基于改进灰狼算法优化的支持向量机锌耗预测

张佳琦; 顾幸生

doi:10.14135/j.cnki.1006-3080.20210128001

基于改进灰狼算法优化的支持向量机锌耗预测

doi: 10.14135/j.cnki.1006-3080.20210128001

张佳琦,
顾幸生^,

华东理工大学能源化工过程智能制造教育部重点实验室，上海 200237

基金项目: 国家自然科学基金(61973120，62076095)

详细信息

作者简介:
张佳琦（1995-），女，江苏海门人，硕士生，主要研究方向为复杂工业过程建模与优化。E-mail：1042940326@qq.com

通讯作者:
顾幸生，E-mail：xsgu@ecust.edu.cn

中图分类号: TP181
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- 文章访问数: 224
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- 被引次数: 0
出版历程
- 收稿日期: 2021-01-28
- 网络出版日期: 2021-04-12

Zinc Consumption Forecast of Support Vector Regression Based on Improved Grey Wolf Algorithm Optimization

ZHANG Jiaqi,
GU Xingsheng^,

Key Laboratory of Smart Manufacturing in Energy Chemical Process, Ministry of Education, East China University of Science and Technology, Shanghai 200237, China

摘要

摘要: 为了提高生产镀锌板的锌锭需求预测精度，提出了一种基于改进灰狼(Improved Grey Wolf Optimization，IGWO)算法优化的支持向量机回归(Support Vector Regression，SVR)的锌耗预测建模方法。针对传统灰狼优化算法收敛快、易早熟的缺陷，首先采用混沌Tent映射策略初始化种群，增强种群的多样性和分布均匀性；其次引入控制参数的自适应调整策略，以平衡算法的搜索能力和开发能力；最后在位置更新过程中融合差分进化，降低算法误收敛的可能性。采用典型基准测试函数进行仿真实验，结果表明IGWO算法的综合性能优越，寻优能力更佳。基于某钢厂某机组的生产实际数据对锌锭消耗量进行建模预测，利用IGWO算法对SVR进行参数优化（IGWO-SVR），实验结果表明，IGWO-SVR具有更高的预测精度、更好的稳定性和更优的泛化能力。
- 支持向量机回归 /
- 灰狼优化算法 /
- Tent映射 /
- 差分进化 /
- 预测建模
Abstract: Zinc ingots are the main raw material for the production of galvanized sheets. The consumption of zinc ingots fluctuates greatly due to the impact of contract orders and product structure, resulting in fluctuating demand. Material demand often presents the characteristics of small sample size and large variation range. Its non-stationarity and non-linearity make the problem of demand forecasting more difficult. The inaccuracy of demand forecasting will be gradually amplified in the information transmission of the supply chain, which will inevitably affect the material procurement plan and inventory management. Therefore, accurate material demand forecasting has important practical significance for the optimization of raw material procurement and production management adjustments of iron and steel enterprises. In order to improve the prediction accuracy of zinc ingot demand, this paper proposes a zinc consumption prediction modeling method based on Support Vector Regression (SVR) optimized by Improved Grey Wolf Optimization (IGWO). Aiming at the shortcomings of fast convergence and premature maturity of traditional gray wolf algorithm, firstly, the chaotic Tent mapping strategy is adopted to enhance the diversity and distribution uniformity of the initial population; secondly, an adaptive adjustment strategy of control parameters is introduced to balance the search ability and development ability; Finally, the differential evolution is integrated in the location update process to reduce the possibility of the algorithm misconvergence. For the improved gray wolf algorithm, a simulation experiment is carried out with a typical benchmark test function, and the result shows that its comprehensive performance is superior. Based on the production performance data of a certain unit of a steel plant, the zinc ingot consumption was modeled and predicted, and the SVR was optimized using the IGWO algorithm. The experimental results showed that IGWO-SVR has higher prediction accuracy, better stability and better generalization ability.
- support vector regression /
- gray wolf optimization algorithm /
- tent mapping /
- differential evolution /
- predictive modeling

