to each process. Each process solves the sub-optimization problem defined by its assigned point-addition criteria to obtain new sample points. All new sample points are obtained through the MPI full collection operation. Step S7: Repeat steps S4 to S6 until the optimization convergence criterion is met.

[0008] In one implementation, the number of processes mentioned in step S2 p The value is dynamically adjusted based on available computing resources and task complexity.

[0009] In one implementation, the experimental design method described in step S3 is Latin hypercube sampling, uniform design, Monte Carlo sampling, or artificially given.

[0010] In one implementation, in step S4, MPI technology is used to call a multi-process parallel submission of sample point analysis tasks to a high-performance computing cluster, and each process summarizes the response values ​​of the sample points through MPI full collection operation.

[0011] In one implementation, in step S5, the surrogate model is one or more of the following: a Kriging model, a gradient boosting Kriging model, a hierarchical Kriging model, a radial basis function model, or a neural network model.

[0012] In one implementation, process variance, hyperparameters, correlation matrix, or their decomposition results are saved during the modeling process to accelerate subsequent model predictions.

[0013] In one implementation, in step S6, the addition criteria include one or more of minimizing model prediction (MSP), improvement probability (PI), improvement expectation (EI), confidence lower bound (LCB), or maximizing mean squared error (MSE).

[0014] In one implementation, the optimization convergence criterion in step S7 is that the relative change between the objective function value and the design variable value is less than a set threshold or the maximum number of response function evaluations is reached.

[0015] In another aspect of this application, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the aforementioned efficient proxy optimization method for parallel modeling and sub-optimization.

[0016] In another aspect of this application, a computer-readable storage medium is provided having a computer program stored thereon that, when executed by a processor, implements the aforementioned efficient proxy optimization method for parallel modeling and sub-optimization.

[0017] The beneficial effects of this application are as follows: 1) Improved optimization efficiency: By introducing an MPI-based parallel computing framework, parallel processing of the surrogate model construction process and the sub-optimization problem solving process was achieved. This method reduces the modeling time to a fraction of that of serial methods. ( (For the number of objective and constraint functions), the sub-optimization time is reduced to ( (This is to increase the number of criteria), thereby significantly reducing the overall computational time cost of high-dimensional complex optimization problems.

[0018] 2) Fully leverages the potential of high-performance computing resources: This application effectively decomposes the two most computationally intensive stages in proxy optimization—modeling and sub-optimization—into parallel tasks, enabling them to fully utilize the multi-core, multi-node parallel computing capabilities of high-performance computing clusters, thus solving the problem of mismatch between existing proxy optimization methods and the development of modern supercomputing architectures.

[0019] 3) Maintaining the reliability of optimization results: This application represents an innovation in parallel computing strategy without altering the mathematical foundation of the surrogate model or the convergence of the optimization algorithm. While ensuring the same optimization results as serial methods, it achieves an order-of-magnitude improvement in computational efficiency, making it particularly suitable for engineering optimization scenarios where computational resources are expensive or time is tight. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating the efficient surrogate optimization method for parallel modeling and sub-optimization proposed in this application; Figure 2 This is the initial proxy model established in parallel in processes 0 and 1 with respect to the objective (left) and constraint (right) functions, respectively, according to Embodiment 1 of this application; Figure 3 These are new sample points obtained by parallel solving of the sub-optimization problem in processes 0-3 of Embodiment 1 of this application; Figure 4 This is the final optimized result of Embodiment 1 of this application; Figure 5 This is a comparison of the time and results of parallel optimization and serial optimization in Embodiment 2 of this application. Detailed Implementation

[0021] The technical solution of this application will be clearly and completely described below with reference to specific embodiments. However, those skilled in the art will understand that the embodiments described below are only some embodiments of this application, not all embodiments, and are only used to illustrate this application, and should not be regarded as limiting the scope of this application. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0022] In one specific embodiment of this application, an efficient surrogate optimization method for parallel modeling and sub-optimization is provided, referring to... Figure 1 As shown, it includes the following steps: Step S1: Define the optimization objective function and constraint functions, and select the set of point-addition criteria, wherein the number of point-addition criteria is... .

