改进北方苍鹰算法及其在智能汽车路径规划中的应用

doi:10.3969/j.issn.1674-8484.2025.01.015

摘要/Abstract

摘要：

针对传统北方苍鹰算法（NGO）存在易陷入局部最优值、寻优精度低、收敛速度慢等问题，提出一种多策略改进北方苍鹰算法（INGO），并应用于智能汽车的路径规划，规划了一条路径最平滑、节点最少、距离最短的汽车路径。采用佳点集分布、融合黄金正弦策略、Levy飞行策略、趋优反向学习、Cauchy变异策略改进北方苍鹰算法，并进行了基准测试函数对比以及智能汽车路径规划仿真。结果表明：相比其他算法，INGO算法在寻优和稳定性上具有明显优势；在2种不同地图上生成的路径最平滑，适应度最优分别下降3.7%、16.3%，节点个数最优分别下降14.3%、21.4%。

关键词: 改进北方苍鹰算法（INGO）, 佳点集, 黄金正弦, Levy飞行, 趋优反向学习, Cauchy变异, 路径规划

Abstract:

To address the issues of the traditional Northern Goshawk Optimization (NGO) algorithm, such as easily falling into local optima, low optimization accuracy, and slow convergence speed, a multi-strategy improved Northern Goshawk Optimization (INGO) algorithm was proposed and applied to the path planning of intelligent vehicles, aiming to plan a path that was the smoothest, had the fewest nodes, and the shortest distance. The improvements included the use of good point set distribution, integration of the golden sine strategy, Levy flight strategy, opposition-based learning, and Cauchy mutation strategy. The improved algorithm was tested on benchmark functions and simulated for intelligent vehicle path planning. The results show that, compared to other algorithms, the INGO algorithm demonstrates significant advantages in optimization and stability. On two different maps, the paths generated by INGO are the smoothest, with fitness values optimally reduced by 3.7% and 16.3%, and the number of nodes optimally reduced by 14.3% and 21.4%, respectively.

Key words: improved Northern Goshawk Optimization (INGO), good point, golden sine, Levy flight, convergent inverse learning, Cauchy variation, path planning

中图分类号:

U463.6

匡兴红, 沈佳成. 改进北方苍鹰算法及其在智能汽车路径规划中的应用[J]. 汽车安全与节能学报, 2025, 16(1): 148-158.

KUANG Xinghong, SHEN Jiacheng. Improved Northern Goshawk Optimization Algorithm and its application in intelligent vehicle path planning[J]. Journal of Automotive Safety and Energy, 2025, 16(1): 148-158.

图/表 12

参考文献 21

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算法	参数
INGO	黄金正弦初始值： a = -π，b = π 黄金正弦常数：$=(\sqrt{5}-1) / 2$
UNGO	μ~N(0, σ_μ²)，v~N(0, σ_v²)
NGO	攻击半径： R = 0.02×(1 - t/maxiter)
SSA	预警值：ST = 0.6 发现者比例：PD = 0.7 警戒者比例：SD = 0.2
WOA	螺旋常数： ? = 1 行为选择概率： p = 0.5
WSA	梯度系数： ε = 10^-6，步长系数： α₀ = 0.3

算法	参数
INGO	黄金正弦初始值： a = -π，b = π 黄金正弦常数：$=(\sqrt{5}-1) / 2$
UNGO	μ~N(0, σ_μ²)，v~N(0, σ_v²)
NGO	攻击半径： R = 0.02×(1 - t/maxiter)
SSA	预警值：ST = 0.6 发现者比例：PD = 0.7 警戒者比例：SD = 0.2
WOA	螺旋常数： ? = 1 行为选择概率： p = 0.5
WSA	梯度系数： ε = 10^-6，步长系数： α₀ = 0.3

函数	定义域	理论值
$F_{1}(x)=\sum_{i=1}^{n}\left\|x_{i}\right\|+\prod_{i=1}^{n}\left\|x_{i}\right\|$	[-10, 10]	0
$F_{2}(x)=\sum_{i=1}^{n}\left(\sum_{j=1}^{t} x_{j}\right)^{2}$	[-100, 100]	0
$F_{3}(x)=\max _{i}\left\{\left\|x_{i}\right\|, 1 \leqslant i \leqslant n\right\}$	[-100, 100]	0
$\begin{aligned} F_{4}(x)= & -20 \exp \left(-0.2 \sqrt{\frac{1}{n} \sum_{i=1}^{n} x_{i}^{2}}\right)- \\ & \exp \left(\frac{1}{n} \sum_{i=1}^{n} \cos \left(2 \pi x_{i}\right)\right)+20+e \end{aligned}$	[-32, 32]	0

函数	定义域	理论值
$F_{1}(x)=\sum_{i=1}^{n}\left\|x_{i}\right\|+\prod_{i=1}^{n}\left\|x_{i}\right\|$	[-10, 10]	0
$F_{2}(x)=\sum_{i=1}^{n}\left(\sum_{j=1}^{t} x_{j}\right)^{2}$	[-100, 100]	0
$F_{3}(x)=\max _{i}\left\{\left\|x_{i}\right\|, 1 \leqslant i \leqslant n\right\}$	[-100, 100]	0
$\begin{aligned} F_{4}(x)= & -20 \exp \left(-0.2 \sqrt{\frac{1}{n} \sum_{i=1}^{n} x_{i}^{2}}\right)- \\ & \exp \left(\frac{1}{n} \sum_{i=1}^{n} \cos \left(2 \pi x_{i}\right)\right)+20+e \end{aligned}$	[-32, 32]	0

函数	指标	INGO	UNGO	NGO	SSA	WOA	WSA
F₁	Max	0.00E+00	1.44E-121	5.61E-45	2.77E-27	1.36E-17	1.28E-71
	Min	0.00E+00	7.63E-128	2.34E-46	0.00E+00	2.92E-50	1.85E-75
	Mean	0.00E+00	1.16E-122	1.02E-45	9.23E-29	8.51E-17	1.02E-72
	Std	0.00E+00	3.52E-122	1.09E-45	5.05E-28	9.86E-17	2.41E-72
F₂	Max	0.00E+00	6.01E-240	3.09E-23	1.58E-42	7.72E+04	2.67E-142
	Min	0.00E+00	4.79E-255	4.12E-29	0.00E+00	3.13E+04	3.32E-152
	Mean	0.00E+00	3.90E-241	5.02E-24	5.27E-44	4.70E+04	1.23E-143
	Std	0.00E+00	0.00E+00	8.93E-24	2.88E-43	1.08E+04	5.08E-143
F₃	Max	0.00E+00	6.07E-123	8.16E-37	5.10E-27	8.57E+01	1.44E-70
	Min	0.00E+00	1.10E-133	1.00E-38	0.00E+00	1.16E+00	1.23E-80
	Mean	0.00E+00	2.46E-124	1.85E-37	1.70E-28	4.67E+01	4.87E-72
	Std	0.00E+00	1.12E-123	1.83E-37	9.31E-28	2.86E+01	2.63E-71
F₄	Max	8.88E-16	8.88E-16	7.99E-15	8.88E-16	7.99E-15	8.88E-16
	Min	8.88E-16	8.88E-16	4.44E-15	8.88E-16	8.88E-16	8.88E-16
	Mean	8.88E-16	8.88E-16	6.80E-15	8.88E-16	3.61E-15	8.88E-16
	Std	0.00E+00	0.00E+00	1.70E-15	0.00E+00	2.22E-15	0.00E+00