Improved Northern Goshawk Optimization Algorithm and its application in intelligent vehicle path planning

doi:10.3969/j.issn.1674-8484.2025.01.015

Abstract

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

CLC Number:

U463.6

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.

Figures/Tables 12

References 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