基于双重随机扰动的人工大猩猩部队优化算法及工程应用

杜晓昕; 郝田茹; 王波; 王振飞; 张剑飞; 金梅

doi:10.13700/j.bh.1001-5965.2023.0404

基于双重随机扰动的人工大猩猩部队优化算法及工程应用

doi: 10.13700/j.bh.1001-5965.2023.0404

杜晓昕^{1, 2, ,},
郝田茹¹,
王波^{1, 2},
王振飞¹,
张剑飞^{1, 2},
金梅^{1, 2}

1.
齐齐哈尔大学计算机与控制工程学院，齐齐哈尔 161006
2.
齐齐哈尔大学黑龙江省大数据网络安全检测分析重点实验室，齐齐哈尔 161006

基金项目:

黑龙江省省属高等学校基本科研业务费自然科学类青年创新人才项目(145209206)

详细信息

通讯作者:
E-mail：xiaoxindu@qqhru.edu.cn

中图分类号: TP301.6
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- 被引次数: 0
出版历程
- 收稿日期: 2023-06-25
- 录用日期: 2023-09-11
- 网络出版日期: 2023-10-20
- 整期出版日期: 2025-06-30

Artificial gorilla troops optimizer based on double random disturbance and its application of engineering problem

DU Xiaoxin^{1, 2
, ,},
HAO Tianru¹,
WANG Bo^{1, 2},
WANG Zhenfei¹,
ZHANG Jianfei^{1, 2},
JIN Mei^{1, 2}

1.
College of Computer and Control Engineering，Qiqihar University，Qiqihar 161006，China
2.
Heilongjiang Key Laboratory of Big Data Network Security Detection and Analysis，Qiqihar University，Qiqihar 161006，China

Funds:

Heilongjiang Provincial Higher Education Institutions Basic Scientific Research Business Funds Natural Science Young Innovative Talents Program (145209206)

More Information

Corresponding author: E-mail：xiaoxindu@qqhru.edu.cn

摘要

摘要:
针对人工大猩猩部队优化算法(GTO)存在易陷入局部最优、收敛速度慢、寻优精度低等问题，提出了基于双重随机扰动策略的人工大猩猩部队优化算法(DGTO)。引入Halton序列初始化种群，增加种群的多样性；在算法寻优阶段使用多维随机数策略，并在探索阶段提出自适应位置搜索机制，提高算法的收敛速度；提出双重随机扰动策略，解决大猩猩的群居效应，增强算法跳出局部最优的能力；采用逐维更新策略更新个体位置，提升算法的收敛精度。通过10个基准测试函数寻优结果及Wilcoxon秩和检验对比可知，改进算法在寻优精度、收敛速度上有较大提升。同时，通过工程优化问题的实验对比分析，进一步验证了改进算法在处理现实工程问题上的优越性。
- 人工大猩猩部队优化算法 /
- Halton序列 /
- 自适应位置搜索 /
- 双重随机扰动策略 /
- 逐维更新
Abstract:
Traditional artificial gorilla troops optimizer (GTO) has the drawbacks of easily falling into local optimum, slow convergence speed, and low optimization accuracy. Aiming at these problems, an artificial gorilla troops optimizer based on a double random disturbance strategy (DGTO) was proposed. Firstly, the Halton sequence was introduced to initialize the population to increase the diversity of the population. Secondly, the method’s convergence speed was increased by using the multi-dimensional random number technique during the algorithm optimization stage and proposing an adaptive position exploration mechanism. Thirdly, a double random disturbance strategy was proposed, which solved the group effect of gorillas and enhanced the ability of the algorithm to jump out of the local optimum. Finally, the individual position was updated by a dimension-by-dimension update strategy, which improved the convergence accuracy of the algorithm. It is evident that the enhanced technique has a greater improvement in optimization accuracy and convergence speed when comparing the Wilcoxon rank sum test results with the optimization results of ten benchmark test functions. In addition, through the experimental comparative analysis of one practical engineering optimization problem, the superiority of the proposed algorithm in dealing with practical engineering problems is further verified.
- artificial gorilla troops optimizer /
- Halton sequence /
- adaptive position exploration /
- double random disturbance strategy /
- dimension-by-dimension update

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图 1 随机分布与Halton序列分布初始化种群空间

Figure 1. Random distribution and Halton distribution initialize population space

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图 2 L和T随迭代次数增加的变化曲线

Figure 2. L and T change curves with increase of iterations

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图 3 双重随机扰动策略示意图

Figure 3. Schematic diagram of double random disturbance strategy

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图 4 一维标准柯西分布与高斯分布概率密度曲线

Figure 4. Probability density curves of one-dimensional standard Cauchy distribution and Gaussian distribution

