融合多策略改进的侏儒猫鼬算法

于明洋; 李婷; 许静

doi:10.13700/j.bh.1001-5965.2023.0613

融合多策略改进的侏儒猫鼬算法

doi: 10.13700/j.bh.1001-5965.2023.0613

于明洋¹,
李婷^{2, 3, ,},
许静¹

1.
南开大学人工智能学院，天津 300350
2.
南开大学计算机学院，天津 300350
3.
天津津航技术物理研究所，天津 300350

基金项目:

天津市自然科学基金(21JCYBJC00110)

详细信息

通讯作者:
E-mail：t24725@126.com

中图分类号: V221⁺.3；TB553
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- 被引次数: 0
出版历程
- 收稿日期: 2023-09-26
- 录用日期: 2023-12-15
- 网络出版日期: 2024-01-19
- 整期出版日期: 2025-11-25

Enhanced dwarf mongoose optimization algorithm with multi-strategy fusion

YU Mingyang¹,
LI Ting^{2, 3
, ,},
XU Jing¹

1.
College of Artificial Intelligence，Nankai University，Tianjin 300350，China
2.
College of Computer Science，Nankai University，Tianjin 300350，China
3.
Tianjin Jinhang Institute of Technical Physics，Tianjin 300350，China

Funds:

Natural Science Foundation of Tianjin Municipality (21JCYBJC00110)

More Information

Corresponding author: E-mail：t24725@126.com

摘要

摘要:
针对侏儒猫鼬优化算法(DMO)易陷入局部最优和收敛效率低的问题，提出一种多策略融合的增强型侏儒猫鼬算法(EDMO)。该算法引入随机反向学习策略增强猫鼬种群的多样性和质量，以增强其全局搜索能力和提高收敛速度。同时，采用自适应的方式更新保姆交换系数，以平衡全局探索与局部开发的需求。在迭代的后期，算法利用黏菌觅食行为，在局部与全局最优解之间进行优化。通过对CEC2017测试函数集的求解，对不同的算法进行比较。结果表明：融合3种策略的EDMO在寻优精度、寻优速度和鲁棒性方面均优于对比的先进算法。通过对无人机三维路径规划的实验验证，EDMO在局部搜索方面表现优于原始DMO算法，同时生成的飞行路径也更为稳定。
- 侏儒猫鼬优化算法 /
- 多策略融合 /
- 随机反向学习 /
- 自适应 /
- 黏菌觅食行为 /
- 三维路径规划
Abstract:
The enhanced multi-strategy dwarf mongoose optimization algorithm (EDMO) is a proposed solution to the dwarf mongoose optimization algorithm's (DMO) low convergence efficiency and susceptibility to local optima. This algorithm employs a random opposite learning strategy to amplify the diversity and quality of the mongoose population, bolstering its global search capability and enhancing convergence accuracy. Concurrently, an adaptive approach is deployed to update the babysitter exchange coefficient, striking a balance between global exploration and local exploitation. In the latter stages of iteration, the algorithm capitalizes on the foraging behavior of the slime mold, optimizing between local and global optimal solutions. By solving the CEC2017 test function set, different algorithms are compared. The findings demonstrate that in terms of optimization accuracy, optimization speed, and resilience, EDMO which combines the three strategies performs better than the sophisticated algorithms under comparison. Through the experimental verification of UAV three-dimensional path planning, the EDMO algorithm performs better than the original DMO algorithm in local search, and the flight path generated is more stable.
- dwarf mongoose optimization algorithm /
- multi-strategy fusion /
- random reverse learning /
- adaptive /
- fungal foraging behavior /
- three-dimensional path planning

