上海交通大学学报 ›› 2024, Vol. 58 ›› Issue (4): 555-564.doi: 10.16183/j.cnki.jsjtu.2022.470
收稿日期:
2022-11-25
修回日期:
2023-01-30
接受日期:
2023-03-03
出版日期:
2024-04-28
发布日期:
2024-04-30
通讯作者:
孙志锋,副教授;E-mail: eeszf@zju.edu.cn.
作者简介:
李博群(1997-),硕士生,从事智能控制算法研究.
基金资助:
Received:
2022-11-25
Revised:
2023-01-30
Accepted:
2023-03-03
Online:
2024-04-28
Published:
2024-04-30
摘要:
针对冠状病毒群体免疫优化(CHIO)算法收敛速度慢、求解精度低的问题,提出一种基于群体划分的冠状病毒群体免疫优化(SD-CHIO)算法.基于适应度均匀原则将初始群体划分为两部分,即全局寻优个体与局部寻优个体.对于全局寻优个体,在其位置更新中加入差分变异与漫反射变异策略,分别用来增强全局寻优个体之间的交流与群体多样性,从而提高算法的全局搜索能力.对于局部寻优个体,在其位置更新中引入一种自适应快速收敛策略:基于增量法进行精英预测,并加入一种自适应收敛系数使局部寻优个体能快速收敛至精英解,以提升算法的局部搜索能力.数值实验表明:SD-CHIO能够有效提高原算法的收敛速度与精度,并表现出明显优于其他元启发式算法的全局与局部搜索能力以及一定的工程价值.
中图分类号:
李博群, 孙志锋. 基于群体划分的冠状病毒群体免疫优化算法[J]. 上海交通大学学报, 2024, 58(4): 555-564.
LI Boqun, SUN Zhifeng. A Coronavirus Herd Immunity Optimizer Based on Swarm Division[J]. Journal of Shanghai Jiao Tong University, 2024, 58(4): 555-564.
表1
基准测试函数
函数名称 | 函数表达式 | 搜索范围 |
---|---|---|
Sphere | F1(x)= | [-100, 100] |
Schwefel P2.21 | F2(x)= | [-100, 100] |
Schwefel P2.22 | F3(x)= | [-10, 10] |
Noise | F4(x)= | [-100, 100] |
Rastrigin | F5(x)= | [-5.12, 5.12] |
Griewank | F6(x)= | [-600, 600] |
Salomon | F7(x)=-cos(2π | [-100, 100] |
Ackley | F8(x)=-20exp(-0.2 | [-32, 32] |
Shifted Griewank | F9(x)= | [-600, 600] |
Shifted Ackley | F10(x)=-20exp(-0.2 | [-32, 32] |
Shifted+Rotated Rastrigin | F11(x)= | [-100, 100] |
Shifted+Rotated Levy | F12(x)=sin2(πw1)+ wj=1+ | [-100, 100] |
表2
不同元启发式算法的函数测试结果
函数 | 算法 | μ/A | s/A | 函数 | 算法 | μ/A | s/A | 函数 | 算法 | μ/A | s/A |
---|---|---|---|---|---|---|---|---|---|---|---|
F1 | PSO | 7.90×10-3 | 1.15×10-2 | F5 | PSO | 5.93×101 | 1.73×101 | F9 | PSO | 2.84×10-2 | 2.04×10-2 |
DE | 5.93×10-4 | 3.42×10-4 | DE | 1.54×102 | 9.87×100 | DE | 3.37×10-2 | 6.18×10-2 | |||
ABC | 2.43×101 | 1.52×101 | ABC | 2.38×102 | 1.25×101 | ABC | 1.20×100 | 9.48×10-2 | |||
WOA | 1.48×10-74 | 6.76×10-74 | WOA | 3.79×10-15 | 2.08×10-14 | WOA | 1.12×101 | 3.58×100 | |||
SSA | 2.45×10-7 | 7.25×10-7 | SSA | 5.16×101 | 1.68×101 | SSA | 1.71×10-2 | 1.49×10-2 | |||
CHIO | 1.21×104 | 3.08×103 | CHIO | 1.71×102 | 1.75×101 | CHIO | 1.48×102 | 3.48×101 | |||
ICHIO | 5.69×10-43 | 1.62×10-43 | ICHIO | 2.07×102 | 7.68×101 | ICHIO | 1.28×102 | 2.35×101 | |||
SD-CHIO | 0 | 0 | SD-CHIO | 0 | 0 | SD-CHIO | 3.76×10-8 | 2.53×10-8 | |||
F2 | PSO | 7.58×100 | 1.79×100 | F6 | PSO | 2.49×10-2 | 1.78×10-2 | F10 | PSO | 2.19×100 | 3.63×100 |
DE | 9.34×100 | 1.81×100 | DE | 3.44×10-2 | 6.30×10-2 | DE | 5.98×10-3 | 1.46×10-3 | |||
ABC | 6.48×101 | 4.07×100 | ABC | 1.22×100 | 9.54×10-2 | ABC | 4.15×100 | 3.25×10-1 | |||
WOA | 4.97×101 | 2.52×101 | WOA | 8.37×10-3 | 4.59×10-2 | WOA | 1.56×101 | 1.27×100 | |||
SSA | 1.25×101 | 3.51×100 | SSA | 1.64×10-2 | 1.12×10-2 | SSA | 2.71×100 | 8.22×10-1 | |||
