An engineering optimization method based on a partitioned hybrid surrogate model
By partitioning the design space and combining multi-objective genetic algorithms to build a partitioned hybrid proxy model, the problems of high computing costs and insufficient prediction accuracy in the existing technology are solved, and more efficient engineering optimization is achieved.
Patent Information
- Application Number
- CN202210422083.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-04-21
- Publication Date
- 2025-07-11
- Estimated Expiration
- 2042-04-21
AI Technical Summary
The existing hybrid agent model has problems such as high computational cost and insufficient prediction accuracy in engineering optimization problems, especially when it comes to multi-objective optimization problems, which are difficult to effectively reduce computing costs and improve optimization efficiency.
The partitioned hybrid proxy model is adopted to divide the design space into multiple subdomains, each subdomain allocates an optimization weight factor, combines a multi-objective genetic algorithm, and update the optimal solution set through initial design samples and adaptive iteration to build the final hybrid proxy model, and use polynomial regression, radial basis function and Kriging model for prediction.
It significantly reduces the calculation cost of engineering optimization problems, improves the Pareto cutting-edge accuracy of prediction, and improves the solution efficiency and accuracy of multi-objective optimization.
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Figure CN114912351B_ABST
Abstract
Description
Technical Field
[0001] The present invention mainly relates to the technical field of engineering optimization, and particularly refers to a multi-objective optimization method for specific engineering problems by combining a partitioned hybrid surrogate model with a multi-objective genetic algorithm. Background Art
[0002] The design of modern engineering systems usually relies on high-fidelity numerical simulations (such as finite element analysis), which are usually very costly in terms of computation. In the optimal design of engineering systems, high-fidelity numerical simulations need to be carried out multiple times, so the computational cost is often too high to be affordable. Especially when dealing with multi-objective engineering optimization problems, the number of computations often increases exponentially, making the computational cost even more unbearable.
[0003] To reduce the computational cost, surrogate models are often used as substitutes for high-fidelity numerical simulations in optimization work, and fitting formulas are generated through the surrogate models to predict the response values under different design variable values. And often there are multiple optimization objectives to be considered in the optimal design of an engineering problem, which requires combining the surrogate model with a multi-objective optimization algorithm.
[0004] The "multi-objective genetic algorithm" is a popular global optimization method that originated from the natural evolution mechanism and genetic principles. The multi-objective genetic algorithm is superior to many traditional multi-objective optimization algorithms because it can avoid getting trapped in local optima and thus can effectively search for the global optimal solution. It uses non-dominated sorting to rank the solutions and assigns fitness according to the ranking. Combining the surrogate model method with the multi-objective genetic algorithm and applying it to engineering optimization problems can achieve the purpose of reducing the computational cost without sacrificing fidelity.
[0005] The "hybrid surrogate model" combines various types of individual surrogate models in the form of a weighted average set, and its accuracy is improved compared with the individual surrogate models used alone. Currently, there are mainly two types of hybrid surrogate models: the "base-point hybrid surrogate model" and the "global average hybrid surrogate model". However, both of these hybrid surrogate models have certain disadvantages and limitations. The base-point hybrid surrogate model usually has better prediction accuracy than the global average hybrid surrogate model because it calculates the weight values of each surrogate model at each design point, but it also takes more time than the global average hybrid surrogate model. In most cases, surrogate models are usually used for engineering design optimization and often need to be called tens of thousands of times for calculation. Therefore, the global average hybrid surrogate model is still the most widely used. However, the lack of prediction accuracy of the global average hybrid surrogate model is still inevitable.
[0006] With the increasing development of technology, engineering problems in various fields are becoming more and more complex. At the same time, the optimization of these projects is becoming increasingly difficult to solve. Solving optimization problems solely by simulation is obviously time-consuming, laborious and ineffective, and the calculation cost has also begun to grow to an unbearable level. Due to the limitations of the above two surrogate models, a new surrogate model method that can integrate the advantages and disadvantages of the above two surrogate models needs to be proposed urgently to better meet the needs of increasingly complex engineering optimization problems. Summary of the Invention
[0007] The technical problem to be solved by the present invention lies in: aiming at the technical problems existing in the prior art, the present invention provides an engineering optimization method based on a partitioned hybrid surrogate model with simple principle, easy operation, wider application range, capable of reducing calculation cost and improving optimization efficiency.
