基于神经网络的时变参数系统仿真优化方法

doi:10.12305/j.issn.1001-506X.2023.02.18

Abstract

Abstract:

Simulation optimization (SO) of time-varying parameters (TVP) systems is an emerging research topic, which is different from traditional SO problems in that the real-time requirements are very high while the accuracy requirements are relatively lower. This paper proposes to transform the SO problem with TVP into a neural network (NN) prediction problem, and theoretically proves the feasibility of the method. Firstly, training samples are generated by offline SO, and an appropriate NN model is designed and trained to describe the relationship between input TVP and the corresponding optimal solutions. Then, the well trained NN model is used to realize online real-time prediction of the optimal solution. Considering the impact of boundary samples on the optimal solution fitting curve, we propose to train internal training samples and boundary training samples respectively so that two different NN models will be built to better reflect the fitting curve. The simulation and empirical study show that, our approach can provide online real-time satisfactory solutions as TVP changes, which presents an approach to SO problems with TVP.

Key words: time-varying parameter (TVP), simulation optimization (SO), neural network (NN), online optimization

CLC Number:

TP391.9

Shihui WU, Yu ZHOU, Zhengxin LI, Xiaodong LIU, Bo HE. Approach to simulation optimization of time-varying parameters system based on neural network[J]. Systems Engineering and Electronics, 2023, 45(2): 472-480.

Figures/Tables 13

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References 33

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样本序号	训练样本参数取值					最优解
样本序号	a₁	a₂	a₃	a₄	a₅	x_min	y_min
1	0.115 6	-0.249 1	-0.311 5	-0.320 9	1.449 7	0.979 4	-0.134 3
2	-0.044 9	0.045 9	0.218 8	-0.164 9	1.680 3	2.752 2	-0.189 4
3	0.094 5	-0.082	-0.398 3	0.023 7	-1.160 1	14.914 4	-0.539 1
4	-0.021 1	0.098 3	0.561 3	-0.487 7	1.344 4	19.5	-0.143 1
5	0.070 8	0.178	-0.028 6	0.290 6	0.608 3	13.406 8	-0.574 7

样本序号	测试样本参数取值					实际最优解		预测最优解
样本序号	a₁	a₂	a₃	a₄	a₅	x_min	y_min	x_p	y_p
1	0.12	-0.213	0.54	-0.17	1.23	3.745 9	-0.23	3.623 2	-0.226 7
2	0.15	-0.3	0.6	-0.4	1.1	4.054 4	-0.070 3	3.414 8	-0.034 4
3	-0.1	0.2	0.5	0.1	1.3	18.332 1	-6.925	18.556 4	-6.797 7
4	-0.2	0.2	-0.54	0.17	-1.23	19.354 6	-23.666 3	19.222 8	-23.477 8

神经网络	训练样本预测值与实际值的相关度 (Training R)	验证样本预测值与实际值的相关度 (Validation R)	测试样本预测值与实际值的相关度 (Test R)
NN₁	0.990 75	0.961	0.956 78
NN₂	0.951 38	0.936 92	0.935 5
NN₀	0.939 4	0.927 2	0.927 97

测试参数集	实际最优解	NN₁预测最优解	NN₂预测最优解	NN₀预测最优解
(3, 4, 4, 4, 5)	x_min=(-0.375, -0.437 5) y_min=3.156 3	x_min=(-0.361 4, -0.283 9)* y_min=3.259 5	x_min=(-2.556 9, -2.140 9) y_min=43.911 3	x_min=(-0.300 4, 0.610 6) y_min=7.879 4
(-7, 2, -3, -6, -8)	x_min=(5, 5) y_min=-265	x_min=(3.707 8, -1.868 2) y_min=-70.773 7	x_min=(5, 5)* y_min=-265	x_min=(4.707 5, 5) y_min=-238.979 8

方法	寻优指标	测试参数集
方法	寻优指标	(3, 4, 4, 4, 5)	(-7, 2, -3, -6, -8)
本文方法	x_min	x_min=(-0.361 4, -0.283 9) y_min=3.259 5	x_min=(5, 5) y_min=-265
	T/s	0.041 1	0.038 1
	N_fevl/次	0	0
文献[32] (样本间隔[0.05, 0.05])	x_min	x_min=(-0.351 16, -0.45) y_min=3.157 4	x_min=(5, 5) y_min=-265
	T/s	29.85	20.22
	N_fevl/次	40 401	40 401
文献[32] (样本间隔[0.1, 0.1])	x_min	x_min=(-0.28, -0.48) y_min=3.174 4	x_min=(5, 5) y_min=-265
	T/s	7.76	7.58
	N_fevl/次	10 201	10 201
文献[33]	x_min	x_min=(-0.374 9, -0.437 5) y_min=3.156 3	x_min=(5, 5) y_min=-265
	T/s	0.096 2	0.096 7
	N_fevl/次	10 410	10 410

Approach to simulation optimization of time-varying parameters system based on neural network

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