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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- 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)优化算法的支持向量机回归(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 and its consumption may fluctuate greatly due to the contract orders and product structure, which further results in fluctuating demand. Material demand often reflects the characteristics of small sample size and large variation range, whose non-stationarity and non-linearity make the demand forecasting more difficult. Meanwhile, 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, the accurate material demand forecasting has important practical significance for the optimization of raw material procurement and the production management scheduling of iron and steel enterprises. In order to improve the prediction accuracy of zinc ingot demand for galvanized sheet production, 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, the chaotic Tent mapping strategy is firstly adopted to initialize the population so as 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 of the algorithm. Finally, the differential evolution is integrated in the location update process to reduce the possibility of false convergence of the algorithm. For the improved gray wolf algorithm, a simulation experiment is made via a typical benchmark test function, whose result verify the superiority of the improved algorithm in comprehensive performance. Furthermore, based on the actual production data of a unit in a steel plant, the zinc ingot consumption is modeled and predicted, and the parameters of SVR is optimized via the IGWO algorithm. The experimental results show 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	$11.167\;3 $	$ 31.491\;8$	$ 75.321\;7$	$ 13.996\;5$
	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	$ 3.225\;4$	$ 5.478\;5$	$ 8.856\;7$	$ 1.241\;1$
	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	$ 26.381\;4$	$ 51.248\;2$	$ 81.500\;7$	$ 14.286\;1$
	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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