[0023] The efficient parallel proxy optimization method first needs to clearly define the objective function and constraint function in the optimization problem, and reasonably select the set of point addition criteria to guide the supplementation of sample points.

[0024] In some embodiments, the objective function and constraint function are collectively referred to as the response function, denoted as . ,in, In this embodiment, This represents the total number of response functions to be modeled, including one objective function and several constraint functions. For example, if the optimization problem contains one objective function and...m Given a constraint function, then = m +1. It is understandable that the response function can be a practical engineering function that is computationally time-consuming, highly nonlinear, or has an implicit unknown mathematical expression, and its specific form does not affect the implementation of this method.

[0025] The point-addition criteria are used to guide the generation of new sample points in each iteration, and their selection directly affects optimization efficiency and convergence performance. The set of point-addition criteria should include several commonly used criteria, the number of which is denoted as [missing information]. .

[0026] In some embodiments, common criteria for adding points include, but are not limited to: Minimize Model Prediction (MSP), which is to directly optimize the predictions of the surrogate model; Expected Improvement (EI) is the expected probability of improving the objective function based on the current best value. The probability of improvement (PI) is used to assess the probability that a new sample point is better than the current best value. The confidence lower bound (LCB) is constructed by combining model predictions with uncertainties; Maximize mean squared error (MSE) by sampling in regions with large prediction variance to improve the global accuracy of the model.

[0027] In some embodiments, one or more of the above criteria are selected based on the characteristics of the optimization problem (such as whether global search is emphasized, whether constraints need to be handled, etc.) to form a set of addition criteria, the number of which is... The number of proxy models can be determined based on computing resources and problem complexity, and is generally not less than the number of proxy models. This allows for the full parallel utilization of computing resources.

[0028] Step S2: Start via message passing interface p 1 process, of which p The value of is chosen to maximize parallel efficiency. Multiple processes are launched using the Message Passing Interface (MPI) standard to fully utilize the multi-core resources of high-performance computing clusters or parallel computing environments, achieving parallel computing and significantly improving optimization efficiency.

[0029] The number of processes launched p The determination of [the parameters] is based on the core objective of maximizing parallel efficiency.

[0030] In some embodiments, the number of processes launched p The specific value selection strategy is as follows: Number of processes p The value is determined based on a combination of the total scale of the parallel tasks and the available computing resources. Its basic principle is:p The value of should be no less than the total number of parallel tasks and no more than the number of available computing cores, so as to achieve full parallelization of the computing load and avoid efficiency degradation caused by resource contention.

[0031] Specifically, parallel tasks mainly come from two aspects: Agent model building tasks: The total number of these tasks is equal to the number of response functions to be modeled. (Including the objective function and all constraint functions); Sub-optimization problem solving tasks: The total number of these sub-optimization problems is equal to the number of selected point addition criteria. .

[0032] Therefore, to maximize parallel efficiency, the number of processes p The optimal value is the maximum of the two tasks mentioned above, that is: .

[0033] This value selection strategy ensures that in each iteration, whether in the model building phase or the sub-optimization problem solving phase, there are a sufficient number of processes to process all tasks in parallel, so that CPU computing resources are fully utilized, thereby minimizing the computation time of a single iteration.

[0034] In some embodiments, the number of processes p It can be dynamically adjusted based on the actual availability of computing resources and the complexity of the task.

[0035] When there are sufficient available compute nodes or cores, strict adherence is required. The strategy is to maximize parallelism. When available computational resources are insufficient to support the theoretically optimal... p Values, for example, fewer than 100 available cores. ,but p The value is the maximum number of cores currently available. At this point, the root process is responsible for... A modeling task or The optimization problems are queued and distributed to available processes in batches for execution. Although the parallelism in this scenario is not theoretically optimal, inter-process scheduling via MPI still significantly outperforms serial execution efficiency.

[0036] Understandably, if the number of proxy models or the number of point criteria are dynamically increased as needed during the optimization process, the MPI environment allows for the dynamic creation or reconfiguration of the number of processes. p To adapt to new task scales and maintain efficient parallel processing capabilities.