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图 1 收敛因子变化曲线

Figure 1. Change curves of convergence factors

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图 2 PSO、ABC、GWO和IGWO在测试函数上的收敛曲线

Figure 2. Convergence curves of PSO, ABC, GWO and IGWO on the test functions

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图 3 IGWO-SVR算法流程图

Figure 3. Flow chart of IGWO-SVR algorithm

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图 4 IGWO-SVR、PSO-SVR、GWO-SVR参数优化过程的适应度下降曲线

Figure 4. Fitness decline curves of IGWO-SVR, PSO-SVR, GWO-SVR parameter optimization process

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图 5 IGWO-SVR锌耗模型预测结果

Figure 5. Prediction results of IGWO-SVR zinc consumption model

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表 1 基准测试函数

Table 1. Benchmark test functions

Function name	Expression	Search range	${f_{\min }}$
Sphere	${f_1}(x) = \displaystyle\sum\limits_{i = 1}^d { {x_i}^2}$	[−100,100]	0
Ackley	${f_2}(x) = - 20\exp \left( { - 0.2\sqrt {\dfrac{1}{d}\displaystyle\sum\limits_{i = 1}^d { {x_i}^2} } } \right) - \exp \left( {\dfrac{1}{d}\displaystyle\sum\limits_{i = 1}^d {\cos \left( {2{\text π} {x_i} } \right)} } \right){\rm{ + 20 + e} }$	[-32,32]	0
Rastrigrin	${f_3}\left( x \right) = \displaystyle\sum\limits_{ {\rm{i = 1} } }^{ {d} } {\left( { {x_i}^2 - 10\cos \left( { {\rm{2} }{\text π} {x_i} } \right) + 10} \right)}$	[−5.12,5.12]	0
Rosenbrock	${f_4}\left( x \right) = \displaystyle\sum\limits_{i = 1}^{d - 1} {\left( {100{ {\left( { {x_{i + 1} } - {x_i}^2} \right)}^2} + { {\left( { {x_i} - 1} \right)}^2} } \right)}$	[−30,30]	0

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表 2 基准测试函数优化结果对比

Table 2. Comparison of optimization results of benchmark test functions

Function	Algorithm	Best	Ave	Worst	Sd
Sphere	PSO	11.1673	31.4918	75.3217	13.9965
	ABC	$2.87 \times {10^{ - 6}}$	$1.14 \times {10^{ - 5}}$	$4.03 \times {10^{ - 5}}$	$9.57 \times {10^{ - 6}}$
	GWO	$9.83 \times {10^{ - 30}}$	$1.61 \times {10^{ - 20}}$	$4.76 \times {10^{ - 19}}$	$8.69 \times {10^{ - 20}}$
	IGWO	$4.99 \times {10^{ - 47}}$	$2.08 \times {10^{ - 43}}$	$2.08 \times {10^{ - 42}}$	$4.91 \times {10^{ - 43}}$
Ackley	PSO	3.2254	5.4785	8.8567	1.2411
	ABC	$3.55 \times {10^{ - 3}}$	$8.01 \times {10^{ - 3}}$	$1.99 \times {10^{ - 2}}$	$4.72 \times {10^{ - 3}}$
	GWO	$6.79 \times {10^{ - 14}}$	$3.00 \times {10^{ - 13}}$	$2.47 \times {10^{ - 12}}$	$4.57 \times {10^{ - 13}}$
	IGWO	$4.44 \times {10^{ - 16}}$	$2.69 \times {10^{ - 15}}$	$7.55 \times {10^{ - 15}}$	$1.98 \times {10^{ - 15}}$
Rastrigin	PSO	26.3814	51.2482	81.5007	14.2861
	ABC	$8.30 \times {10^{ - 5}}$	$8.19 \times {10^{ - 4}}$	$8.28 \times {10^{ - 3}}$	$1.49 \times {10^{ - 3}}$
	GWO	0	$1.84 \times {10^{ - 15}}$	$1.78 \times {10^{ - 14}}$	$3.94 \times {10^{ - 15}}$
	IGWO	0	0	0	0
Rosenbrock	PSO	40.1590	100.1135	182.7656	43.2070
	ABC	4.1571	44.9819	102.0892	36.6747
	GWO	27.6587	28.4042	28.8850	0.3519
	IGWO	27.2512	28.4154	28.9241	0.3632