[0008] To solve the above technical problems, the present invention adopts the following technical solutions:
[0009] An engineering optimization method based on a partitioned hybrid surrogate model, the steps of which include:
[0010] Step S100: Obtain an initial design sample according to the engineering optimization goal;
[0011] Step S200: Obtain an initial hybrid surrogate model;
[0012] Step S300: Based on the initial hybrid surrogate model, perform preliminary multi-objective optimization to obtain an optimal solution set P;
[0013] Step S400: Utilize the continuously updated optimal solution set P, and set the best hybrid surrogate model obtained thereby as the final hybrid surrogate model.
[0014] As a further improvement of the method of the present invention: the step S100 includes:
[0015] Determine the optimization goal and the design variables associated with the optimization goal;
[0016] Generate an initial design sample by the full factorial method, and the initial design sample is used to construct a basic surrogate model and will be used to calculate the weight factor of each basic surrogate model; the basic surrogate models include polynomial regression PR, radial basis function RBF and Kriging KRG.
[0017] As a further improvement of the method of the present invention: the initial design sample is updated by adding specific additional samples in each adaptive iteration process.
[0018] As a further improvement of the method of the present invention: the step S200 includes:
[0019] Divide the design domain into several sub-regions;
[0020] Calculate the weight factor for each sub-region and construct an individual basic surrogate model in each divided region;
[0021] Construct a basic surrogate model based on the entire design domain;
[0022] Combine the created basic surrogate model with the weight factor to form an initial hybrid surrogate model.
[0023] As a further improvement of the method of the present invention: the weight factor of each individual basic surrogate model is determined by the following equation, which requires each basic surrogate model to be constructed ndes times in each sub-region, where ndes refers to the number of design points in that region:
[0024]
[0025] w i * =(E i +αE avg ) β α < 1, β < 0
[0026]
[0027]
[0028] where w i is the normalized weight factor of the i-th basic model in this region, w i * is the calculated weight factor of the i-th basic model in this region (the calculated weight factor is normalized to obtain the final normalized weight factor), α and β are control constants, and it is recommended to take α = 0.05 and β = -1. E avg is the average error of all basic models in this region, E i is the average error of the i-th basic surrogate model at each design point in this region. M is the number of basic surrogate models, ndes is the number of design points in this region, x k is the k-th design point, y(x k ) is the actual response value at x k , is the predicted response value of the i-th basic surrogate model generated using (ndes - 1) design points.
[0029] As a further improvement of the method of the present invention: the initial hybrid surrogate model is regenerated in subsequent adaptive iteration processes.
[0030] As a further improvement of the method of the present invention: in the steps S300 and S400, the multi-objective genetic algorithm NSGA-II is used for preliminary multi-objective optimization to obtain the optimal solution set P; the optimal solution set P obtained in each adaptive iteration is retained for subsequent convergence judgment.
[0031] As a further improvement of the method of the present invention: N = N1 + N2 additional design samples are selected from the optimal solution set P, and the objective response values and constraint function values of the selected N additional design points are calculated; the N additional design samples are added to the initial design samples and located in the divided regions according to the design variable values of the new samples, thereby updating the design samples; if the Pareto front (i.e., the optimal solution set P) converges, the best weight factors of each region and the weight factors on the region boundaries are retained; and the latest obtained best hybrid surrogate model is set as the final hybrid surrogate model; the principles for selecting additional design points from the optimal solution set P include Principle 1 and Principle 2, where Principle 1 generates N1 additional design points and Principle 2 generates N2 additional design points; the said Principle 1 is the BOE method, and the said Principle 2 is the BOL method.
[0032] As a further improvement of the method of the present invention: the process of the BOE method includes:
[0033] Select several existing design points close to the predicted Pareto set as specific design points;
[0034] Using the hybrid surrogate model constructed in the current iteration, obtain the predicted response values of these selected specific design points;
[0035] Calculate the errors between the predicted response values and the actual response values of the specific design points, and arrange these specific design points in descending order according to the errors;
[0036] Select the nearest optimization point corresponding to each specific design point, and arrange these selected optimization points according to the order of their corresponding specific design points;
[0037] Select the N1 best points in the sorting as additional design points.
[0038] As a further improvement of the method of the present invention: the BOL method is a method based on the position of the best points distributed in the design space, and points are selected in the blank areas where the best points are far from the existing design points.