[0037] Step S3: The root process extracts an initial sample point set using the experimental design method and broadcasts the sample point set to all processes.

[0038] In some embodiments, the generation of the initial sample point set includes: the root process first extracting a certain number of initial sample points within the design space of the variables to form the initial sample point set. ,in, n The initial number of sample points. For the first i The vector representation of each sample point. The quality of the initial sample points directly affects the initial accuracy of the surrogate model and the efficiency of subsequent optimization processes.

[0039] In some embodiments, the experimental design method employs Latin hypercube sampling (LHS). This method is a stratified random sampling technique, and its execution process is as follows: a. Variable space hierarchical division: the design interval of each dimension variable is divided into equal intervals. n Each level.

[0040] b. Random sampling: randomly select a sample value within each level of each dimension of the variable.

[0041] c. Random combination: The sample values ​​of each dimension variable are randomly paired and combined within their respective levels to form n sample points.

[0042] This embodiment uses the Latin hypercube sampling method, which ensures that the projection on each dimension variable uniformly covers its entire design interval, avoiding the sample point clustering phenomenon that may occur in simple random sampling, thereby obtaining a more representative sample of the design space with fewer sample points.

[0043] In some embodiments, after the initial sample point set is generated in the root process, it needs to be acquired by all parallel processes so that each process can execute its assigned computation or modeling task. This data synchronization process is achieved through MPI broadcast operations.

[0044] The root process calls the MPI broadcast routine, passing the address of the data buffer storing the initial sample point set, the amount of data, and the data type as parameters. All other processes (non-root processes) call the same MPI broadcast routine. The MPI communication library is responsible for efficiently distributing the data in the root process's buffer to the corresponding buffers in all processes. After the operation is complete, every process in the cluster has an identical copy of the initial sample point set.

[0045] Step S4: Distribute the computation task of the initial sample point set evenly to each process. Each process independently calculates the response value of the sample point. After the computation is completed, the response set of the initial sample point set is obtained through the MPI full collection operation.

[0046] In some embodiments, the computation task of the initial sample point set is evenly distributed among the processes, and each process independently calculates the response value of the sample points, including the following steps: The root process evenly distributes the computational tasks contained in the initial sample point set to all p There are parallel processes, and each process is assigned a subset of sample points. Subsequently, each process independently and in parallel calls the computing program or simulation software to calculate each sample point it is assigned. The program calculates the true response value. It allows simultaneous calculations for multiple sample points, significantly reducing data acquisition time, and is particularly suitable for engineering problems where analyzing a single sample point is time-consuming.

[0047] In some embodiments, for the time-consuming problem of sample point analysis, MPI technology is used to invoke multiple processes, submitting the sample point analysis task in parallel to different computing nodes of a high-performance computing cluster (HPC) for computation. The MPI environment is responsible for task allocation, scheduling, and inter-process communication, thereby efficiently utilizing the large number of computing cores of the cluster to accelerate computationally intensive tasks.

[0048] In some embodiments, each process obtains a subset of local sample points after completing its assigned local computing task. The actual response values ​​are then collected. To ensure that all processes have a complete initial sample response set for subsequent modeling, data is aggregated through an MPI Allgather operation. Specifically, each process sends its calculated local response value data to all other processes in the MPI communicator, while simultaneously receiving data from all other processes. The MPI Allgather operation ensures that after the operation, each process possesses a complete, global initial sample response set. , .

[0049] Step S5: Distribute the modeling tasks for the objective function and constraint function evenly to each process. Each process independently builds a proxy model. After the modeling is completed, the model parameters are sent to the root process.

[0050] In some embodiments, the total number of agent models to be established is Each objective function and all constraint functions corresponds to an independent surrogate model, and the root process will... Each modeling task is evenly distributed among the available tasks. p There are 12 parallel processes, each assigned to one or more modeling tasks and independently responsible for completing these tasks. Each process uses its assigned initial sample response set. The model training process includes initializing model parameters, model fitting, and hyperparameter optimization. The modeling work in each process is independent and executed in parallel, thus efficiently completing the construction of all surrogate models.