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图 5 中心位置计算示意图

Figure 5. Schematic diagram of central location calculation

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图 6 整体更新位置方式

Figure 6. Entire update position way

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图 7 逐维更新位置方式

Figure 7. Dimension-by-dimension update position way

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图 8 本文算法流程

Figure 8. Flowchart of the proposed algorithm

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图 9 DGTO算法与其他改进GTO算法的部分收敛曲线

Figure 9. Partial convergence plots of DGTO and other improved GTO algorithms

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图 10 各算法在函数f₁～f₁₀的收敛曲线

Figure 10. Convergence curves of each algorithm in functions f₁−f₁₀

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图 11 弹簧设计模型

Figure 11. Mode of spring design

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表 1 元学习与其他学习方法的潜在关联

Table 1. Potential correlation between meta-learning and other learning methods

学习方法	与元学习关联
对比学习	对比学习的核心是将正样本和负样本在特征空间进行对比，使得模型能够学习到样本的重要内在特征。而元学习在学习特征表示时，有时也会通过正样本和负样本比对的方式实现
迁移学习	迁移学习的核心是找到已有知识和新知识之间的相似性，通过这种相似性的迁移达到迁移学习的目的。元学习基于任务展开学习，然而生物体及其一生，学习的永远不止一个任务，因而迁移学习可以将元学习在某一任务的学习方式迁移到相似任务中

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表 2 参数设置

Table 2. Parameters setting

算法	主要参数
GTO	s=0.03,w=0.8,$\beta $=3
GWO
DE	F=0.5,R_C=0.3
WOA	b=1
DGTO	s=0.03,w=0.8,$\beta $=3

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表 3 基准测试函数

Table 3. Benchmark test functions

编号	函数名	定义域	维度	最优值
f₁	Sphere	[−100,100]	10/30	0
f₂	Schwefel’ problem 2.22	[−10,10]	10/30	0
f₃	Schwefel’ problem 1.2	[−100,100]	10/30	0
f₄	Schwefel’ problem 2.21	[−100,100]	10/30	0
f₅	Generalized Rosenbrock’s function	[−30,30]	10/30	0
f₆	Step function	[−100,100]	10/30	0
f₇	Generalized Schwefel’s problem 2.26	[−500,500]	10/30	−418.98×维度
f₈	Generalized penalized function 2	[−50,50]	10/30	0
f₉	Kowalik’s function	[−5,5]	4	0.000 3
f₁₀	Hatman’s function 2	[0,1]	6	−3.32

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表 4 DGTO算法与其他改进GTO算法寻优结果对比

Table 4. Comparison of optimization results of DGTO and other improved GTO algorithms

参数	算法	平均值	标准差
f₁	GTO	0	0
	IGTO	0	0
	MGTO	0	0
	DGTO	0	0
f₂	GTO	6.67×10⁻¹⁹⁵	0
	IGTO	0	0
	MGTO	0	0
	DGTO	0	0
f₃	GTO	0	0
	IGTO	0	0
	MGTO	0	0
	DGTO	0	0
f₄	GTO	1.01×10⁻¹⁹²	0
	IGTO	0	0
	MGTO	0	0
	DGTO	0	0
f₅	GTO	3.17×10⁰	8.22×10⁰
	IGTO	7.46×10⁻⁵	8.57×10⁻⁵
	MGTO	2.54×10⁻⁵	3.94×10⁻⁵
	DGTO	7.42×10⁻⁶	3.39×10⁻⁵
f₆	GTO	2.56×10⁻⁷	4.19×10⁻⁷
	IGTO	1.01×10⁻⁷	1.15×10⁻⁷
	MGTO	3.37×10⁻¹⁴	3.76×10⁻¹⁴
	DGTO	2.03×10⁻³²	1.66×10⁻³²
f₇	GTO	−1.26×10⁴	3.05×10⁻⁵
	IGTO	−1.26×10⁴	3.02×10⁻⁵
	MGTO	−1.26×10⁴	1.03×10⁻⁶
	DGTO	−1.26×10⁴	4.64×10⁻¹²
f₈	GTO	3.30×10⁻³	5.12×10⁻³
	IGTO	1.14×10⁻⁷	3.34×10⁻⁷
	MGTO	1.00×10⁻⁷	1.43×10⁻⁷
	DGTO	7.24×10⁻³²	2.30×10⁻³¹
f₉	GTO	4.17×10⁻⁴	3.01×10⁻⁴
	IGTO	3.07×10⁻⁴	4.06×10⁻¹⁹
	MGTO	3.07×10⁻⁴	3.29×10⁻¹⁹
	DGTO	3.07×10⁻⁴	1.74×10⁻¹⁹
f₁₀	GTO	−3.29×10⁰	5.39×10⁻²
	IGTO	−3.31×10⁰	3.63×10⁻²
	MGTO	−3.30×10⁰	4.51×10⁻²
	DGTO	−3.32×10⁰	0