[0039] Compared with the prior art, the advantages of the present invention are as follows:
[0040] 1. An engineering optimization method based on a partitioned hybrid surrogate model of the present invention has a simple principle and is easy to operate. On the premise of ensuring correctness and accuracy, it can significantly reduce the computational cost of engineering optimization problems, thereby improving the solution efficiency of engineering optimization problems.
[0041] 2. An engineering optimization method based on a partitioned hybrid surrogate model of the present invention, wherein the predicted Pareto front has higher accuracy than the method based on a single basic surrogate model. This is because the method of the present invention can continuously select new design samples from the iteration of the Pareto front, so as to find the optimal design point. For the method based on a single basic surrogate model, more design samples are required to achieve the same accuracy as the method of the present invention, which means more computational cost. Therefore, compared with the commonly used surrogate model methods at present, the method of the present invention is more efficient, especially in solving the actual engineering multi-objective optimization problems. BRIEF DESCRIPTION OF THE DRAWINGS
[0042] Figure 1 is a schematic flow chart of the method of the present invention.
[0043] Figure 2 is a detailed flow chart of the present invention in a specific application example.
[0044] Figure 3 is a schematic diagram of the principle of Principle 1 for selecting additional design points in a specific application example of the present invention.
[0045] Figure 4 is a schematic diagram of the principle of Principle 2 for selecting additional design points in a specific application example of the present invention.
[0046] Figure 5 is a schematic diagram of the principle of design domain partitioning in a specific application example of the present invention. DETAILED DESCRIPTION OF THE INVENTION
[0047] The following will further describe the present invention in detail with reference to the accompanying drawings of the specification and specific embodiments.
[0048] An engineering optimization method based on a partitioned hybrid surrogate model of the present invention adopts a multi-region optimization weight factor hybrid surrogate model. In this new hybrid surrogate model, the design space is divided into multiple sub-domains, and each sub-domain is assigned a set of optimized weight factors. The multi-region optimization weight factor hybrid surrogate model in the present invention is composed of three typical single surrogate models combined, namely polynomial regression (PR), radial basis function (RBF) and Kriging (KRG). The present invention further combines this new hybrid surrogate model with a multi-objective genetic algorithm to obtain a new engineering optimization method based on a partitioned hybrid surrogate model.
[0049] As Figure 1 shown, the steps of the engineering optimization method based on a partitioned hybrid surrogate model of the present invention include:
[0050] Step S100: Obtain initial design samples according to engineering optimization objectives;
[0051] Step S200: Obtain an initial hybrid surrogate model;
[0052] Step S300: Based on the initial hybrid surrogate model, perform preliminary multi-objective optimization to obtain an optimal solution set P;
[0053] Step S400: Utilize the continuously updated optimal solution set P, and set the best hybrid surrogate model obtained thereby as the final hybrid surrogate model.
[0054] In a specific application example, the detailed process of the present invention is as Figure 2 shown, including:
[0055] Step S1: Determine the optimization objectives and design variables;
[0056] That is: Determine the optimization objectives of the current engineering problem, and select the design variables associated with the optimization objectives;
[0057] According to the needs of actual applications, in specific applications, it can be a single optimization objective, or multiple optimization objectives, as well as the selection of design variables associated with the optimization objectives.
[0058] According to the needs of actual applications, the design variables can be single variables, or multiple design variables.
[0059] Step S2: Generate an initial design sample;
[0060] Generate an initial design sample through the full factorial method. The initial design sample is used to construct a basic surrogate model and will be used to calculate the weight factors of each basic surrogate model; the basic surrogate models include polynomial regression (PR), radial basis function (RBF), and Kriging (KRG);
[0061] In a specific application example, the initial design sample will be updated by adding specific additional samples in each adaptive iteration process.
[0062] Step S3: Divide the design domain into several sub-regions; for example, divide the design domain into c = i × j × k sub-regions; where i, j, and k are all constants, indicating the number of sub-regions into which each variable in the design domain is divided.
[0063] According to the needs of actual applications, as Figure 5 shown. The dimension of the design domain depends on the number of design variables. For example, if there are two design variables in the optimization problem, then the design domain is a two-dimensional space, as Figure 5 (a); if there are three design variables in the optimization problem, then the design domain is a three-dimensional space, as Figure 5 (b). In general, the size of each sub-region is equal.
