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
计量
- 文章访问数: 1100
- HTML全文浏览量: 1009
- PDF下载量: 113
- 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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参考文献(25)

[1]	刘小龙. 改进多元宇宙算法求解大规模实值优化问题[J]. 电子与信息学报, 2019, 41(7): 1666–1673. doi: 10.11999/JEIT180751 LIU Xiaolong. Application of improved multiverse algorithm to large scale optimization problems[J]. Journal of Electronics &Information Technology, 2019, 41(7): 1666–1673. doi: 10.11999/JEIT180751
[2]	MIRJALILI S and LEWIS A. The whale optimization algorithm[J]. Advances in Engineering Software, 2016, 95: 51–67. doi: 10.1016/j.advengsoft.2016.01.008
[3]	MAFARJA M M and MIRJALILI S. Hybrid whale optimization algorithm with simulated annealing for feature selection[J]. Neurocomputing, 2017, 260: 302–312. doi: 10.1016/j.neucom.2017.04.053
[4]	ABDEL-BASSET M, MANOGARAN G, EL-SHAHAT D, et al. A hybrid whale optimization algorithm based on local search strategy for the permutation flow shop scheduling problem[J]. Future Generation Computer Systems, 2018, 85: 129–145. doi: 10.1016/j.future.2018.03.020
[5]	XIONG Guojiang, ZHANG Jing, SHI Dongyuan, et al. Parameter extraction of solar photovoltaic models using an improved whale optimization algorithm[J]. Energy Conversion and Management, 2018, 174: 388–405. doi: 10.1016/j.enconman.2018.08.053
[6]	CHEN Huiling, XU Yueting, WANG Mingjing, et al. A balanced whale optimization algorithm for constrained engineering design problems[J]. Applied Mathematical Modelling, 2019, 71: 45–59. doi: 10.1016/j.apm.2019.02.004
[7]	MAHDAD B. Improvement optimal power flow solution under loading margin stability using new partitioning whale algorithm[J]. International Journal of Management Science and Engineering Management, 2019, 14(1): 64–77. doi: 10.1080/17509653.2018.1488225
[8]	吴书强, 栾飞. 基于改进型鲸鱼算法的云制造资源配置研究[J]. 制造业自动化, 2019, 41(12): 95–98, 124. WU Shuqiang and LUAN Fei. Optimal allocation method for cloud manufacturing resource based on improved whale optimization algorithm[J]. Manufacturing Automation, 2019, 41(12): 95–98, 124.
[9]	孙琪, 于永进, 王玉彬, 等. 采用改进鲸鱼算法的配电网综合优化[J/OL]. 电力系统及其自动化学报. 2021, 30(5): 22–29. doi:10.19635/j.cnki.csu-epsa.000553. SUN Qi, YU Yongjin, WANG Yubin, et al. Comprehensive optimization of distribution network with improved whale algorithm[J/OL]. The CSU-EPSA. 2021, 30(5): 22–29. doi:10.19635/j.cnki.csu-epsa.000553.
[10]	吴坤, 谭劭昌. 基于改进鲸鱼优化算法的无人机航路规划[J]. 航空学报, 2020, 41(S2): 724286. doi: 10.7527/S1000-6893.2020.24286 WU Kun and TAN Shaochang. Path planning of UAVs based on improved whale optimization algorithm[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(S2): 724286. doi: 10.7527/S1000-6893.2020.24286
[11]	SUN Yongjun, WANG Xilu, CHEN Yahuan, et al. A modified whale optimization algorithm for large-scale global optimization problems[J]. Expert Systems With Applications, 2018, 114: 563–577. doi: 10.1016/j.eswa.2018.08.027
[12]	龙文, 蔡绍洪, 焦建军, 等. 求解大规模优化问题的改进鲸鱼优化算法[J]. 系统工程理论与实践, 2017, 37(11): 2983–2994. doi: 10.12011/1000-6788(2017)11-2983-12 LONG Wen, CAI Shaohong, JIAO Jianjun, et al. Improved whale optimization algorithm for large scale optimization problems[J]. Systems Engineering-Theory &Practice, 2017, 37(11): 2983–2994. doi: 10.12011/1000-6788(2017)11-2983-12
[13]	褚鼎立, 陈红, 王旭光. 基于自适应权重和模拟退火的鲸鱼优化算法[J]. 电子学报, 2019, 47(5): 992–999. doi: 10.3969/j.issn.0372-2112.2019.05.003 CHU Dingli, CHEN Hong, and WANG Xuguang. Whale optimization algorithm based on adaptive weight and simulated annealing[J]. Acta Electronica Sinica, 2019, 47(5): 992–999. doi: 10.3969/j.issn.0372-2112.2019.05.003
