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

摘要/Abstract

摘要：

时变参数系统的仿真优化问题是一个新兴的研究课题, 相比传统仿真优化, 时变参数系统对实时性的要求高, 而对解的精度要求不高。本文提出将该问题转换为一类神经网络预测问题, 并从理论上证明了该方法的可行性。首先, 线下构建神经网络模型描述输入参数到最优解的映射关系; 然后, 利用训练好的神经网络模型线上实时预测最优解。考虑到边界样本对最优解拟合曲面的影响, 提出构建中心样本和边界样本，分别训练两个神经网络模型。仿真和实例表明, 该方法能够随时变参数的变化实时给出满意解, 从而为求解时变参数仿真优化问题提供一种新的解决思路。

关键词: 时变参数, 仿真优化, 神经网络, 在线优化

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

中图分类号:

TP391.9

吴诗辉, 周宇, 李正欣, 刘晓东, 贺波. 基于神经网络的时变参数系统仿真优化方法[J]. 系统工程与电子技术, 2023, 45(2): 472-480.

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.

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参考文献 33

1	DONG K S , HUANG H Q , HUANG C Q , et al. Trajectory online optimization for unmanned combat aerial vehicle using combined strategy[J]. Journal of Systems Engineering and Electronics, 2017, 28 (5): 963- 970. doi: 10.21629/JSEE.2017.05.14
2	AZADIVAR F. Simulation optimization methodologies[C]//Proc. of the Winter Simulation Conference, 1999: 93-100.
3	AMARAN S , SAHINIDIS N V , SHARDA B , et al. Simulation optimization: a review of algorithms and applications[J]. Annals of Operations Research, 2016, 240 (1): 351- 380. doi: 10.1007/s10479-015-2019-x
4	LIU R , XIE X L , YU K Y , et al. A survey on simulation optimization for the manufacturing system operation[J]. International Journal of Modelling & Simulation, 2018, 38 (2): 116- 127.
5	BARTON R R, MECKESHEIMER M. Chapter 18: Metamodel-based simulation optimization[M]//HENDERSON S G, NELSON B L, ed. Handbooks in operation research & management science. Amsterdam: North Holland, 2006.
6	HONG L J , JIANG G . Offline simulation online application: a new framework of simulation-based decision making[J]. Asia-Pacific Journal of Operational Research, 2019, 36 (6): 1940015. doi: 10.1142/S0217595919400153
7	KLEIJNEN J P C . Regression metamodels for generalizing simulation results[J]. IEEE Trans.on Systems, Man, and Cyberne-tics, 1979, 9 (2): 93- 96. doi: 10.1109/TSMC.1979.4310155
8	CAN B , HEAVEY C . A comparison of genetic programming and artificial neural networks in metamodeling of discrete-event simulation models[J]. Computers Operations Research, 2012, 39 (2): 424- 436. doi: 10.1016/j.cor.2011.05.004
9	TRIKI M, CHABCHOUB H. A neural network-based simulation meta model for a process parameters optimization: a case study[C]//Proc. of the 4th International Conference on Logistics, 2011: 323-328.
10	FONSECA D J , NAVARESSE D O , MOYNIHAN G P . Simulation metamodeling through artificial neural networks[J]. Engineering Applications of Artificial Intelligence, 2003, 16 (3): 177- 183. doi: 10.1016/S0952-1976(03)00043-5
11	GHOSH S , ROY A , CHAKRABORTY S . Support vector regression based metamodeling for seismic reliability analysis of structures[J]. Applied Mathematical Modelling, 2018, 64, 584- 602. doi: 10.1016/j.apm.2018.07.054
12	ROY A , MANNA R , CHAKRABORTY S . Support vector regression based metamodeling for structural reliability analysis[J]. Probabilistic Engineering Mechanics, 2019, 55, 78- 89. doi: 10.1016/j.probengmech.2018.11.001
13	KLEIJNEN J P C . Kriging metamodeling in simulation: a review[J]. European Journal of Operational Research, 2009, 192 (3): 707- 716. doi: 10.1016/j.ejor.2007.10.013
14	WANG S , NG S H , HASKELL W B . A multilevel simulation optimization approach for quantile functions[J]. INFORMS Journal on Computing, 2022, 34 (1): 569- 585. doi: 10.1287/ijoc.2020.1049
15	李耀辉. 基于Kriging模型的全局近似与SO方法[D]. 武汉: 华中科技大学, 2015.
	LI Y H. The Kriging-based global approximation and simulation optimization methods[D]. Wuhan: Huazhong University of Science & Technology, 2015.
