JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (3): 37-50.doi: 10.6040/j.issn.1671-9352.7.2023.3667

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Optimization of hydrogeological parameters based on improved butterfly optimization algorithm

Xiuxi WEI1(),Maosong PENG2,Huajuan HUANG1,*()   

  1. 1. College of Artificial Intelligence, Guangxi Minzu University, Nanning 530006, Guangxi, China
    2. College of Electronic Information, Guangxi Minzu University, Nanning 530006, Guangxi, China
  • Received:2023-04-25 Online:2024-03-20 Published:2024-03-06
  • Contact: Huajuan HUANG E-mail:weixiuxi@163.com;hhj-025@163.com

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Abstract:

In order to solve the problems of insufficient accuracy of hydrogeological parameters and low efficiency of traditional routing methods, an optimization strategy of hydrogeological parameters based on golden sine weighted butterfly optimization algorithm (GSWBOA) is proposed. Firstly, the golden sine operator is introduced in the global and local search phase of butterfly optimization algorithm to reduce the solution space of the algorithm. Secondly, adaptive weights are introduced to adjust the individual moving step size and search direction in the later stage of the algorithm. The comparison test results of 6 benchmark test functions show that the GSWBOA has higher optimization accuracy and faster convergence. The optimization strategy is applied to the optimization of hydrogeological parameters water conductivity coefficient and water storage coefficient to achieve the minimum depth reduction error, and the optimization strategy is compared with particle swarm optimization algorithm, wiring method and other optimization strategies. The results show that the golden sinusoidal weighted butterfly optimization algorithm can effectively optimize the hydrogeological parameters, improve the calculation performance of Theis formula, and obtain a smaller drawdown error, which provides a new method for the subsequent pumping test.

Key words: butterfly optimization algorithm, golden sine operator, adaptive weight coefficient, hydrogeological parameters, pumping test

CLC Number: 

  • TP183

Table 1

Parameters of Algorithms"

算法 参数设置
BOA α=0.1, c=0.01, P=0.8
GSWBOA α=0.1, c=0.01, P=0.8, a=-π, b=π,$\tau=(\sqrt{5}-1) / 2$
DGBOA α=0.1, c=0.01, σmax=1.5, σmin=0.4, Pmax=0.8, Pmin=0.3
GWO α, β, δ=+∞
MSBOA C=0.5, αmax=1, αmin=1e-4, δ=1, Pmax=0.9, Pmin=0.6, β=1

Table 2

Information of test functions"

代号 函数表达式 定义域 维度 最优值
F1 $F_1(x)=\sum\limits_{i=1}^n x_i^2$ [-100, 100] 30 0
F2 $F_3(x)=\sum\limits_{i=1}^D\left(10^6\right)^{\frac{i-1}{D-1}} x_i^2$ [-100, 100] 50 0
F3 $F_3(x)=x_1^2+10^6 \sum\limits_{i=2}^D x_i^2$ [-100, 100] 50 0
F4 $F_4(x)=-20 \exp \left(-0.2 \sqrt{\frac{1}{D} \sum\limits_{i=1}^D x_i^2}\right)-\exp \left(\frac{1}{D} \sum\limits_{i=1}^D \cos \left(2 \pi x_i\right)\right)+20+\mathrm{e}$ [-32, 32] 50 8.88E-16
F5 $F_5(x)=\sum\limits_{i=1}^D\left[x_i^2-10 \cos \left(2 \pi x_i\right)+10\right]$ [-5.12, 5.12] 30 0
F6 $F_6(x)=\left[\frac{1}{D-1} \sum\limits_{i=1}^{D-1}\left(\sqrt{s_i}\left(\sin \left(50 s_i^{0.2}\right)+1\right)\right)\right]^2, s_i=\sqrt{x_i^2+x_{i+1}^2}$ [-100, 100] 50 0

Table 3

Optimization results of different algorithms"

