基于改进哈里斯鹰算法的机器人路径规划研究

doi:10.16182/j.issn1004731x.joss.23-1342

摘要/Abstract

摘要：

为提升哈里斯鹰优化算法收敛精度，解决易陷入局部最优等问题，提出了一种基于迭代混沌精英反向学习和黄金正弦策略的哈里斯鹰优化算法（gold sine HHO，GSHHO）。利用无限迭代混沌映射初始化种群，运用精英反向学习策略筛选优质种群，提高种群质量，增强算法的全局搜索能力；使用一种收敛因子调整策略重新计算猎物能量，平衡算法的全局探索和局部开发能力；在哈里斯鹰的开发阶段引入黄金正弦策略，替换原有的位置更新方法，提升算法的局部开发能力；在9个测试函数和不同规模的栅格地图上评估GSHHO的有效性。实验结果表明：GSHHO在不同测试函数中具有较好的寻优精度和稳定性能，在2次机器人路径规划中路径长度较原始HHO算法分别减少4.4%、3.17%，稳定性分别提升52.98%、63.12%。

关键词: 哈里斯鹰优化算法, 迭代混沌, 精英反向学习, 黄金正弦算法, 栅格法, 路径规划

Abstract:

In order to improve the convergence accuracy of the HHO algorithm, this paper proposes a GSHHO(gold sine harris hawks optimization) algorithm based on multi-strategies. An infinite iterative chaotic map is used to initialize the population, and an elite reverse learning strategy is used to improve population quality; A convergence factor adjustment strategy is used to recalculate prey energy, balancing the global exploration and local development capabilities of the algorithm; In the development phase of Harris Eagle, the golden sine strategy was introduced to replace the original position update method and improve the local development ability of the algorithm; Experiments were conducted to evaluate the optimization performance of GSHHO. Experimental results show that the path length of GSHHO is reduced by 4.4% and 3.17% respectively and the stability is increased by 52.98% and 63.12% respectively compared with the original HHO algorithm.

Key words: HHO algorithm, iterative chaos, elite reverse learning, golden sine algorithm, grid method, path planning

中图分类号:

TP391.9

白宇鑫,陈振亚,石瑞涛等 . 基于改进哈里斯鹰算法的机器人路径规划研究[J]. 系统仿真学报, 2025, 37(3): 742-752.

Bai Yuxin,Chen Zhenya,Shi Ruitao,et al . Research on Robot Path Planning Based on Improved Harris Hawks Algorithm[J]. Journal of System Simulation, 2025, 37(3): 742-752.

图/表 9

图1

图2

表1

9个测试函数

函数类别	表达式	取值范围
单峰测试函数	$F 1 (x) = ∑ i = 1 30 x i 2$	(-100，100)
	$F 2 (x) = ∑ i = 1 30 ∑ j = 1 i x j 2$	(-100，100)
	$F 3 (x) = ∑ i = 1 29 100 (x i + 1 - x i 2) + (x i - 1) 2$	(-30，30)
多峰测试函数	$F 4 (x) = - ∑ i = 1 30 x i s i n x i$	(-100，100)
	$F 5 (x) = ∑ i = 1 30 x i 2 - 10 c o s (2 π x i) + 10$	(-10，10)
	$F 6 (x) = 1 4 000 ∑ i = 1 30 x i 2 - ∏ i = 1 30 c o s x i i + 1$	(-100，100)
固定维多峰测试函数	$F 7 (x) = 1500 + ∑ j = 1 25 1 j + ∑ i = 1 2 (x i - a i j) 6 - 1$	(-65.536，65.536)
	$F 8 (x) = - ∑ i = 1 4 c i e x p - ∑ j = 1 6 a i j (x j - p i j) 2$	(0，1)
	$F 9 (x) = - ∑ i = 1 10 (x - a i) (x - a i) T + c i - 1$	(0，10)