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表 3 各算法的参数寻优结果

Table 3. Parameters optimization results of each algorithms

Algorithm	C	$\gamma $
PSO	26.9901	3.4351
GWO	86.9902	0.1664
IGWO	85.9735	0.1669

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表 4 SVR、PSO-SVR、GWO-SVR、IGWO-SVR模型性能对比结果

Table 4. Performance comparison results of SVR, PSO-SVR, GWO-SVR and IGWO-SVR models

Model	MSE	MAPE/%	R²
SVR	5.2099	5.2405	0.8269
PSO-SVR	4.2594	3.7778	0.8585
GWO-SVR	3.7877	3.1730	0.8742
IGWO-SVR	3.7873	3.1726	0.8743

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参考文献(29)

[1]	贡文伟, 黄晶. 基于灰色理论与指数平滑法的需求预测综合模型[J]. 统计与决策, 2017, 33(1): 72-76.
[2]	高鹍, 邢国平, 孙德翔, 等. 灰色关联支持向量机在备件库存消耗预测中的应用[J]. 电光与控制, 2012, 19(3): 100-105. doi: 10.3969/j.issn.1671-637X.2012.03.023
[3]	赵建忠, 徐廷学, 刘勇, 等. 基于粗糙集和熵权以及改进支持向量机的导弹备件消耗预测[J]. 兵工学报, 2012, 33(10): 1258-1265.
[4]	白朝阳, 宋林杰, 李晓琳. 基于EMD-PSO-LSSVR的物料需求组合预测模型[J]. 统计与决策, 2018, 34(18): 185-188.
[5]	荆园园, 李红娟. 汽车制造业物料供应需求优化预测仿真研究[J]. 计算机仿真, 2016, 33(10): 421-424. doi: 10.3969/j.issn.1006-9348.2016.10.091
[6]	CAO L J, TAY F E H. Support vector machine with adaptive parameters in financial time series forecasting[J]. IEEE Transactions on neural networks, 2003, 14(6): 1506-1518. doi: 10.1109/TNN.2003.820556
[7]	CASTRO-NETO M, JEONG Y S, JEONG M K, et al. Online-SVR for short-term traffic flow prediction under typical and atypical traffic conditions[J]. Expert Systems with Applications, 2009, 36(3): 6164-6173. doi: 10.1016/j.eswa.2008.07.069
[8]	PAI P F, HONG W C. Forecasting regional electricity load based on recurrent support vector machines with genetic algorithms[J]. Electric Power Systems Research, 2005, 74(3): 417-425. doi: 10.1016/j.jpgr.2005.01.006
[9]	LIU X, JIA D, LI H, et al. Research on kernel parameter optimization of support vector machine in speaker recognition[J]. Science Technology and Engineering, 2010, 10(7): 1669-1673.
[10]	ZHANG Y, WANG S, JI G, et al. An MR brain images classifier system via particle swarm optimization and kernel support vector machine[J]. Scientific World Journal, 2013, 2013: 1-9.
[11]	CHEN P W, WANG J Y, LEE H M. Model selection of SVMs using GA approach[C]//2004 IEEE International Joint Conference on Neural Networks. Hungary: IEEE, 2004: 2035-2040.
[12]	AKAY B, KARABOGA D. A modified artificial bee colony algorithm for real-parameter optimization[J]. Information Sciences, 2012, 192: 120-142. doi: 10.1016/j.ins.2010.07.015
[13]	陈汉宇, 王华忠, 颜秉勇. 基于 CUDA 和布谷鸟算法的 SVM 在工控入侵检测中的应用[J]. 华东理工大学学报 (自然科学版), 2019, 45(1): 101-109.