16	COELHO G F , PINTO L R . Kriging-based simulation optimization: an emergency medical system application[J]. Journal of the Operational Research Society, 2018, 69 (12): 2006- 2020. doi: 10.1080/01605682.2017.1418149
17	ANKENMAN B E , NELSON B L , STAUM J . Stochastic Kriging for simulation metamodeling[J]. Operations Research, 2010, 58 (2): 371- 382. doi: 10.1287/opre.1090.0754
18	FAN Q , HU J Q . Surrogate-based promising area search for lipschitz continuous simulation optimization[J]. INFORMS Journal on Computing, 2018, 30 (4): 677- 693. doi: 10.1287/ijoc.2017.0801
19	BARTON R R. Simulation metamodels[C]//Proc. of the Winter Simulation Conference, 1998: 167-176.
20	KLEIJNEN J P C , SARGENT R G . A methodology for fitting and validating metamodels in simulation[J]. European Journal of Operational Research, 2000, 120 (1): 14- 29. doi: 10.1016/S0377-2217(98)00392-0
21	BOZAGAC D , BATMAZ I , OGUZTUZUN H . Dynamic simulation metamodeling using MARS: a case of radar simulation[J]. Mathematics and Computers in Simulation, 2016, 124, 69- 86. doi: 10.1016/j.matcom.2016.01.005
22	WANG Q , FANG H B , SHEN L . Reliability analysis of tunnels using a metamodeling technique based on augmented radial basis functions[J]. Tunnelling and Underground Space Technology, 2016, 56, 45- 53. doi: 10.1016/j.tust.2016.02.007
23	ZHANG C , WEI H K , XIE L P , et al. Direct interval forecasting of wind speed using radial basis function neural networks in a multi-objective optimization framework[J]. Neurocomputing, 2016, 205, 53- 63. doi: 10.1016/j.neucom.2016.03.061
24	HUSSAIN M F , BARTON R R , JOSHI S B . Metamodeling: radial basis functions, versus polynomials[J]. European Journal of Operational Research, 2002, 138 (1): 142- 154. doi: 10.1016/S0377-2217(01)00076-5
25	DUNKE F , NICKEL S . Neural networks for the metamodeling of simulation models with online decision making[J]. Simulation Modelling Practice and Theory, 2020, 99 (14): 102016.
26	HURRION R D , BIRGIL S . A comparison of factorial and random experimental design methods for the development of regression and neural network simulation metamodels[J]. Journal of the Operational Research Society, 1999, 50, 1018- 1033.
27	BADIRU A B , SIEGER D B . Neural network as a simulation metamodel in economic analysis of risky projects[J]. European Journal of Operational Research, 1998, 105 (1): 130- 142. doi: 10.1016/S0377-2217(97)00029-5
28	CHRYSSOLOURIS G , LEE M , DOMROESE M . The use of neural networks in determining operational policies for manufacturing systems[J]. Journal of Manufacturing Systems, 1991, 10 (2): 166- 175. doi: 10.1016/0278-6125(91)90018-W
29	VAN GELDER L , DAS P , JANSSEN H , et al. Comparative study of meta modelling techniques in building energy simulation: guidelines for practitioners[J]. Simulation Modelling Practice and Theory, 2014, 49, 245- 257. doi: 10.1016/j.simpat.2014.10.004
30	MOUELHI-CHIBANI W , PIERREVAL H . Training a neural network to select dispatching rules in real time[J]. Computers & Industrial Engineering, 2010, 58 (2): 249- 256.
31	吴诗辉, 刘晓东, 邵悦, 等. 一种基于神经网络的SO方法[J]. 系统仿真学报, 2018, 30 (1): 36- 44.
	WU S H , LIU X D , SHAO Y , et al. Optimization via simulation based on neural network[J]. Journal of System Simulation, 2018, 30 (1): 36- 44.
32	吴诗辉, 张发, 李正欣, 等. 基于神经网络的SO算法设计[J]. 系统工程与电子技术, 2019, 41 (6): 1324- 1335.
	WU S H , ZHANG F , LI Z X , et al. Design of algorithm for neural network based optimization via simulation[J]. Systems Engineering and Electronics, 2019, 41 (6): 1324- 1335.
33	CHANG X K , DONG M , YANG D . Multi-objective real-time dispatching for integrated delivery in a Fab using GA based simulation optimization[J]. Journal of Manufacturing Systems, 2013, 32 (4): 741- 751. doi: 10.1016/j.jmsy.2013.07.001

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