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