多种群纵横双向学习和信息互换的鲸鱼优化算法

刘小龙

doi:10.11999/JEIT201080

多种群纵横双向学习和信息互换的鲸鱼优化算法

doi: 10.11999/JEIT201080

刘小龙^,

华南理工大学工商管理学院广州 510641

基金项目: 中央高校基本科研业务费(XYZD201911)

详细信息

作者简介:
刘小龙：男，1977年生，讲师，研究方向为仿生优化与计算智能

通讯作者:
刘小龙　xlliu@scut.edu.cn

中图分类号: TP301.6
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- 文章访问数: 914
- HTML全文浏览量: 710
- PDF下载量: 109
- 被引次数: 0
出版历程
- 收稿日期: 2020-12-25
- 修回日期: 2021-03-12
- 网络出版日期: 2021-03-24
- 刊出日期: 2021-11-23

Whale Optimization Algorithm for Multi-group with Information Exchange and Vertical and Horizontal Bidirectional Learning

Xiaolong LIU^,

School of Business Administration, South China University of Technology, Guangzhou 510641, China

Funds: The Fundamental Research Funds for the Central University (XYZD201911)

摘要

摘要: 鲸鱼优化算法(WOA)相较于传统的群体智能优化算法，具有较好的寻优能力和鲁棒性，但仍存在全局寻优能力有限、局部极值难以跳出等问题。针对上述不平衡问题，该文提出一种多种群纵横双向学习的种群划分思路，子群相互独立，子群内个体受到来自横向和纵向两个方向的最优值影响，从而规避局部最优，在探索和开发之间取得均衡。对纵向种群的所有个体，该文提出一种线性下降概率的个体置换策略，促进不同子群的信息流动，加快算法收敛。基于不同个体的历史进化信息，来进行策略算子选择，从而区别于现有基于随机数的策略算子选择方法。利用基准函数进行跨文献对比，数值结果表明该文算法具有很好的优越性和稳定性，在大多数问题上都获得了全局极值，具有较好的问题适用性。
- 鲸鱼优化算法 /
- 多种群纵横双向学习 /
- 子群个体互换 /
- 历史信息
Abstract: Compared with traditional swarm intelligence optimization algorithms, the Whale Optimization Algorithm(WOA) has better optimization capabilities and robustness, but there are still problems such as limited global optimization capabilities and difficulty in jumping out of local extremes. Considering the above-mentioned imbalance problem, a multi-group population division idea with vertical and horizontal bidirectional learning is proposed. The subgroups are independent of each other, and the individuals in the subgroups are affected by the optimal values from both the horizontal and vertical directions, thereby avoiding the local optimal and getting the balance between exploration and development.For all individuals in the vertical population, an individual replacement strategy with linearly decreasing probability is proposed to promote the information flow of different subgroups and accelerate the algorithm convergence.The selection of strategy operators is based on the historical evolution information of different individuals, which is different from the existing strategy operator selection methods based on random numbers.The benchmark function is used for cross-document comparison. The numerical results show that the algorithm in this thesis has good superiority and stability. It obtains global extreme on most problems and has good problem applicability.
- Whale Optimization Algorithm(WOA) /
- Multi-Group with vertical and horizontal bidirectional learning /
- Subgroup individual exchange /
- Historical information

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图 1 改进鲸鱼优化算法的多种群纵横双向结构

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表 1 本文算法参数C 和P_p的基准函数测试均值精度等级(D=30)

实验	F₁	F₂	F₃	F₄	F₅	F₆	F₇	F₈	F₉	F₁₀	F₁₁	F₁₂	F₁₃
1	0	e-167	0	e-169	e-004	e-009	e-004	–12569	0	e-016	0	e-010	e-009
2	e-323	e-168	0	e-167	0	0	e-004	–12332	0	e-016	0	e-032	e-032
3	0	e-167	0	e-169	0	0	e-004	–12331	0	e-016	0	e-032	e-032
4	0	e-168	0	e-164	0	0	e-004	–12214	0	e-016	0	e-032	e-032
5	e-055	e-019	e-011	e-066	0	0	e-004	–10347	1.98	e-016	0	e-032	e-032

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表 2 本文算法参数A的基准函数测试均值精度等级(D=30)

实验	F₁	F₂	F₃	F₄	F₅	F₆	F₇	F₈	F₉	F₁₀	F₁₁	F₁₂	F₁₃
6	0	e-194	0	e-192	0	0	e-004	–11740	0	e-016	0	e-032	e-032
7	0	e-218	0	e-218	0.9569	0	e-004	–11977	0	e-016	0	e-032	e-032
8	0	e-229	0	e-226	0	0	e-004	–11793	2.984	e-016	0	e-032	e-032

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表 3 本文算法种群参数p和k的基准函数测试均值精度等级(D=30)

实验	F₁	F₂	F₃	F₄	F₅	F₆	F₇	F₈	F₉	F₁₀	F₁₁	F₁₂	F₁₃
9	0	0	0	0	2.87	0	e-004	–11026	8.954	e-016	0	e-032	e-032
10	0	e-164	0	e-168	0	0	e-004	–11977	1.989	e-016	0	e-032	e-032
11	e-264	e-133	e-260	e-134	0	0	e-004	–12569	0	e-016	0	e-032	e-032
12	e-214	e-108	e-212	e-101	0	0	e-004	–12569	0	e-016	0	e-032	e-032

