QQ群聊

• CN 62-1112/TF
• ISSN 1005-2518
• 创刊于1988年

## Optimization of Multi-objective Filling Slurry Ratio Based on Neural Network and Genetic Algorithm

XIAO Wenfeng,, CHEN Jianhong,, CHEN Yi, WANG Ximei

School of Resources and Safety Engineering, Central South University, Changsha 410083, Hunan, China

 基金资助: 国家自然科学基金青年基金项目“基于人工智能的矿山技术经济指标动态优化”.  51404305国家自然科学基金项目“基于属性驱动的矿体动态建模及更新方法研究”.  51504286中国博士后科学基金面上项目“辰州矿业采掘计划可视化编制与优化研究”.  2015M 572269湖南省科技计划项目“辰州矿业采掘计划可视化编制与优化研究”.  2015RS4060

Received: 2019-03-22   Revised: 2019-05-23   Online: 2019-08-08

Abstract

As the mining depth continues to increase, the pressure management of the stope and goaf is becoming more and more difficult.In order to maintain the stability of the stope,ensure the safety of the operation and prevent the collapse of the goaf,the filling method has become the preferred method for underground mining and has been widely applied.The filling method is to fill the filling body in the goaf to form a filling body with a certain compressive strength, and then carry out underground management by the supporting action of the filling body.Therefore, in the process of mining using the filling method, it is the key to efficient and safe mining of the mine to prepare the filling slurry with reasonable ratio and considerable economy to ensure that the compressive strength of the filling body can meet the needs of ground pressure management.However, there is no simple linear mapping between the filling ratio and the compressive strength of the filling body, and it is usually difficult to calculate by general mathematical methods.To this end, many researchers have conducted a lot of research on the ratio of filling slurry and the optimization of compressive strength of the filling body.Most of these studies only consider optimization under single-objective conditions, and there are few studies on multi-objective conditions.Therefore, other methods should be found to carry out multi-objective optimization research. In this paper, based on artificial neural network and genetic algorithm, a new optimization method of filling ratio is proposed.Firstly, the parameters of cement filling ratio, fly ash mass fraction and tailings mass fraction were optimized parameters, and the backfill strength was used as the optimization target to establish a BP neural network of 3-9-1.The BP neural network is optimized based on genetic algorithm, and the GA_BP neural network with higher prediction accuracy was established.Then,the GA_BP neural network with higher prediction accuracy is used as the fitness function, combined with the cost calculation function, and multi-objective optimization is performed by genetic algorithm to obtain the optimal filling slurry ratio parameter.The results show that when the compressive strength of the filling body is 1.5 MPa, the cement mass fraction is 8%, the fly ash mass fraction is 2.3%, the tailings mass fraction is 66.3%, the cost is the lowest, and the lowest cost is 29.3 yuan/t.The optimization results are consistent with the actual situation.

Keywords： filling body compressive strength ; filling method ; filling slurry ratio optimization ; GA_BP neural network ; genetic algorithm ; multi-objective optimization

XIAO Wenfeng, CHEN Jianhong, CHEN Yi, WANG Ximei. Optimization of Multi-objective Filling Slurry Ratio Based on Neural Network and Genetic Algorithm[J]. Gold Science and Technology, 2019, 27(4): 581-588 doi:10.11872/j.issn.1005-2518.2019.04.581

### 1.1 样本数据收集与处理

Table 1  Filling slurry ratio data of learning samples

123456789101112
ω115.2014.8014.0010.8610.008.448.227.786.916.734.694.38
ω2000000000000
ω360.8059.2056.0065.1460.0067.5665.7862.2269.0967.2770.3167.50

131415161718192021222324
ω14.387.788.448.676.366.913.503.8010.576.367.093.90
ω2015.5616.8917.7312.7313.8214.0015.200014.1815.60
ω365.6346.6750.6752.0050.9155.2752.5057.0063.4363.6456.7358.50

Table 2  Normalized samples data of filling slurry ratio

123456789101112
ω110.9650.8970.6290.5550.4220.4030.3650.2910.2760.1010.085
ω2000000000000
ω30.5970.5300.3940.7810.5630.8830.8080.6570.9480.87110.881

131415161718192021222324
ω10.0750.3650.4220.4410.2440.29100.0250.6040.2440.3060.034
ω200.8970.97410.7340.7970.8070.877000.8180.900
ω30.80200.1690.2250.1790.3630.2460.4370.7090.7170.4250.500

$xi¯=xi-xminxmax-xmin$

### 1.2 BP神经网络结构设计

$n1=n+m+a$

$MAE=1N∑i=1Nyi'-yiyi,i=1,2,...,n$

Table 3  Comparison of network errors for number of neurons in different hidden layers