[0064] Step S4: Calculate the weight factor for each sub-region and construct a separate basic surrogate model (i.e., including PR, RBF, and KRG) in each divided region.
[0065] In a specific application example, the weight factor of each separate basic surrogate model is determined by the following equation (1). This equation (1) requires that each basic surrogate model be constructed ndes times in each sub-region, where ndes refers to the number of design points in that region.
[0066]
[0067] where, w i is the normalized weight factor of the i-th basic model in this region, w i * is the calculated weight factor of the i-th basic model in this region (the calculated weight factor is normalized to obtain the final normalized weight factor), α and β are control constants, and it is recommended to take α = 0.05 and β = -1. E avg is the average error of all basic models in this region, E i is the average error of the i-th basic surrogate model at each design point in this region. M is the number of basic surrogate models, ndes is the number of design points in this region, x k is the k-th design point, y(x k ) is the actual response value at x k . is the predicted response value of the i-th basic surrogate model generated using (ndes - 1) design points.
[0068] Step S5: Construct a basic surrogate model based on the entire design domain, i.e., PR, RBF, and KRG.
[0069] The above basic surrogate model will be used to form an initial hybrid surrogate model. The basic surrogate model will also be updated as other design samples are added.
[0070] Step S6: Combine the basic surrogate model created in Step S5 with the weight factor calculated in Step S4 to form an initial hybrid surrogate model. Since the weight factor and the basic surrogate model will be updated in the later adaptive iteration, the initial hybrid surrogate model will be regenerated in the subsequent adaptive iteration process.
[0071] Step S7: Based on the initial hybrid surrogate model obtained in Step S6, perform a preliminary multi-objective optimization using the multi-objective genetic algorithm NSGA-II.
[0072] Step S8: Obtain the optimal solution set P (Pareto front). The optimal solution set P obtained in each adaptive iteration is retained for subsequent convergence judgment.
[0073] In a specific application example, the convergence judgment step includes: performing a Kolmogorov-Smirnov test on the two most recent consecutive Pareto fronts P saved in step S8. Set the rejection range to 0.95. If the significance level P > 0.95, considering that the convergence condition is met, the program proceeds to step S12. If the significance level P < 0.95, it indicates that the convergence test fails, and the program proceeds to step S9 to execute the adaptive process.
[0074] Step S9: Select N = N1 + N2 additional design samples from the latest Pareto front P.
[0075] The principles for selecting additional design points from the Pareto front include Principle 1 and Principle 2. Among them, Principle 1 generates N1 additional design points, and Principle 2 generates N2 additional design points.
[0076] Principle 1:
[0077] See Figure 3 , the BOE method: The BOE method includes the following steps:
[0078] 1) Select several existing design points close to the predicted Pareto set as specific design points. See Appendix Figure 2 .
[0079] 2) Use the hybrid surrogate model constructed in the current iteration to obtain the predicted response values of these selected specific design points.
[0080] 3) Calculate the error between the predicted response value and the actual response value of the specific design points, and arrange these specific design points in descending order according to the error.
[0081] 4) Select the nearest optimization point corresponding to each specific design point, and arrange these selected optimization points according to the order of their corresponding specific design points.
[0082] 5) Select the N1 best points in the sorting as additional design points.
[0083] Principle 2:
[0084] The BOL method is the BOL method based on the positions of the best points distributed in the design space, such as Figure 4As shown. Different from the BOE method, the principle of the BOL method is to select points in the blank area, where the best points are far from the existing design points. In the blank area, there is less information on the actual response value, and the error between the predicted response value and the actual response value is larger. Therefore, it makes sense to select additional design points in these blank areas. Use the BOL principle to select N2 design points as additional design points.
[0085] Step S10: Calculate the objective response value and constraint function value of the selected N additional design points.
[0086] In specific applications, since the multi-objective optimization problem of the operation is an engineering problem, this may be a time-consuming step.
[0087] Step S11: Add the N additional design samples to the initial design samples, and locate them in the divided regions according to the design variable values of the new samples, so as to update the design samples, and then go to Step S4.
[0088] Step S12: If the Pareto front converges, retain the best weight factor of each region and the weight factor on the boundary of the region; and set the latest obtained best hybrid surrogate model as the final hybrid surrogate model; then terminate the program.
[0089] Step S13: End.