[0051] In some embodiments, the surrogate model may be selected as one or more of the following: a Kriging model, a gradient-enhanced Kriging (GEK) model, or a hierarchical Kriging (HK) model. The specific choice depends on the characteristics of the problem. Kriging models are suitable for most continuous response problems without gradient information. Gradient-enhanced Kriging (GEK) models are suitable for problems where the gradient (first derivative) of the response value can be efficiently computed; by incorporating gradient information, a more accurate model can be built with fewer sample points. Hierarchical Kriging (HK) models are suitable for problems with data of varying confidence levels; they can fuse data from models or computational sources of different accuracy to reduce computational costs while maintaining accuracy.

[0052] After each process completes its assigned modeling task, it saves the parameters of the model it has built. To accelerate subsequent large-scale predictions based on this model (such as those frequently called in sub-optimal searches), intermediate results or correlation matrix decomposition results generated during the modeling process can also be saved.

[0053] In some embodiments, model parameters saved and sent during the modeling process include, but are not limited to, one or more of the following: process variance, hyperparameters, correlation matrix, or their decomposition results, to accelerate subsequent model prediction.

[0054] After modeling is complete, each process sends the key parameters (and optional decomposition results for accelerated prediction) of the surrogate model it is responsible for back to the root process. In some embodiments, this sending operation can be accomplished via MPI's point-to-point Send or Gather operation. The root process is responsible for receiving and storing the complete parameter sets of all surrogate models.

[0055] Step S6: Distribute the point-addition criteria equally among the processes. The root process sends the model parameters to each process. Each process solves the sub-optimization problem defined by its assigned point-addition criteria to obtain new sample points. All new sample points are obtained through the MPI full collection operation.

[0056] In some embodiments, the total number of sub-optimization problems to be solved is equal to the number of selected point-addition criteria. If they are equal, the root process will... The task of solving the sub-optimization problems is evenly distributed among the available resources. pThere are 12 parallel processes. Each process is assigned a specific addition criterion and its defined sub-optimization problem.

[0057] In some embodiments, to ensure that each process can independently solve its sub-optimization problem, the root process first sends the parameters of all surrogate models (including objective and constraint functions) collected in step S5 to all participating processes via MPI broadcast or scatter operation. This process ensures that each process has all the information needed to construct all response function surrogate models (such as process variance, hyperparameters, correlation matrices and their decomposition results), thereby enabling it to perform model predictions independently and quickly locally without frequently requesting data from the root process, greatly reducing communication overhead and accelerating the solution process.

[0058] In some embodiments, each process constructs and solves a corresponding sub-optimization problem based on its assigned point-addition criteria. The point-addition criteria include, but are not limited to, minimizing the model prediction (MSP), the probability of improvement (PI), the expected improvement (EI), the lower confidence bound (LCB), or maximizing the mean squared error (MSE).

[0059] Step S7: Repeat steps S4 to S6 until the optimization convergence criterion is met. By repeatedly executing steps S4 to S6, the number of sample points is gradually increased to update the surrogate model, thereby driving the optimization process to approach the true optimal solution. This iterative cycle will continue until the preset optimization convergence criterion is met.

[0060] In some embodiments, each iteration loop includes the following three core components: 1) Parallel computation of new sample response values ​​(corresponding to step S4): The response values ​​obtained in the previous round through step S6 are... The root process assigns a new sample point as the computational task for this iteration. This task is then evenly distributed among the processes, with each process computing in parallel the true response values ​​(objective function value and constraint function value) for its assigned sample point. After computation, an MPI full collection operation aggregates the response values ​​of all new sample points across all processes and adds this new data to the continuously growing global sample dataset.

[0061] 2) Parallel update of the proxy model (corresponding to step S5): Using the expanded global sample dataset, the root process will update... The tasks for each proxy model are then evenly distributed among the processes. Each process independently updates the proxy model it is responsible for (including re-optimizing hyperparameters, etc.) and sends the updated model parameters back to the root process.