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表 5 各算法寻优结果对比

Table 5. Comparison of optimization results of each algorithm

函数	算法	最优值	最差值	平均值	标准差
f₁	DGTO	0	0	0	0
	GTO	0	0	0	0
	GWO	2.62×10⁻⁶⁹	6.96×10⁻⁶³	3.93×10⁻⁶⁴	1.28×10⁻⁶³
	DE	6.09×10⁻²⁰	1.86×10⁻¹⁸	5.05×10⁻¹⁹	4.44×10⁻¹⁹
	WOA	2.04×10⁻⁹⁴	5.80×10⁻⁸¹	1.23×10⁻⁸²	8.19×10⁻⁸²
f₂	DGTO	0	0	0	0
	GTO	7.39×10⁻²¹⁷	3.67×10⁻¹⁹⁷	7.69×10⁻¹⁹⁹	0
	GWO	3.25×10⁻³⁹	8.12×10⁻³⁶	5.90×10⁻³⁷	1.30×10⁻³⁶
	DE	1.91×10⁻¹²	2.93×10⁻¹¹	9.68×10⁻¹²	4.55×10⁻¹²
	WOA	1.10×10⁻⁶¹	5.26×10⁻⁵²	1.12×10⁻⁵³	7.43×10⁻⁵³
f₃	DGTO	0	0	0	0
	GTO	0	0	0	0
	GWO	3.82×10⁻³⁷	3.02×10⁻²⁷	8.81×10⁻²⁹	4.33×10⁻²⁸
	DE	2.63×10⁰	2.74×10¹	8.17×10⁰	5.41×10⁰
	WOA	2.73×10⁻⁸	6.89×10²	1.16×10²	1.46×10²
f₄	DGTO	0	0	0	0
	GTO	2.01×10⁻²¹⁸	4.03×10⁻²⁰⁰	1.18×10⁻²⁰¹	0
	GWO	9.71×10⁻²⁴	2.86×10⁻¹⁹	1.79×10⁻²⁰	4.48×10⁻²⁰
	DE	2.60×10⁻⁵	1.31×10⁻⁴	6.72×10⁻⁵	2.38×10⁻⁵
	WOA	2.21×10⁻⁵	2.20×10¹	1.35×10⁰	4.37×10⁰
f₅	DGTO	7.46×10⁻³⁰	2.25×10⁻¹¹	6.34×10⁻¹³	3.28×10⁻¹²
	GTO	4.91×10⁻¹⁵	1.41×10⁰	1.07×10⁻¹	3.06×10⁻¹
	GWO	5.32×10⁰	9.54×10⁰	6.70×10⁰	7.69×10⁻¹
	DE	1.74×10⁰	1.75×10¹	7.58×10⁰	2.78×10⁰
	WOA	3.49×10⁰	8.95×10⁰	6.58×10⁰	6.38×10⁻¹
f₆	DGTO	0	1.23×10⁻³²	5.55×10⁻³⁴	1.94×10⁻³³
	GTO	9.24×10⁻³²	9.98×10⁻²³	2.18×10⁻²⁴	1.14×10⁻²³
	GWO	1.11×10⁻⁶	6.33×10⁻⁶	2.97×10⁻⁶	1.13×10⁻⁶
	DE	5.02×10⁻²⁰	2.93×10⁻¹⁸	4.00×10⁻¹⁹	4.42×10⁻¹⁹
	WOA	2.62×10⁻⁵	1.17×10⁻³	3.12×10⁻⁴	2.70×10⁻⁴
f₇	DGTO	−4.19×10³	−4.19×10³	−4.19×10³	2.13×10⁻¹²
	GTO	−4.19×10³	−4.19×10³	−4.19×10³	5.29×10⁻¹²
	GWO	−3.56×10³	−2.08×10³	−2.84×10³	3.65×10²
	DE	−7.94×10⁷	−8.23×10¹⁴	−2.09×10¹³	1.20×10¹⁴
	WOA	−4.19×10³	−2.49×10³	−3.46×10³	5.61×10²
f₈	DGTO	1.35×10⁻³²	1.35×10⁻³²	1.35×10⁻³²	1.11×10⁻⁴⁷
	GTO	7.26×10⁻³⁰	7.46×10⁻²	5.34×10⁻³	1.25×10⁻²
	GWO	1.15×10⁻⁶	1.04×10⁻¹	1.00×10⁻²	3.04×10⁻²
	DE	4.37×10⁻²¹	4.46×10⁻¹⁹	8.94×10⁻²⁰	8.94×10⁻²⁰
	WOA	2.57×10⁻⁴	1.10×10⁻¹	1.44×10⁻²	2.57×10⁻²
f₉	DGTO	3.07×10⁻⁴	3.07×10⁻⁴	3.07×10⁻⁴	1.74×10⁻¹⁹
	GTO	3.07×10⁻⁴	1.22×10⁻³	4.17×10⁻⁴	3.01×10⁻⁴
	GWO	3.07×10⁻⁴	2.04×10⁻²	2.78×10⁻³	6.56×10⁻³
	DE	5.16×10⁻⁴	1.30×10⁻³	8.97×10⁻⁴	1.48×10⁻⁴
	WOA	3.08×10⁻⁴	2.17×10⁻³	6.93×10⁻⁴	4.89×10⁻⁴
f₁₀	DGTO	−3.32×10⁰	−3.32×10⁰	−3.32×10⁰	0
	GTO	−3.32×10⁰	−3.20×10⁰	−3.29×10⁰	5.39×10⁻²
	GWO	−3.32×10⁰	−3.09×10⁰	−3.27×10⁰	7.57×10⁻²
	DE	−3.32×10⁰	−3.20×10⁰	−3.31×10⁰	3.17×10⁻²
	WOA	−3.32×10⁰	−2.43×10⁰	−3.22×10⁰	1.45×10⁻¹