CHIO | 7.37×101 | 3.41×100 | CHIO | 1.13×102 | 3.12×101 | CHIO | 1.73×101 | 7.18×10-1 | |||
ICHIO | 4.25×10-22 | 9.60×10-23 | ICHIO | 0 | 0 | ICHIO | 1.63×101 | 3.05×10-1 | |||
SD-CHIO | 9.51×10-163 | 0 | SD-CHIO | 0 | 0 | SD-CHIO | 1.88×10-5 | 5.49×10-6 | |||
F3 | PSO | 1.39×100 | 3.45×100 | F7 | PSO | 9.68×10-1 | 1.99×10-1 | F11 | PSO | 1.62×101 | 2.78×100 |
DE | 4.89×10-3 | 1.53×10-3 | DE | 8.74×10-1 | 1.03×10-1 | DE | 3.72×101 | 2.25×100 | |||
ABC | 2.96×10-1 | 7.37×10-2 | ABC | 3.17×100 | 4.13×10-1 | ABC | 3.66×101 | 5.15×100 | |||
WOA | 3.84×10-51 | 1.51×10-50 | WOA | 1.43×10-1 | 6.26×10-2 | WOA | 3.14×101 | 2.17×101 | |||
SSA | 2.08×100 | 1.49×100 | SSA | 1.90×100 | 4.60×10-1 | SSA | 1.62×101 | 7.29×100 | |||
CHIO | 8.19×104 | 4.46×105 | CHIO | 1.84×101 | 1.30×100 | CHIO | 7.26×101 | 9.96×100 | |||
ICHIO | 2.87×10-22 | 4.10×10-23 | ICHIO | 4.46×10-1 | 5.71×10-2 | ICHIO | 4.93×101 | 8.15×100 | |||
SD-CHIO | 4.26×10-164 | 0 | SD-CHIO | 0 | 0 | SD-CHIO | 1.02×101 | 2.81×100 | |||
F4 | PSO | 4.73×10-2 | 1.34×10-2 | F8 | PSO | 5.26×10-1 | 7.42×10-1 | F12 | PSO | 2.99×10-3 | 1.63×10-2 |
DE | 1.60×10-1 | 3.11×10-2 | DE | 7.47×10-3 | 2.10×10-3 | DE | 1.39×10-12 | 7.12×10-12 | |||
ABC | 3.09×10-1 | 8.71×10-2 | ABC | 4.17×100 | 3.96×10-1 | ABC | 3.07×10-5 | 5.28×10-5 | |||
WOA | 3.14×10-3 | 2.68×10-3 | WOA | 4.09×10-15 | 3.00×10-15 | WOA | 1.81×100 | 1.60×100 | |||
SSA | 2.38×10-1 | 9.11×10-2 | SSA | 2.53×100 | 8.36×10-1 | SSA | 3.77×10-1 | 4.89×10-1 | |||
CHIO | 1.36×102 | 1.33×102 | CHIO | 1.67×101 | 8.05×10-1 | CHIO | 2.77×100 | 6.26×10-1 | |||
ICHIO | 1.65×10-3 | 6.31×10-4 | ICHIO | 1.13×10-14 | 2.94×10-15 | ICHIO | 1.36×100 | 3.81×10-1 | |||
SD-CHIO | 1.51×10-4 | 8.50×10-5 | SD-CHIO | 8.88×10-16 | 0 | SD-CHIO | 4.90×10-13 | 7.87×10-13 |
表3
光伏电池参数辨识中不同元启发式算法的搜索结果
算法 | μ/A | s/A | Fpv, min/A | Eiden/% | Iph/A | Isd/μA | Ac | Rs/Ω | Rsh/Ω |
---|---|---|---|---|---|---|---|---|---|
PSO | 4.27×10-3 | 9.19×10-3 | 1.55×10-3 | 28.77 | 0.7604 | 0.5933 | 1.5455 | 0.0338 | 79.7655 |
DE | 1.56×10-3 | 1.11×10-4 | 1.42×10-3 | 23.33 | 0.7605 | 0.5466 | 1.5367 | 0.0341 | 73.7699 |
ABC | 2.09×10-3 | 2.65×10-4 | 1.60×10-3 | 27.32 | 0.7599 | 0.5812 | 1.5435 | 0.0337 | 77.7783 |
WOA | 3.72×10-2 | 2.91×10-2 | 1.36×10-3 | 9.10 | 0.7596 | 0.2638 | 1.4613 | 0.0373 | 66.2019 |
SSA | 3.10×10-3 | 3.34×10-3 | 1.26×10-3 | 19.23 | 0.7600 | 0.4574 | 1.5174 | 0.0351 | 79.7338 |
CHIO | 6.21×10-2 | 4.14×10-2 | 4.63×10-3 | 31.37 | 0.7646 | 0.5986 | 1.5466 | 0.0348 | 87.1315 |
ICHIO | 7.42×10-2 | 5.45×10-2 | 9.82×10-3 | 32.61 | 0.7574 | 0.0267 | 1.2671 | 0.0473 | 67.8832 |
SD-CHIO | 1.27×10-3 | 1.09×10-4 | 1.03×10-3 | 4.33 | 0.7607 | 0.3591 | 1.4924 | 0.0360 | 58.3065 |
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