[0062] 3) Parallel Solving of Sub-Optimization Problems to Obtain New Points (corresponding to step S6): The root process broadcasts the latest model parameters to all processes. Each process, based on its assigned point-addition criteria and the updated, more accurate surrogate model, solves the new sub-optimization problem in parallel, thus obtaining a new round of... The candidate sample points are collected and summarized through a full collection operation.

[0063] In some embodiments, the optimization convergence criterion employs one or more of the following judgment conditions to evaluate whether to terminate the loop after each iteration: the relative change in the objective function value or the design variable value is less than a set threshold, the maximum number of response function evaluations is reached, and other optional criteria, such as the maximum number of iterations, the surrogate model prediction error, or the degree of constraint violation (which has been sufficiently satisfied).

[0064] Once any of the above convergence criteria is met, the iteration loop ends. The root process outputs the historical global best sample point and its response value as the final optimization result.

[0065] Example 1: Standard Optimized Test Cases for Two-Dimensional Branin Functions The optimized model is:

[0066] There are three extreme points, where the global optimal solution is: ; The two local optimal solutions are: and .

[0067] Implementation steps: Step S1: Select the Kriging model to model the objective and constraints. There are two surrogate models in total. Select four point-adding criteria: MSP, EI, PI, and LCB. The number of points added in each round is 4. Step S2: Start parallel agent optimization by launching 4 processes via MPI; Step S3: The root process extracts 4 initial sample points using Latin hypercube: , And broadcast to the other three processes; Step S4: Distribute the four sample points evenly across four process processors to begin parallel computation of the sample response values. After computation, obtain the initial sample objective function response set through MPI full collection. and the response set of the constraint function : , ; Step S5: Model the objective function and constraint functions in process 0 and process 1 respectively, and the results are as follows. Figure 2 .

[0068] After modeling is complete, the kriging model parameters are sent to the root process, including: process variance. hyperparameters And related matrices:

[0069] Model parameters, etc.

[0070] In step S6, the root process sends the model parameters to processes 0-3, and the four sub-optimization problems defined by the selected MSP, EI, PI, and LCB point addition criteria are evenly distributed to the four processes for solving.

[0071] Process 0 solves the sub-optimization problem defined by the MSP criterion: ; in, The Kriging model for the objective function. This is the kriging model for the constraint function.

[0072] Process 1 solves the sub-optimization problem defined by the EI criterion: ; ; in, The improvement amount of the objective function This is the minimum value in the current sample set. and These are the standard normal cumulative distribution function and the standard normal probability density function, respectively.

[0073] Process 2 solves the sub-optimization problem defined by the PI criterion: ; ; in, To improve the probability of the objective function, Let be the mean square error of the objective function.

[0074] Process 3 solves the sub-optimization problem defined by the LCB criterion: ; in, A This is a constant that defines the size of the confidence interval.

[0075] After all solutions are completed, the full collection yields four new sample points, such as... Figure 3 As shown.

[0076] Step S7: Repeat steps S4-S6 until the optimization converges. The final optimization result of this example is as follows: Figure 4 As shown.

[0077] Example 2 The optimized model is:

[0078] The feasible region of this example is small, accounting for only 0.5% of the entire design space, classifying it as a strongly constrained problem. Furthermore, the objective function varies significantly, ranging from 10... 3 Quantity up to 10 7 This is a test case of immense scale and high optimization difficulty, conforming to international standard optimization criteria. Currently, the internationally known optimal solution is: .

[0079] Implementation steps: Step S1: Select the GEK model to model the objectives and constraints. There are a total of 5 surrogate models. Select five point-adding criteria: MSP, EI, PI, LCB, and MSE. The number of points added in each round is 5. Step S2: Start parallel agent optimization by launching 5 processes via MPI; Step S3: The root process extracts 10 initial sample points using Latin hypercube and broadcasts them to the other three processes. Step S4: Distribute the 10 sample points evenly across 5 process processors to begin parallel computation of sample response values ​​and gradient values. After computation, obtain the initial sample response set through MPI full collection. Step S5: Model the objective function and constraint function in processes 0-4 respectively. After completion, send the GEK model parameters to the root process, including process variance, hyperparameters, correlation matrix and other model parameters. To accelerate model prediction, the matrix decomposition results are also saved.