[0090] The above is only the preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions falling within the idea of the present invention belong to the protection scope of the present invention. It should be noted that for those of ordinary skill in the art, several improvements and refinements made without departing from the principle of the present invention should be regarded as the protection scope of the present invention.
Claims
1. An engineering optimization method based on a partitioned hybrid surrogate model, characterized by the steps Including: Step S100: Obtain an initial design sample according to the engineering optimization goal; Step S200: Obtain an initial hybrid surrogate model; Step S300: Based on the initial hybrid surrogate model, conduct preliminary multi-objective optimization to obtain the optimal solution set P; Step S400: Utilize the continuously updated optimal solution set P, and set the best hybrid surrogate model obtained thereby as the final hybrid surrogate model; In the said Step S300 and Step S400, use the multi-objective genetic algorithm NSGA-II to conduct preliminary multi-objective optimization to obtain the optimal solution set P; the optimal solution set P obtained in each adaptive iteration is retained for subsequent convergence judgment; Select N = N1 + N2 additional design samples from the optimal solution set P, calculate the objective response values and constraint function values of the selected N additional design points; add the N additional design samples to the initial design sample, and locate them in the divided regions according to the design variable values of the new samples, thereby updating the design sample; if the Pareto front converges, retain the best weight factor of each region and the weight factor on the region boundary; and set the latest obtained best hybrid surrogate model as the final hybrid surrogate model; the principles for selecting additional design points from the optimal solution set P include Principle 1 and Principle 2, where Principle 1 generates N1 additional design points and Principle 2 generates N2 additional design points; said Principle 1 is the BOE method, and said Principle 2 is the BOL method.
2. The engineering optimization method based on the partitioned hybrid surrogate model according to claim 1, wherein The said Step S100 includes: Determine the optimization goal and the design variables associated with the optimization goal; Generate an initial design sample by the full factorial method, and the initial design sample is used to construct the basic surrogate model and will be used to calculate the weight factor of each basic surrogate model; the basic surrogate model includes polynomial regression PR, radial basis function RBF, and Kriging KRG.
3. The engineering optimization method based on the partitioned hybrid surrogate model according to claim 2, wherein The initial design sample is updated by adding specific additional samples in each adaptive iteration process.
4. The engineering optimization method based on the partitioned hybrid surrogate model according to claim 1, wherein The said Step S200 includes: Divide the design domain into several sub-regions; Calculate the weight factor of each sub-region, and construct a separate basic surrogate model in each divided region; Construct a basic surrogate model based on the entire design domain; Combine the created basic surrogate models with the weight factors into an initial hybrid surrogate model.
5. The engineering optimization method based on the partitioned hybrid surrogate model according to claim 4, characterized in that The weight factor of each separate basic surrogate model is determined by the following equation, and this equation requires each basic surrogate model to be constructed ndes times in each sub-region, where ndes refers to the number of design points in this region: where, w i is the normalized weight factor of the i-th basic model in this region, w i * is the calculated weight factor of the i-th basic model in this region, α and β are control constants, E avg is the average error of all basic models in this region, E i is the average error of the i-th basic surrogate model at each design point in this region; M is the number of basic surrogate models, ndes is the number of design points in this region, x k is the k-th design point, y(x k ) is the actual response value at x k , is the predicted response value of the i-th basic surrogate model generated using (ndes - 1) design points.
6. The engineering optimization method based on the partitioned hybrid surrogate model according to claim 4, characterized in that, The initial hybrid surrogate model is regenerated in subsequent adaptive iteration processes.
7. The engineering optimization method based on the partitioned hybrid surrogate model according to claim 1, wherein The process of the said BOE method includes: Select several existing design points close to the predicted Pareto set as specific design points; Use the hybrid surrogate model constructed in the current iteration to obtain the predicted response values of these selected specific design points; Calculate the error between the predicted response value and the actual response value of the specific design points, and arrange these specific design points in descending order according to the error; Select the nearest Pareto optimization point corresponding to each specific design point, and arrange these selected optimization points according to the order of their corresponding specific design points; Select N1 of the best points in the selection sort as additional design points.
8. The engineering optimization method based on the partitioned hybrid surrogate model according to claim 1, characterized in that The BOL method is a method based on the positions of the best points distributed in the design space, which selects points in the blank area where the best points are far from the existing design points.