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图 1 非线性比例因子γ

Figure 1. Nonlinear scaling factor γ

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图 2 EDMO流程

Figure 2. Flow of EDMO

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图 3 α和f₁₄拟合曲线

Figure 3. Fitted curve with α and f₁₄

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图 4 收敛曲线对比

Figure 4. Convergence curves comparison

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图 5 三维威胁地图

Figure 5. Three-dimensional threat topographic map

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图 6 二维航迹规划（DMO）

Figure 6. Two-dimensional track plan （DMO）

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图 7 三维航迹规划（DMO）

Figure 7. Three-dimensional track plan （DMO）

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图 8 适应度变化曲线（DMO）

Figure 8. Fitness change curve （DMO）

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图 9 二维航迹规划（EDMO）

Figure 9. Two-dimensional track plan （EDMO）

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图 10 三维航迹规划（EDMO）

Figure 10. Three-dimensional track plan （EDMO）

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图 11 适应度变化曲线（EDMO）

Figure 11. Fitness change curve （EDMO）

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表 1 29个CEC2017测试函数

Table 1. 29 CEC2017 test functions

函数	函数名称	最优适应度值	函数	函数名称	最优适应度值
f₁	Shifted and Rotated Bent Cigar Function	100	f₁₇	Hybrid Function 6(N=4)	1700
f₃	Shifted and Rotated Zakharov Function	300	f₁₈	Hybrid Function 6(N=5)	1800
f₄	Shifted and Rotated Rosenbrock’s Function	400	f₁₉	Hybrid Function 6(N=5)	1900
f₅	Shifted and Rotated Rastrigin’s Function	500	f₂₀	Hybrid Function 6(N=6)	2000
f₆	Shifted and Rotated Expanded Scaffer’s F6 Function	600	f₂₁	Composition Function 1(N=3)	2100
f₇	Shifted and Rotated Lunacek Bi-Rastrigin Function	700	f₂₂	Composition Function 2(N=3)	2200
f₈	Shifted and Rotated Non-Continuous Rastrigin’s Function	800	f₂₃	Composition Function 3(N=4)	2300
f₉	Shifted and Rotated Lévy Function	900	f₂₄	Composition Function 4(N=4)	2400
f₁₀	Shifted and Rotated Schwefel’s Function	1000	f₂₅	Composition Function 5(N=5)	2500
f₁₁	Hybrid Function 1(N=3)	1100	f₂₆	Composition Function 6(N=5)	2600
f₁₂	Hybrid Function 2(N=3)	1200	f₂₇	Composition Function 7(N=6)	2700
f₁₃	Hybrid Function 3(N=3)	1300	f₂₈	Composition Function 8(N=6)	2800
f₁₄	Hybrid Function 4(N=4)	1400	f₂₉	Composition Function 9(N=3)	2900
f₁₅	Hybrid Function 5(N=4)	1500	f₃₀	Composition Function 10(N=3)	3000
f₁₆	Hybrid Function 5(N=4)	1600

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表 2 消融实验结果γ值对比

Table 2. Comparison of ablation results of γ

函数	DMO^[10]	EDMO1	EDMO2	EDMO3	函数	DMO^[10]	EDMO1	EDMO2	EDMO3
f₁	0.00	0.32	0.72	0.03	f₁₇	0.84	0.95	0.96	0.88
f₃	0.51	0.52	0.92	0.31	f₁₈	0.02	0.78	0.77	0.32
f₄	0.83	0.85	0.88	0.88	f₁₉	0.39	0.53	0.78	0.48
f₅	0.88	0.92	0.94	0.88	f₂₀	0.88	0.95	0.94	0.91
f₆	0.98	0.97	0.98	1.00	f₂₁	0.99	0.98	0.98	0.95
f₇	0.84	0.93	0.88	0.87	f₂₂	0.57	0.68	1.04	0.77
f₈	0.95	0.96	0.97	0.90	f₂₃	0.97	0.98	0.97	0.97
f₉	0.33	0.51	0.49	0.67	f₂₄	1.00	0.96	1.01	0.98
f₁₀	0.54	0.61	0.52	0.55	f₂₅	0.98	0.98	0.99	0.99
f₁₁	1.05	1.12	1.11	1.12	f₂₆	0.79	0.81	0.77	0.72
f₁₂	0.39	0.65	0.46	0.43	f₂₇	0.93	0.99	0.99	0.98
f₁₃	0.31	0.41	0.45	0.55	f₂₈	0.92	0.96	0.97	0.99
f₁₄	2.14	8.33	0.13	0.04	f₂₉	0.83	0.91	0.89	0.91
f₁₅	0.12	0.21	0.23	0.24	f₃₀	0.06	0.43	0.21	0.43
f₁₆	0.83	0.88	0.88	0.79