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表 4 针对基本测试函数的算法性能均值指标对比(D=30)

	F₁	F₂	F₃	F₄	F₅	F₆	F₇	F₈	F₉	F₁₀	F₁₁	F₁₂	F₁₃
本文算法	e-157	e-81	e-153	e-81	0	0	e-04	–12569	0	e-16	0	e-32	e-32
HHO	e-97	e-51	e-63	e-47	e-02	e-04	e-04	e+04	0	e-16	0	e-06	e-04
WOA	e-30	e-21	e-07	e-02	27.86	3.11	e-03	–5080	0	7.40	e-04	0.339	1.889

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表 5 本文算法与现有文献的性能指标对比(D=30)

	W-SA-WOA^[13]		CWOA^[14]		EGolden-SWOA^[15]		IMWOA^[16]		本文算法
	平均值	标准差	平均值	标准差	平均值	标准差	平均值	标准差	平均值	标准差
F₁	0	0	0	0	0	0	0	0	2.7e-157	1.4e-156
F₂	2.57e-21	6.68e-121	4.56e-223	0	6.69e-202	0	8.82e-181	0	3.8e-081	9.1e-81
F₃	0	0	–	–	0	0	0	0	1.2e-153	6.8e-153
F₄	3.56e-94	4.90e-94	3.6e-265	0	3.58e-191	0	4.27e-184	0	1.6e-081	3.0e-081
F₅	27.3357	0.2956	0.274	5.17e-00	3.75e-09	7.45e-09	4.29e-05	1.33e-04	0	0
F₆	0.0271	0.0201	0	0	6.86e-10	1.29e-09	0	0	0	0
F₇	1.17e-04	1.0E-04	3.61e-05	3.73e-05	3.25e-05	2.55e-05	0	0	1.4e-04	1.25e-04
F₈	–12447	873.3422	–	–	–5.58e-101	1.67e + 102	–12455.6	172.0869	–12569	1.8e-12
F₉	0	0	0	0	0	0	0	0	0	0
F₁₀	3.02e-15	1.77e-15	8.88e-016	4.01e-31	8.88e-16	0	8.88e-016	1.00e-031	8.88e-016	0
F₁₁	0.0015	0.0073	0	0	0	0	0	0	0	0
F₁₂	0.0785	2.40e-08	3.09e-02	1.37e-02	8.53e-14	2. 61e-10	1.68e-08	1.70e-08	1.5e-032	5.5e-48
F₁₃	0.0421	0.0289	–	–	2.63e-11	6.65e-10	5.69e-06	1.96e-05	1.3e-032	5.5e-48

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表 6 大规模(D=1000)测试函数的算法性能指标对比

	Rosenbrock			Penalized1
	均值	标准差	成功率	均值	标准差	成功率
本文算法	0	0	100	4.7116e-034	68.6991e-050	100
文献[11]	1.38e-17	4.2e-17	100	4.13e-28	0	100
文献[12]	9.92e+02	8.29e-01	0	1.59e-01	6.19e-02	0
文献[14]	9.90e+02	4.51e-01	0	3.46e-02	1.76e-02	3.33
文献[16]	2.66e-08	4.96e-08	100	3.14e-09	4.24e-09	100
文献[24]	0.3318	0.3973	10	2.20e-06	3.56e-06	100

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表 7 本文算法与文献[12,23]的性能对比(D=1000)

函数	IWOA^[12]			GWOA^[23]			本文算法
函数	均值	标准差	成功率	均值	标准差	成功率	均值	标准差	成功率
f₁	1.86e-111	9.0e-112	100	1.60e-114	5.01e-114	100	8.7516e-157	2.707e-156	100
f₂	3.00e-065	3.37e-065	100	1.56e-073	2.09e-073	100	7.2131e-080	1.7043e-079	100
f₃	3.15e-112	6.20e-112	100	9.59e-114	2.03e-113	100	4.0063e-153	2.1768e-152	100
f₄	3.00e-182	0	100	4.29e-168	0	100	1.4807e-161	8.1032e-161	100
f₅	9.92e+02	8.29e-01	0	9.88e+ 02	6.18e-004	0	0	0	100
f₆	3.06e-003	2.52e-003	20	2.07e-002	3.53e-002	30	2.2722e-04	1.7054e-04	100
f₇	1.10e-001	2.25e-002	40	1.05e-007	3.14e-007	100	4.7116e-034	8.6991e-050	100
f₈	0	0	100	0	0	100	0	0	100
f₉	5.15e-015	2.89e-015	100	8.88e-016	0	100	8.8818e-016	0	100
f₁₀	0	0	100	0	0	100	0	0	100
f₁₁	1.02e-066	1.63e-066	100	0	0	100	1.0549e-076	5.7776e-076	100
f₁₂	6.58e-112	1.30e-111	100	6.32e-122	1.58e-122	100	1.3948e-122	6.6809e-122	100
f₁₃	0	0	100	0	0	100	0	0	100
f₁₄	1.66e-115	3.30e-115	100	3.64e-130	4.58e-130	100	1.3498e-130	5.5674e-130	100
f₁₅	5.52e-103	1.20e-102	100	3.33e-105	1.05e-104	100	2.2266e-153	9.0116e-153	100

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