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Multi-objective optimization method based on Gaussian process simultaneous MIMO model

A multi-objective optimization, Gaussian process technology, applied in the multi-objective optimization design field of Gaussian process simultaneous modeling combined with optimization algorithm, can solve the problem of insufficient utilization of system information, cross-correlation model fitting or prediction accuracy of category input variables Unable to capture, small sample size, etc.

Active Publication Date: 2013-10-02
GUANGXI UNIV
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Problems solved by technology

[0008] The purpose of the present invention is to propose a multi-objective optimization method based on the Gaussian process simultaneous MIMO (multiple inputs and multiple outputs) model. With the Gaussian process simultaneous MIMO model, the model-related parameters are less, easy to implement, and the sample size is small. Advantages, to solve the problem of long time-consuming optimization calculation, insufficient utilization of system information, multi-objective proxy model cannot use the cross-correlation of category input variables to improve the accuracy of model fitting or prediction for unknown points, and cannot capture different types of correlation between output terminals The problem

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  • Multi-objective optimization method based on Gaussian process simultaneous MIMO model

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Embodiment 1

[0053] Numerical examples for solving multi-objective problems

[0054] A multi-objective optimization method based on a Gaussian process simultaneous MIMO model, including experimental design method sampling, standard Gaussian process simultaneous MIMO model and multi-objective optimization algorithm optimization, including the following steps:

[0055] Step 1. According to the numerical multi-objective problem given by the user, its mathematical description is as formula (9), and the experimental design is carried out through the Latin hypercube experimental design method, and 20 sample points are obtained by sampling in the variable x∈[0,1]. And substitute into the analytical formula f of formula (9) 1 , g(x 1 ,x 2 ), get the corresponding response value, and form the training data set of the model together with the sample set of variable x;

[0056] f 1 =x 1

[0057] f 2 =g(x 1 ,x 2 )h(x 1 ,x 2 )

[0058] g(x 1 ,x 2 )=11+x 2 2 -10cos(2px 2 ) ...

Embodiment 2

[0088] Application of Multi-objective Optimization Method Based on Gaussian Process Simultaneous MIMO Model in Sheet Metal Drawing

[0089] Using the multi-objective optimization method based on the Gaussian process simultaneous MIMO model to optimize the rear cover of an automobile axle housing, such as Image 6 with Figure 7 As shown, the multi-objective optimization of deep drawing process parameters, the optimization process flow chart is as follows Figure 8 shown, including the following steps:

[0090] Step 1. Select the forming process parameters to be optimized according to the process documents formulated by the customer, and determine their value ranges as follows: 80≤BHF(kN)≤500, 275≤Bill diameter D(mm)≤325, 0.10≤Static friction coefficient μ between sheet metal and die 1 ≤0.15, 0.10≤Static friction coefficient μ of sheet metal and blank holder ring 2 ≤0.15, through the enhanced translation propagation Latin hypercube (ETPLHD) sampling method for experimental ...

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Abstract

Provided is a multi-objective optimization method based on a Gaussian process simultaneous MIMO model. According to the method, samples are obtained in an experiment design method, a mapping relation between design variables and responses to be studied is approximately set by utilizing the Gaussian process simultaneous MIMO model, multi-objective optimization is carried out on the Gaussian process simultaneous MIMO model in a Gaussian variation hybrid genetic algorithm, an ant colony algorithm and the like, then Pareto front related to design variable combinations is obtained, furthermore, distribution quality of solution sets in the Pareto front is judged, finally, one design variable combination in the Pareto front is selected according to specific demands for high-accuracy analysis and solution, and physical experiments are carried out when obtained results are satisfactory. According to the multi-objective optimization, experiment design, the high-accuracy analysis and solution, an agent model technology and an optimization algorithm are integrated and applied to the optimization design, therefore, time consumption and computation cost of the optimization design are reduced greatly, and work efficiency is greatly improved.

Description

technical field [0001] The invention relates to a multi-objective optimization method in which proxy model technology is combined with optimization algorithm, in particular to a multi-objective optimization design method in which Gaussian process simultaneous modeling is combined with optimization algorithm. Background technique [0002] The development of surrogate model technology provides an effective bridge for the introduction of optimization technology. The sample data is obtained through advanced experimental design methods, and the mapping relationship between design variables and the response to be investigated is approximated by using surrogate model technology. Finally, the optimization algorithm is used to solve the relationship. The model obtains the optimal combination of design variables. This method of integrating experimental design, high-precision analysis and solving, surrogate model technology, and optimization algorithms into optimal design can not only ...

Claims

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Application Information

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IPC IPC(8): G06F17/50
Inventor 夏薇杨欢廖小平龙凤英曹高翔
Owner GUANGXI UNIV
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