[14]	王坚浩, 张亮, 史超, 等. 基于混沌搜索策略的鲸鱼优化算法[J]. 控制与决策, 2019, 34(9): 1893–1900. doi: 10.13195/j.kzyjc.2018.0098 WANG Jianhao, ZHANG Liang, SHI Chao, et al. Whale optimization algorithm based on chaotic search strategy[J]. Control and Decision, 2019, 34(9): 1893–1900. doi: 10.13195/j.kzyjc.2018.0098
[15]	肖子雅, 刘升. 精英反向黄金正弦鲸鱼算法及其工程优化研究[J]. 电子学报, 2019, 47(10): 2177–2186. doi: 10.3969/j.issn.0372-2112.2019.10.020 XIAO Ziya and LIU Sheng. Study on elite opposition-based golden-sine whale optimization algorithm and its application of project optimization[J]. Acta Electronica Sinica, 2019, 47(10): 2177–2186. doi: 10.3969/j.issn.0372-2112.2019.10.020
[16]	吴泽忠, 宋菲. 基于改进螺旋更新位置模型的鲸鱼优化算法[J]. 系统工程理论与实践, 2019, 39(11): 2928–2944. doi: 10.12011/1000-6788-2018-2156-17 WU Zezhong and SONG Fei. Whale optimization algorithm based on improved spiral update position model[J]. Systems Engineering-Theory &Practice, 2019, 39(11): 2928–2944. doi: 10.12011/1000-6788-2018-2156-17
[17]	张达敏, 徐航, 王依柔, 等. 嵌入Circle映射和逐维小孔成像反向学习的鲸鱼优化算法[J]. 控制与决策, 2021, 36(5): 1173–1180. doi: 10.3195/j.kzyjc.2019.1362 ZHANG Damin, XU Hang, WANG Yirou, et al. Whale optimization algorithm for embedded circle mapping and one dimensional oppositional learning based small hole imaging[J]. Control and Decision, 2021, 36(5): 1173–1180. doi: 10.3195/j.kzyjc.2019.1362
[18]	刘景森, 马义想, 李煜. 改进鲸鱼算法求解工程设计优化问题[J]. 计算机集成制造系统, 2021, 27(7): 1884–1897. doi: 10.13196/j.cims.2021.07.004 LIU Jingsen, MA Yixiang, and LI Yu. Improved whale algorithm for solving engineering design optimization problems[J]. Computer Integrated Manufacturing Systems, 2021, 27(7): 1884–1897. doi: 10.13196/j.cims.2021.07.004
[19]	黄清宝, 李俊兴, 宋春宁, 等. 基于余弦控制因子和多项式变异的鲸鱼优化算法[J]. 控制与决策, 2020, 35(3): 559–568. doi: 10.13195/j.kzyjc.2018.0463 HUANG Qingbao, LI Junxing, SONG Chunning, et al. Whale optimization algorithm based on cosine control factor and polynomial mutation[J]. Control and Decision, 2020, 35(3): 559–568. doi: 10.13195/j.kzyjc.2018.0463
[20]	黄飞, 吴泽忠. 基于阈值控制的一种改进鲸鱼算法[J]. 系统工程, 2020, 38(2): 133–148. HUNAG Fei and WU Zezhong. An improved whale optimization algorithm based on threshold control[J]. Systems Engineering, 2020, 38(2): 133–148.
[21]	WATKINS W A and SCHEVILL W E. Aerial observation of feeding behavior in four baleen whales: Eubalaena glacialis, Balaenoptera borealis, Megaptera novaeangliae, and Balaenoptera physalus[J]. Journal of Mammalogy, 1979, 60(1): 155–63. doi: 10.2307/1379766
[22]	杜永兆, 范宇凌, 柳培忠, 等. 多种群协方差学习差分进化算法[J]. 电子与信息学报, 2019, 41(6): 1488–1495. doi: 10.11999/JEIT180670 DU Yongzhao, FAN Yuling, LIU Peizhong, et al. Multi-populations covariance learning differential evolution algorithm[J]. Journal of Electronics &Information Technology, 2019, 41(6): 1488–1495. doi: 10.11999/JEIT180670
[23]	徐建中, 晏福. 改进鲸鱼优化算法在电力负荷调度中的应用[J]. 运筹与管理, 2020, 29(9): 149–159. doi: 10.12005/orms.2020.0238 XU Jianzhong and YAN Fu. The application of improved whale optimization algorithm in power load dispatching[J]. Operations Research and Management Science, 2020, 29(9): 149–159. doi: 10.12005/orms.2020.0238
[24]	郭振洲, 王平, 马云峰, 等. 基于自适应权重和柯西变异的鲸鱼优化算法[J]. 微电子学与计算机, 2017, 34(9): 20–25. doi: 10.19304/j.cnki.issn1000-7180.2017.09.005 GUO Zhenzhou, WANG Ping, MA Yunfeng, et al. Whaleoptimization algorithm based on adaptive weight and Cauchy mutation[J]. Microelectronics &Computer, 2017, 34(9): 20–25. doi: 10.19304/j.cnki.issn1000-7180.2017.09.005
[25]	HEIDARI A A, MIRJALILI S, FARIS H, et al. Harris hawks optimization: Algorithm and applications[J]. Future Generation Computer Systems, 2019, 97: 849–872. doi: 10.1016/j.future.2019.02.028