3-4-10.28381593-9-10.176891
3-5-10.2298873-10-10.1791120
3-6-10.2238793-11-10.195994
3-8-10.19611233-12-10.202248

### 1.3 BP神经网络参数设计

BP神经网络的构建，首要任务是选择对网络训练有很大影响的学习速率，如果学习速率选择过小，将会大幅增加网络的训练时间；如果学习速率选择过大，则很可能会使得网络输出在最优值之间震荡，甚至会远离最优值而使网络无法收敛[18]。因此，本文将学习速率设为0.1，并选用学习速率可以改变的梯度下降算法“traingda”。同时，通过大量试验，隐含层的传递函数选用“tansig”，输出层的传递函数选用线性函数“purelin”，训练次数设为1 000。

### 图1

Fig.1   Flow chart of GA_BP neural network construction

（1）初始种群生成。根据已建立BP神经网络的3-9-1结构可得，需要优化的权值个数为：3×9+9×1=36个，阈值个数为：9+1=10个，待优化参数共46个，如表4所示。参数的编码方式为二进制，将每一个待优化的参数均编码成10位的二进制串，一个染色体由46个参数和460个二进制编码组成，其中1~270位代表输入层到隐含层的权值，271~360位代表隐含层的阈值，361~450位代表隐含层到输出层的权值，451~460位代表输出层阈值。

Table 4  Parameters to be optimized and their quantity

（2）适应度函数。遗传算法在迭代过程中，基本不会接受外界的信息，因此适应度函数的选取对收敛速度和寻找最优解起到了决定性的作用[22]。设本模型适应度函数为

$F=1Y1-Y2$

（3）遗传算子。选择操作是模拟自然界的“物竞天择”，适应度值高的染色体更能适应环境，将优良基因遗传给下一代的概率更高。交叉操作的目的是产生新的解，是指从遗传空间中以一定的概率选取不同的解，通过基因的交换产生新的解，交叉概率的选取一般是采用自适应的方法。变异操作是保持遗传空间多样性的主要方式，是从遗传空间中任选一个染色体，以某种概率选择染色体基因串上的某一点进行变换。在本文中，选择算子采用随机遍历抽样（sus）；交叉算子采用单点交叉算子，交叉概率为0.7；变异以某个确定的概率随机选择变异的基因，变异概率为0.01；种群大小为40；最大遗传代数为50代。

### 图2

Fig.2   Training process of GA_BP neural network

### 图3

Fig.3   Prediction of compressive strength effect by GA_BP neural network

Table 5  Comparison between GA_BP and BP neural network

220.900.90050.050.96116.79
231.851.84920.081.74925.45
240.740.73970.040.78245.73

### 3.1 初始种群生成及遗传算子选择

Table 6  Parameters to be optimized and their range of values

ω12%~16%ω350%~75%
ω20%~20%

Table 7  Globally optimized genetic operator parameters

### 3.2 目标函数及适应度函数选择

$f1(ω1,ω2,ω3)=ω1×340+ω2×70+ω3×1+(1-ω1-ω2-ω3)×0.8$
$f2(ω1,ω2,ω3)=sim(net,[ω1;ω2;ω3])$

$f1(ω1,ω2,ω3)=ω1×340+ω2×70+ω3×1+(1-ω1-ω2-ω3)×0.8$
$f2(ω1,ω2,ω3)=-sim(net,[ω1;ω2;ω3])$

### 图4

Fig.4   Optimum proportion combination

Table 8  Minimum cost and corresponding ratio parameter value under different compressive strength

1.2 MPa1.3 MPa1.4 MPa1.5 MPa1.6 MPa1.7 MPa1.8 MPa1.9 MPa2.0 MPa
ω17.07.47.68.06.86.58.17.27.1
ω22.52.22.92.39.212.05.710.912.5
ω367.267.367.566.866.366.467.867.569.0

## 4 结论

（1）通过对样本数据进行分析，建立了3-9-1的BP神经网络，基于遗传算法对BP神经网络初始权值和阈值进行优化，构建GA_BP神经网络，经过测试集数据验证了GA_BP神经网络相比BP神经网络其网络预测精度大幅提高，能够更精确地描述充填料浆配比参数与充填体抗压强度之间的非线性关系。

（2）将已建立的GA_BP神经网络用作目标函数，结合充填料浆总成本的目标函数，通过遗传算法多目标寻优，优化得到每一个充填体抗压强度下的最低成本及对应充填料浆配比参数。优化结果显示，充填体抗压强度为1.5 MPa时的最低成本是29.3元/t，此时的配比组合：水泥质量分数为8%，粉煤灰质量分数为2.3%，尾砂质量分数为66.8%。本文在满足实际生产要求的情况下，采用遗传算法寻找多目标最优解，创新了充填体抗压强度的优化方法，提供了新的思路，在生产实践中具有一定的指导意义。

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