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  • CN 31-1691/TQ

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

张佳琦, 顾幸生. 基于改进灰狼算法优化的支持向量机锌耗预测[J]. 华东理工大学学报(自然科学版). doi: 10.14135/j.cnki.1006-3080.20210128001
引用本文: 张佳琦, 顾幸生. 基于改进灰狼算法优化的支持向量机锌耗预测[J]. 华东理工大学学报(自然科学版). doi: 10.14135/j.cnki.1006-3080.20210128001
ZHANG Jiaqi, GU Xingsheng. Zinc Consumption Forecast of Support Vector Regression Based on Improved Grey Wolf Algorithm Optimization[J]. Journal of East China University of Science and Technology. doi: 10.14135/j.cnki.1006-3080.20210128001
Citation: ZHANG Jiaqi, GU Xingsheng. Zinc Consumption Forecast of Support Vector Regression Based on Improved Grey Wolf Algorithm Optimization[J]. Journal of East China University of Science and Technology. 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
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

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

  • 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。

     

  • 图  1  收敛因子变化曲线

    Figure  1.  Change curves of convergence factors

    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

    图  3  IGWO-SVR算法流程图

    Figure  3.  Flow chart of IGWO-SVR algorithm

    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

    图  5  IGWO-SVR锌耗模型预测结果

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

    表  1  基准测试函数

    Table  1.   Benchmark test functions

    Function nameExpressionSearch 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
    下载: 导出CSV

    表  2  基准测试函数优化结果对比

    Table  2.   Comparison of optimization results of benchmark test functions

    FunctionAlgorithmBestAveWorstSd
    SpherePSO11.167331.491875.321713.9965
    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}}$$4.91 \times {10^{ - 43}}$
    AckleyPSO3.22545.47858.85671.2411
    ABC$3.55 \times {10^{ - 3}}$$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}}$
    RastriginPSO26.381451.248281.500714.2861
    ABC$8.30 \times {10^{ - 5}}$$8.19 \times {10^{ - 4}}$$8.28 \times {10^{ - 3}}$$1.49 \times {10^{ - 3}}$
    GWO0$1.84 \times {10^{ - 15}}$$1.78 \times {10^{ - 14}}$$3.94 \times {10^{ - 15}}$
    IGWO0000
    RosenbrockPSO40.1590100.1135182.765643.2070
    ABC4.157144.9819102.089236.6747
    GWO27.658728.404228.88500.3519
    IGWO27.251228.415428.92410.3632
    下载: 导出CSV

    表  3  各算法的参数寻优结果

    Table  3.   Parameters optimization results of each algorithms

    AlgorithmC$\gamma $
    PSO26.99013.4351
    GWO86.99020.1664
    IGWO85.97350.1669
    下载: 导出CSV

    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

    ModelMSEMAPE/%R2
    SVR5.20995.24050.8269
    PSO-SVR4.25943.77780.8585
    GWO-SVR3.78773.17300.8742
    IGWO-SVR3.78733.17260.8743
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-01-28
  • 网络出版日期:  2021-04-12

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