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表 3 CEC2017测试结果

Table 3. Test results for CEC 2017

函数	CMA-ES^[27] 均值(标准差)	LSHADE_cnEpsin^[28] 均值(标准差)	LSHADE^[29] 均值(标准差)	DMO^[10] 均值(标准差)	IDMO^[15] 均值(标准差)	EDMO 均值(标准差)
f₁	1.32×10¹⁰(4.86×10⁹)/+	1.73×10¹⁰(5.77×10⁹)/+	2.38×10⁷(2.23×10⁷)/+	5.26×10⁶(1.13×10⁷)/+	1.98×10⁴(3.53×10⁴)/+	5.71×10²(7.02×10²)
f₃	6.35×10⁴(9.89×10³)/+	4.19×10⁴(1.02×10⁴)/+	6.44×10⁴(1.05×10⁴)/+	4.21×10⁴(9.81×10³)/+	1.62×10⁴(4.67×10³)/−	2.05×10⁴(2.01×10³)
f₄	1.37×10³(7.52×10²)/+	2.30×10³(1.59×10³)/+	5.35×10²(31.4)/+	5.20×10²(32.0)/+	5.21×10²(33.2)/+	4.39×10²(36.9)
f₅	7.12×10²(48.2)/+	7.73×10²(37.4)/+	6.83×10²(31.9)/+	6.31×10²(30.5)/+	6.54×10²(33.9)/+	5.57×10²(8.73)
f₆	6.38×10²(6.68)/+	6.62×10²(8.40)/+	6.43×10²(10.4)/+	6.22×10²(8.73)/+	6.33×10²(10.6)/+	6.02×10²(2.49×10^-13)
f₇	1.08×10³(61.4)/+	1.28×10³(54.7)/+	1.05×10³(52.4)/+	9.40×10²(59.5)/+	9.97×10²(67.7)/+	7.75×10²(6.11)
f₈	9.87×10²(39.5)/+	9.96×10²(26.0)/+	9.58×10²(25.7)/+	9.18×10²(19.6)/+	9.16×10²(24.7)/+	8.65×10²(10.6)
f₉	5.54×10³(1.40×10³)/+	5.86×10³(5.75×10²)/+	3.88×10³(4.76×10²)/+	3.45×10³(1.65×10³)/+	3.14×10³(8.49×10²)/+	1.14×10³(1.13×10²)
f₁₀	6.64×10³(1.43×10³)/+	5.34×10³(3.92×10²)/+	5.65×10³(2.85×10²)/+	5.73×10³(9.75×10²)/+	5.02×10³6.75×10²)/+	3.15×10³(2.67×10²)
f₁₁	3.75×10³(1.57×10³)/+	2.13×10³(6.78×10²)/=	1.23×10³(40.5)/=	1.32×10³(65.6)/=	1.27×10³(54.4)/=	1.35×10³(22.7)
f₁₂	9.57×10⁸(1.13×10⁹)/+	1.28×10⁹(1.26×10⁹)/+	1.63×10⁶(1.18×10⁶)/+	1.28×10⁶(9.25×10⁵)/+	8.78×10⁵(8.12×10⁵)/=	4.56×10⁵(2.58×10⁵)
f₁₃	4.76×10⁸(1.33×10⁹)/+	1.85×10⁷(5.16×10⁷)/=	1.75×10⁴(1.37×10⁴)/=	4.38×10⁴(2.86×10⁴)/+	2.08×10⁴(1.97×10⁴)/=	1.26×10⁴(6.56×10³)
f₁₄	1.18×10⁶(1.19×10⁶)/+	2.37×10⁴(2.42×10⁴)/−	2.76×10⁴(3.20×10⁴)/−	4.97×10⁴(5.13×10⁴)/−	1.50×10⁴(2.18×10⁴)/−	1.07×10⁵(6.23×10⁴)
f₁₅	1.58×10⁷(3.31×10⁷)/+	5.16×10⁴(4.74×10⁴)/+	5.66×10³(3.55×10³)/+	1.98×10⁴(2.24×10⁴)/+	9.73×10³(1.08×10⁴)/+	2.21×10³(1.63×10³)
f₁₆	2.95×10³(3.88×10²)/+	3.14×10³(3.98×10²)/+	2.88×10³(1.62×10²)/+	2.74×10³(4.02×10²)/+	2.76×10³(2.83×10²)/+	2.24×10³(1.35×10²)
f₁₇	2.34×10³(2.12×10²)/+	2.26×10³(1.84×10²)/+	2.03×10³(1.35×10²)/+	2.27×10³(1.65×10²)/+	2.38×10³(1.98×10²)/+	1.94×10³(88.2)