[14]	MIRJALILI S, MIRJALILI S M, LEWIS A. Grey wolf optimizer[J]. Advances in Engineering Software, 2014, 69: 46-61. doi: 10.1016/j.advengsoft.2013.12.007
[15]	EMARY E, ZAWBAA H M, HASSANIEN A E. Binary grey wolf optimization approaches for feature selection[J]. Neurocomputing, 2016, 172: 371-381. doi: 10.1016/j.neucom.2015.06.083
[16]	AHMED H M, YOUSSEF B A B, ELKORANY A S, et al. Hybrid gray wolf optimizer–artificial neural network classification approach for magnetic resonance brain images[J]. Applied Optics, 2018, 57(7): 25-31. doi: 10.1364/AO.57.000B25
[17]	姚鹏, 王宏伦. 基于改进流体扰动算法与灰狼优化的无人机三维航路规划[J]. 控制与决策, 2016, 31(4): 701-708.
[18]	KOMAKI G M, KAYVANFAR V. Grey wolf optimizer algorithm for the two-stage assembly flow shop scheduling problem with release time[J]. Journal of Computational Science, 2015, 8: 109-120. doi: 10.1016/j.jocs.2015.03.011
[19]	SAREMI S, MIRJALILI S Z, MIRJALILI S M. Evolutionary population dynamics and grey wolf optimizer[J]. Neural Computing and Applications, 2015, 26(5): 1257-1263. doi: 10.1007/s00521-014-1806-7
[20]	ZHANG S, ZHOU Y. Grey wolf optimizer based on Powell local optimization method for clustering analysis[J]. Discrete Dynamics in Nature and Society, 2015: 1-7.
[21]	郭振洲, 刘然, 拱长青, 等. 基于灰狼算法的改进研究[J]. 计算机应用研究, 2017, 34(12): 3603-3606. doi: 10.3969/j.issn.1001-3695.2017.12.019
[22]	ZHU A, XU C, LI Z, et al. Hybridizing grey wolf optimization with differential evolution for global optimization and test scheduling for 3D stacked SoC[J]. Journal of Systems Engineering and Electronics, 2015, 26(2): 317-328. doi: 10.1109/JSEE.2015.00037
[23]	龙文, 蔡绍洪, 焦建军, 等. 求解高维优化问题的混合灰狼优化算法[J]. 控制与决策, 2016, 31(11): 1991-1997.
[24]	张新明, 王霞, 康强. 改进的灰狼优化算法及其高维函数和FCM优化[J]. 控制与决策, 2019, 34(10): 2073-2084.
[25]	PURUSHOTHAMAN R, RAJAGOPALAN S P, DHANDAPANI G. Hybridizing grey wolf optimization (GWO) with grasshopper optimization algorithm (GOA) for text feature selection and clustering[J]. Applied Soft Computing, 2020, 96: 106651. doi: 10.1016/j.asoc.2020.106651
[26]	VAPNIK V. The Nature of Statistical Learning Theory[M]. 2nd ed. New York: Springer, 1999: 138-141.
[27]	CORTES C, VAPNIK V. Support-vector networks[J]. Machine Learning, 1995, 20(3): 273-297.
[28]	单梁, 强浩, 李军, 等. 基于 Tent 映射的混沌优化算法[J]. 控制与决策, 2005, 20(2): 179-182. doi: 10.3321/j.issn:1001-0920.2005.02.013
[29]	MITTAL N, SINGH U, SOHI B S. Modified grey wolf optimizer for global engineering optimization[J]. Applied Computational Intelligence and Soft Computing, 2016: 197-212.