函数 算法 最差值 最优值 平均值 标准差 运行时间/s
F1 BOA 7.06E+04 1.07E-11 1.08E+03 6.65E+03 0.153 17
MSBOA 4.80E+04 0.00E+00 3.40E+02 3.22E+03 2.388 90
DGBOA 6.65E+04 1.65E-09 9.46E+02 6.07E+03 0.502 14
GSWBOA 3.71E-03 0.00E+00 7.43E-06 1.66E-04 0.168 31
PPSO 3.04E+04 6.03E-05 9.61E+01 1.53E+03 0.135 65
GWO 5.78E+04 3.92E-40 4.42E+02 3.86E+03 0.259 07
F2 BOA 3.56E+09 1.24E-11 2.57E+07 2.44E+08 0.881 89
MSBOA 2.66E+09 0.00E+00 1.18E+07 1.51E+08 6.571 10
DGBOA 3.79E+09 1.51E-09 2.63E+07 2.59E+08 1.289 00
GSWBOA 1.24E+03 0.00E+00 2.47E+00 5.53E+01 0.900 74
PPSO 2.22E+09 4.35E+02 1.54E+07 1.45E+08 0.531 52
GWO 4.92E+09 1.60E-25 2.63E+07 2.76E+08 0.750 64
F3 BOA 9.22E+10 1.36E-11 4.83E+08 5.35E+09 0.195 42
MSBOA 4.27E+10 0.00E+00 1.46E+08 2.09E+09 3.165 60
DGBOA 8.30E+10 1.55E-09 4.35E+08 4.81E+09 0.592 81
GSWBOA 1.06E+04 0.00E+00 2.13E+01 4.75E+02 0.207 82
PPSO 6.28E+10 5.77E+01 3.19E+08 3.77E+09 0.160 43
GWO 1.25E+11 4.38E-23 1.19E+09 8.96E+09 0.409 04
F4 BOA 2.15E+01 5.37E-10 5.47E+00 8.88E+00 0.327 86
MSBOA 2.12E+01 8.88E-16 9.60E+00 1.05E+01 11.450 10
DGBOA 2.14E+01 4.30E-08 7.19E+00 9.68E+00 0.742 90
GSWBOA 2.97E+00 8.88E-16 6.08E-03 1.33E-01 0.278 86
PPSO 2.11E+01 2.00E+01 2.00E+01 4.94E-02 0.200 83
GWO 2.15E+01 2.10E+01 2.10E+01 3.94E-02 0.472 05
F5 BOA 3.84E+02 0.00E+00 1.03E+02 1.15E+02 0.217 50
MSBOA 1.10E+00 0.00E+00 3.17E-02 1.22E-01 17.951 20
DGBOA 3.87E+02 2.84E-12 8.55E+01 1.07E+02 0.562 25
GSWBOA 1.72E+02 0.00E+00 3.44E-01 7.69E+00 0.213 58
PPSO 3.44E+02 9.45E-05 3.20E+00 2.65E+01 0.152 93
GWO 4.54E+02 0.00E+00 1.92E+01 6.25E+01 0.275 94
F6 BOA 1.08E+01 2.38E-06 1.42E+00 2.78E+00 2.357 80
MSBOA 2.54E+00 0.00E+00 2.35E-02 1.59E-01 5.307 70
DGBOA 1.15E+01 1.97E-03 1.32E+00 2.66E+00 2.672 40
GSWBOA 1.00E-01 0.00E+00 2.39E-04 4.54E-03 1.137 50
PPSO 9.31E+00 2.79E-02 1.42E-01 7.40E-01 1.259 90
GWO 1.04E+01 1.39E-08 4.06E-01 1.48E+00 1.487 40

Table 4

Results of the Wilcoxon rank sum test"

GSWBOA BOA MSBOA DGBOA PPSO GWO
F1 2.82E-184 3.42E-117 2.36E-184 8.24E-185 6.73E-182
F2 3.81E-184 3.89E-116 3.96E-184 1.58E-186 4.28E-183
F3 1.19E-180 5.02E-110 1.27E-180 7.78E-183 2.42E-179
F4 2.75E-180 6.36E-64 5.07E-181 3.18E-214 4.58E-202
F5 7.47E-168 2.25E-48 4.29E-184 2.05E-183 5.85E-186
F6 2.33E-181 2.87E-109 3.64E-182 4.73E-182 1.80E-178

Fig.1

Convergence curves graphs of test functions F1—F4"

Fig.2

Convergence curves graphs of test functions F5, F6"

Fig.3

Boxplot of test functions F1, F2"

Fig.4

Boxplot of test functions F3—F6"

Table 5

Single well observation data"

编号 t/min s/m 编号 t/min s/m
1 10 0.16 10 210 1.55
2 20 0.48 11 270 1.70
3 30 0.54 12 330 1.83
4 40 0.65 13 400 1.89
5 60 0.75 14 450 1.98
6 80 1.00 15 645 2.17
7 100 1.12 16 870 2.38
8 120 1.22 17 990 2.46
9 150 1.36 18 1 185 2.54

Fig.5

Optimization comparison of single well observation"

Table 6

Comparison of optimization results of different strategies[6]"

策略 T/(m2/d) S 误差
GSWBOA 219.381 1 0.000 224 79 0.006 195
PSO 198.860 1 0.000 264 69 0.007 639
人工配线法 197.670 0 0.000 298 70 0.009 642
LinWPSO[6] 216.892 2 0.000 229 94 0.007 339

Table 7

Observation wells data"

抽水试验参数 1 2 3 4 5 6 7 8
距抽水井距离/m 8.8 10.7 13.4 18.3 25.9 30.5 38.1 49.7
s/m 4.54 4.21 3.87 3.57 3.08 2.93 2.62 2.13

Fig.6

Optimization comparison of multiple wells observation"

Table 8

Comparison of optimization results of different strategies"

策略 T/(m2/d) S 误差大小
GSWBOA 225.964 90 0.000 616 78 0.003 091 20
PSO 205.136 60 0.000 936 04 0.007 359 80
人工配线法 237.400 00 0.000 448 41 1.904 250 00
最小二乘法[6] 229.791 70 0.000 604 48 0.005 701 20
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