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《山东大学学报(理学版)》 ›› 2024, Vol. 59 ›› Issue (3): 37-50.doi: 10.6040/j.issn.1671-9352.7.2023.3667

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基于改进蝴蝶算法的水文地质参数优化

韦修喜1(),彭茂松2,黄华娟1,*()   

  1. 1. 广西民族大学人工智能学院, 广西 南宁 530006
    2. 广西民族大学电子信息学院, 广西 南宁 530006
  • 收稿日期:2023-04-25 出版日期:2024-03-20 发布日期:2024-03-06
  • 通讯作者: 黄华娟 E-mail:weixiuxi@163.com;hhj-025@163.com
  • 作者简介:韦修喜(1980—)，男，博士，副教授，硕士生导师，研究方向为机器学习、计算智能及应用. E-mail: weixiuxi@163.com
  • 基金资助:
    国家自然科学基金资助项目(62266007);广西自然科学基金资助项目(2021GXNSFAA220068)

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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摘要：

针对水文地质参数求解精度不足以及传统配线法等策略在求参过程中效率低下等的问题, 提出一种基于黄金正弦加权蝴蝶优化算法的水文地质参数优化策略。首先在蝴蝶优化算法的全局与局部搜索阶段引入黄金正弦算子, 缩小算法解空间; 其次引入自适应权重, 调整算法后期种群个体移动步长与搜索方向。通过6个基准测试函数的寻优对比测试结果表明: 黄金正弦加权蝴蝶优化算法的寻优精度较高且收敛速度较快。将该优化策略应用于水文地质参数导水系数与贮水系数的优化以达到最小降深误差, 并与粒子群优化算法、配线法等优化策略进行实验对比。结果表明黄金正弦加权蝴蝶优化算法能有效优化水文地质参数并提高泰斯公式计算性能, 获得更小抽水降深误差, 为后续抽水试验提供了新方法。

关键词: 蝴蝶优化算法, 黄金正弦算子, 自适应权重, 水文地质参数, 抽水试验

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

中图分类号: 

  • TP183

表1

各算法参数"

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

表2

测试函数详细信息"

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

表3

不同算法寻优结果"

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

表4

Wilcoxon秩和检验结果p"

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

图1

F1—F4测试函数的适应度收敛曲线图"

图2

F5、F6测试函数的适应度收敛曲线图"

图3

F1、F2测试函数的箱线图"

图4

F3—F6测试函数的箱线图"

表5

单观测孔数据"

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

图5

单孔观测优化对比"

表6

不同策略优化结果对比"

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

表7

观测孔数据"

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

图6

多孔观测优化对比"

表8

不同策略优化结果对比"

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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