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表 6 不同算法的平均绝对值误差

Table 6. Mean absolute error of different algorithms

算法	平均绝对值误差
DGTO	3.09×10⁻³
GTO	1.73×10⁻²
GWO	1.36×10²
DE	2.09×10¹²
WOA	8.54×10¹

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表 7 Wilcoxon秩和检验结果

Table 7. Wilcoxon rank sum test results

函数	p值
函数	GTO	GWO	DE	WOA
f₁	NAN	3.31×10⁻²⁰	3.31×10⁻²⁰	3.31×10⁻²⁰
f₂	3.31×10⁻²⁰	3.31×10⁻²⁰	3.31×10⁻²⁰	3.31×10⁻²⁰
f₃	NAN	3.31×10⁻²⁰	3.31×10⁻²⁰	3.31×10⁻²⁰
f₄	3.31×10⁻²⁰	3.31×10⁻²⁰	3.31×10⁻²⁰	3.31×10⁻²⁰
f₅	7.97×10⁻¹⁸	7.07×10⁻¹⁸	7.07×10⁻¹⁸	7.07×10⁻¹⁸
f₆	6.35×10⁻¹⁹	6.35×10⁻¹⁹	6.35×10⁻¹⁹	6.35×10⁻¹⁹
f₇	4.32×10⁻¹²	3.43×10⁻¹⁹	3.43×10⁻¹⁹	3.43×10⁻¹⁹
f₈	1.30×10⁻¹⁸	1.30×10⁻¹⁸	1.30×10⁻¹⁸	1.30×10⁻¹⁸
f₉	2.79×10⁻¹⁶	5.92×10⁻¹⁸	5.92×10⁻¹⁸	5.92×10⁻¹⁸
f₁₀	2.71×10⁻⁷	4.73×10⁻²⁰	6.69×10⁻¹¹	4.73×10⁻²⁰
注：参数p小于5×10⁻²表示DGTO与对比算法有显著差异，NAN表示无法进行显著性判断。

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表 8 弹簧设计问题各算法最优解

Table 8. Optimal solution of each algorithm for spring design problem

算法	d	D_a	P	最优解
DGTO	0.05172	0.35750	11.24294	0.012665252
GTO	0.05162	0.35504	11.38775	0.012665321
GWO	0.05120	0.34507	12.00899	0.012672677
DE	0.05161	0.35479	11.40314	0.012665876
WOA	0.05148	0.35182	11.58231	0.012666117
SHO^[30]	0.05114	0.34375	12.09550	0.012674000
MVO^[30]	0.05000	0.31596	14.22623	0.012816930
SCA^[30]	0.05078	0.33478	12.72269	0.012709667
GSA^[30]	0.05000	0.31731	14.22867	0.012873881

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