[0080] In step S6, the root process sends the model parameters to processes 0-4, and distributes the five sub-optimization problems defined by the selected MSP, EI, PI, LCB, and MSE point addition criteria equally among the five processes for solving. After each process completes its work, five new sample points are collected.

[0081] Step S7: Repeat steps S4-S6 until the optimization converges.

[0082] To verify the optimization and acceleration effect of the present invention, the serial proxy optimization method was used to execute the example, and the results were compared with those of the present invention. Figure 5 When the optimization results are similar, the optimization time of this invention is 1 / 3 of that of the serial method.

[0083] Although the embodiments of this application have been described above in conjunction with the accompanying drawings, this application is not limited to the specific embodiments and application fields described above. The specific embodiments described above are merely illustrative and instructive, not restrictive. Those skilled in the art can make many other forms based on the guidance of this specification and without departing from the scope of protection of the claims of this application, and these are all within the scope of protection of this application.

Claims

1. A highly efficient surrogate optimization method for parallel modeling and sub-optimization, characterized in that, Includes the following steps: Step S1: Define the optimization objective function and constraint functions, and select the set of point-addition criteria, wherein the number of point-addition criteria is... ; Step S2: Start via message passing interface p 1 process, of which p The value of is chosen with the goal of maximizing parallel efficiency; Step S3: The root process extracts an initial sample point set using the experimental design method and broadcasts the sample point set to all processes; Step S4: Distribute the computation task of the initial sample point set evenly to each process. Each process independently calculates the response value of the sample point. After the computation is completed, the response set of the initial sample is obtained through the MPI full collection operation. Step S5: Distribute the modeling tasks for the objective function and constraint function evenly to each process. Each process independently builds a proxy model. After the modeling is completed, the model parameters are sent to the root process. Step S6: Distribute the point-addition criteria equally among the processes. The root process sends the model parameters to each process. Each process solves the sub-optimization problem defined by its assigned point-addition criteria to obtain new sample points. All new sample points are obtained through the MPI full collection operation. Step S7: Repeat steps S4 to S6 until the optimization convergence criterion is met.

2. The efficient proxy optimization method according to claim 1, characterized in that, The number of processes mentioned in step S2 p The value is dynamically adjusted based on available computing resources and task complexity.

3. The efficient proxy optimization method according to claim 1, characterized in that, The experimental design method described in step S3 is Latin hypercube sampling, uniform design, Monte Carlo sampling, or a given method.

4. The efficient proxy optimization method according to claim 1, characterized in that, In step S4, MPI technology is used to call multiple processes to submit sample point analysis tasks to the high-performance computing cluster in parallel. Each process summarizes the response values ​​of the sample points through the MPI full collection operation.

5. The efficient proxy optimization method according to claim 1, characterized in that, In step S5, the surrogate model is one or more of the following: Kriging model, gradient boosting Kriging model, hierarchical Kriging model, radial basis function model, or neural network model.

6. The efficient proxy optimization method according to claim 5, characterized in that, During the modeling process, one or more of the following can be saved: process variance, hyperparameters, correlation matrix, or their decomposition results, to accelerate subsequent model predictions.

7. The efficient proxy optimization method according to claim 1, characterized in that, In step S6, the addition criteria include one or more of minimizing model prediction, improving probability, improving expectation, confidence lower bound, or maximizing mean square error.

8. The efficient proxy optimization method according to claim 1, characterized in that, The optimization convergence criterion mentioned in step S7 is that the relative change between the objective function value and the design variable value is less than a set threshold or the maximum number of response function evaluations is reached.

9. A computer device, characterized in that, It includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the efficient surrogate optimization method for parallel modeling and sub-optimization as described in any one of claims 1 to 8.

10. A computer-readable storage medium, characterized in that, It stores a computer program that, when executed by a processor, implements the efficient surrogate optimization method for parallel modeling and sub-optimization as described in any one of claims 1 to 8.

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