f₁₈	1.67×10⁶(1.94×10⁶)/+	4.97×10⁵(5.87×10⁵)/=	2.43×10⁵(1.94×10⁵)/=	2.07×10⁷(1.03×10⁸)/+	1.57×10⁵(1.55×10⁵)/=	1.46×10⁵(5.52×10⁴)
f₁₉	1.26×10⁷(3.22×10⁷)/+	1.63×10⁶(1.73×10⁶)/+	8.34×10³(7.38×10³)/+	9.64×10³(1.32×10⁴)/+	9.96×10³(1.13×10⁴)/+	3.61×10³(1.57×10³)
f₂₀	2.63×10³(1.89×10²)/+	2.52×10³(1.55×10²)/+	2.46×10³(1.05×10²)/+	2.60×10³(2.17×10²)/+	2.58×10³(2.28×10²)/+	2.25×10³(1.05×10²)
f₂₁	2.48×10³(41.2)/+	2.55×10³(73.6)/+	2.44×10³(25.7)/+	2.41×10³(22.6)/+	2.43×10³(30.2)/+	2.35×10³(44.4)
f₂₂	6.28×10³(2.67×10³)/+	5.76×10³(1.64×10³)/+	2.32×10³(31.0)/−	4.24×10³(2.81×10³)/+	4.92×10³(2.38×10³)/+	2.38×10³(39.4)
f₂₃	2.92×10³(63.4)/+	3.06×10³(91.5)/+	2.82×10³(32.4)/+	2.82×10³(75.3)/+	2.84×10³(45.5)/+	2.72×10³(11.1)
f₂₄	3.12×10³(71.5)/+	3.22×10³(67.6)/=	2.97×10³(34.5)/=	2.97×10³(77.8)/=	2.97×10³(57.5)/+	2.95×10³(25.3)
f₂₅	3.11×10³(1.25×10²)/+	3.35×10³(1.83×10²)/+	2.97×10³(24.7)/+	2.95×10³(22.8)/+	2.94×10³(18.4)/+	2.88×10³(0.879)
f₂₆	6.18×10³(6.04×10²)/+	7.22×10³(1.45×10³)/+	5.19×10³(1.70×10³)/+	4.72×10³(9.84×10²)/+	5.66×10³(1.47×10³)/+	3.71×10³(8.32×10²)
f₂₇	3.42×10³(79.2)/+	3.37×10³(65.6)/+	3.22×10³(16.4)/+	3.46×10³(24.2×10²)/+	3.27×10³(38.8)/+	3.23×10³(4.97)
f₂₈	3.92×10³(2.99×10²)/+	4.12×10³(4.07×10²)/+	3.33×10³(36.7)/+	3.56×10³(1.13×10³)/+	3.27×10³(25.6)/+	3.20×10³(10.5)
f₂₉	4.26×10³(2.46×10²)/+	4.58×10³(4.43×10²)/+	4.14×10³(2.23×10²)/+	4.22×10³(4.15×10²)/+	4.20×10³(2.81×10²)/+	3.52×10³(76.7)
f₃₀	4.06×10⁷(3.28×10⁷)/+	1.18×10⁷(8.86×10⁶)/+	2.94×10⁴(3.28×10⁴)/+	1.37×10⁵(2.82×10⁵)/+	2.13×10⁴(1.12×10⁴)/+	7.58×10³(1.22×10³)

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表 4 风险区域二维坐标参数

Table 4. 2D coordinate parameters of risk area

风险区域	中心点坐标/km	风险半径/km
1	(10,60)	5
2	(40,50)	6
3	(60,50)	5
4	(100,30)	8

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表 5 无人机三维路径规划结果统计

Table 5. Statistics of UAV three-dimensional path planning results

实验算法	最优代价	最差代价	平均代价	标准差	平均迭代次数	平均运行时间/ s
EDMO	72.92	72.97	72.96	0.03	124.53	37.41
DMO^[10]	72.96	73.07	73.01	0.08	117.60	39.77

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