表1

表2

图3

表3

图4

图5

表4

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函数	指标	GWO	WOA	HHO	GA	PSO	GSHHO
F1	最优值	1.400 1×10^-125	2.765 4×10^-218	2.765 4×10^-218	0.025 4	2.935 9×10^-11	2.765 4×10^-218
	平均值	3.113 5×10^-117	1.980 6×10^-156	3.017 2×10^-189	1.470 2	3.014 2×10^-9	6.717 5×10^-191
	标准差	9.360 5×10^-117	6.240 4×10^-156	0	2.087 3	5.743 6×10^-9	0
F2	最优值	4.557 1×10^-65	1.546×10^-193	1.546×10^-193	8.330 3×10²	1.338 3×10^-4	1.546 0×10^-193
	平均值	9.318 8×10^-52	18.815 4	1.144 6×10^-163	3.982 3×10³	0.001 8	1.853 0×10^-165
	标准差	5.033 1×10^-51	52.093 2	9.987 6×10^-161	2.398 5×10³	0.001 9	0
F4	最优值	-3.716 0×10³	-4.189 8×10³	-4.189 8×10³	-1.845 4×10³	-3.064 7×10³	-4.189 8×10³
	平均值	-2.804 3×10³	-3.434 4×10³	-4.164 8×10³	-1.228 6×10³	-2.493 1×10³	-4.189 8×10³
	标准差	3.403 2×10²	5.785 2×10²	1.369 9×10²	2.7755×10²	3.672 1×10²	0.033 0
F6	最优值	0.998 0	0.998 0	0.998 0	0.998 0	0.998 0	0.998 0
	平均值	5.107 7	3.314 9	1.196 8	1.023 4	3.103 3	0.998 0
	标准差	4.441 2	3.858 7	0.404 4	0.129 7	2.322 3	2.375 4×10^-10
F8	最优值	-3.322 0	-3.315 6	-3.315 6	-2.607 5	-3.322 0	-3.410 2
	平均值	-3.256 5	-3.256 9	-3.122 3	-1.608 8	-3.278 4	-3.383 7
	标准差	0.069 8	0.089 1	0.097 3	0.548 3	0.058 3	0.072 3
F9	最优值	-10.536 4	-10.536 3	-10.536 3	-2.123 4	-10.536 4	-10.536 6
	平均值	-10.535 9	-7.911 9	-5.302 8	-1.217 0	-9.862 5	-10.588 1
	标准差	3.030 3	3.098 7	0.960 9	0.422 7	2.086 7	0.077 6

地图	实验次数	GA	PSO	GWO	WOA	HHO	GSHHO
简单	1	28.577 7	29.827 2	28.577 7	31.964 0	28.577 7	28.419 3
	2	28.531 2	31.052 5	28.577 7	30.809 8	30.484 9	28.139 5
	3	31.052 5	29.411 7	29.892 6	31.424 7	28.577 7	28.577 7
	4	28.725 2	29.411 7	28.419 3	29.890 2	31.052 5	28.419 3
	5	30.533 9	28.577 7	28.577 7	32.339 9	30.475 2	28.577 7
	6	29.233 5	29.411 7	28.577 7	31.655 4	29.264 6	28.139 5
	7	30.188 5	30.188 5	30.188 5	33.095 2	30.767 4	28.631 5
	8	31.052 5	30.188 5	29.954 7	33.090 8	30.297 6	29.901 7
	9	29.954 7	31.073 3	28.577 7	30.282 0	28.577 7	28.577 7
	10	30.892 7	28.577 7	28.725 2	32.483 8	31.052 5	28.577 7
复杂	1	60.566 8	65.052 5	64.069 5	76.828 4	69.022 7	58.925
	2	63.927 5	61.259 2	63.434 7	76.828 4	60.784 9	59.562 1
	3	61.165 8	70.924 4	65.277 0	75.656 9	62.269 9	61.326 7
	4	66.620 5	62.837 5	61.699 2	76.828 4	67.363 0	61.240 7
	5	59.891 9	66.227 2	59.891 0	76.828 4	68.086 0	59.708 6
	6	60.532 0	71.424 3	66.544 3	75.656 9	63.954 6	59.804 9
	7	73.447 9	71.317 6	78.519 7	76.828 4	59.985 6	58.241 0
	8	59.522 4	62.891 8	59.669 0	76.828 4	61.778 5	59.141 0
	9	60.572 1	67.537 7	63.545 4	76.242 6	65.359 1	58.082 5
	10	61.820 5	62.561 2	62.506 0	76.828 4	64.570 5	60.870 2

地图环境	算法	最优值	平均值	标准差
简单	GA	28.531 2	29.874 2	0.978 3
	PSO	28.577 7	29.772 1	0.832 2
	GWO	28.419 3	29.006 9	0.665 2
	WOA	29.890 2	31.703 6	1.055 0
	HHO	28.577 7	29.912 8	0.994 4
	GSHHO	28.139 5	28.596 2	0.467 6
复杂	GA	62.806 7	59.522 4	4.088 6
	PSO	66.203 3	61.259 2	3.725 8
	GWO	64.515 6	59.669	5.098 7
	WOA	76.535 5	75.656 9	0.472 2
	HHO	64.317 5	59.985 6	2.979 6
	GSHHO	59.690 3	58.082 5	1.098 9

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