系统工程与电子技术 ›› 2021, Vol. 43 ›› Issue (6): 1596-1605.doi: 10.12305/j.issn.1001-506X.2021.06.17
魏锋涛*, 张洋洋, 黎俊宇, 史云鹏
收稿日期:
2020-08-07
出版日期:
2021-05-21
发布日期:
2021-05-28
通讯作者:
魏锋涛
作者简介:
张洋洋(1996—), 男, 硕士研究生, 主要研究方向为现代优化设计方法|黎俊宇(1997—), 男, 硕士研究生, 主要研究方向为结构优化设计|史云鹏(1996—), 男, 硕士研究生, 主要研究方向为优化设计理论
基金资助:
Fengtao WEI*, Yangyang ZHANG, Junyu LI, Yunpeng SHI
Received:
2020-08-07
Online:
2021-05-21
Published:
2021-05-28
Contact:
Fengtao WEI
摘要:
针对正余弦算法存在易陷入局部最优、求解精度不高、收敛速度较慢等问题, 提出一种基于动态分级策略的改进正余弦算法。首先, 引入拉丁超立方抽样法, 将搜索空间均匀划分, 使初始种群覆盖整个搜索空间, 以保持初始种群的多样性。其次, 采用动态分级策略, 根据适应度值的排序情况, 将种群动态划分为好中差3个等级, 并应用破坏策略与精英引导方法对其进行扰动, 以提高算法的收敛精度, 增强跳出局部最优的能力。最后, 引入反向学习方法, 设计了动态反向学习全局搜索策略, 以提高算法的收敛速度,同时对改进算法在复杂度、收敛性和稳定性方面进行性能测试, 选取15个标准测试函数在低维和高维状态下进行仿真实验分析, 并与粒子群算法、回溯搜索算法和其他改进正余弦算法进行比较。仿真分析结果表明, 所提算法有效地提高了算法的收敛性和稳定性。
中图分类号:
魏锋涛, 张洋洋, 黎俊宇, 史云鹏. 基于动态分级策略的改进正余弦算法[J]. 系统工程与电子技术, 2021, 43(6): 1596-1605.
Fengtao WEI, Yangyang ZHANG, Junyu LI, Yunpeng SHI. Improved sine cosine algorithm based on dynamic classification strategy[J]. Systems Engineering and Electronics, 2021, 43(6): 1596-1605.
表1
测试函数"
编号 | 函数名 | 是否多峰 | 搜索范围 | 最优值 |
f1 | Sphere | 否 | [-100, 100] | 0 |
f2 | Schwefel 2.22 | 否 | [-10, 10] | 0 |
f3 | Quartic | 否 | [-1.28, 1.28] | 0 |
f4 | Rosenbrock | 否 | [-10, 10] | 0 |
f5 | Elliptic | 否 | [-100, 100] | 0 |
f6 | Step | 否 | [-100, 100] | 0 |
f7 | Quartic1.1 | 否 | [-1.28, 1.28] | 0 |
f8 | Rastrigin | 是 | [-5.12, 5.12] | 0 |
f9 | Ackley | 是 | [-32, 32] | 0 |
f10 | Griewank | 是 | [-600, 600] | 0 |
f11 | Sumsquares | 是 | [-10, 10] | 0 |
f12 | Sumpower | 是 | [-10, 10] | 0 |
f13 | Alpine | 是 | [-10, 10] | 0 |
f14 | Zakharov | 是 | [-5, 10] | 0 |
f15 | Michalewicz | 是 | [0, π] | -0.801 3 |
表2
不同算法测试结果比较(D=50)"
函数 | SCA | PSO | BSA | MSCA | GSCA | ISCA | DSCA | |
f1 | Best | 7.19E-01 | 1.49E+04 | 8.95E+04 | 2.84E-24 | 1.05E-17 | 5.81E-03 | 1.87E-61 |
Mean | 7.79E+01 | 2.31E+04 | 9.72E+04 | 2.72E-21 | 3.40E-15 | 1.25E+00 | 1.17E-48 | |
Std | 6.36E+01 | 6.67E+03 | 5.61E+03 | 5.80E-21 | 5.45E-15 | 2.50E+00 | 3.58E-48 | |
f2 | Best | 1.04E-04 | 9.03E+01 | 2.95E+02 | 1.09E-18 | 3.90E-13 | 5.46E-04 | 4.15E-223 |
Mean | 7.88E-03 | 1.37E+02 | 3.42E+02 | 1.07E-16 | 5.28E-12 | 7.82E-02 | 2.18E-198 | |
Std | 1.01E-02 | 2.94E+01 | 2.24E+01 | 7.82E-17 | 5.08E-12 | 9.62E-02 | 0.00E+00 | |
f3 | Best | 2.32E-03 | 4.07E+00 | 1.48E+02 | 5.49E-43 | 1.60E-29 | 8.73E-12 | 0.00E+00 |
Mean | 2.44E-01 | 1.11E+01 | 2.75E+02 | 1.88E-38 | 6.59E-26 | 9.77E-04 | 0.00E+00 | |
Std | 4.76E-01 | 6.06E+00 | 7.50E+01 | 4.54E-38 | 1.87E-25 | 2.91E-03 | 0.00E+00 | |
f4 | Best | 1.05E+03 | 1.29E+07 | 3.04E+08 | 4.85E+01 | 4.86E+01 | 4.90E+01 | 4.81E+01 |
Mean | 8.02E+05 | 2.28E+07 | 3.77E+08 | 4.91E+01 | 4.94E+01 | 5.42E+01 | 4.86E+01 | |
Std | 1.23E+06 | 9.09E+06 | 5.52E+07 | 7.57E-01 | 1.49E+00 | 9.88E+00 | 3.32E-01 | |
f5 | Best | 2.37E+01 | 8.94E+07 | 3.18E+09 | 4.39E-22 | 1.37E-14 | 8.29E-20 | 9.22E-126 |
Mean | 7.00E+03 | 2.35E+08 | 4.74E+09 | 4.24E-19 | 1.53E-12 | 2.17E-10 | 3.88E-103 | |
Std | 8.36E+03 | 1.62E+08 | 9.70E+08 | 1.30E-18 | 2.25E-12 | 4.60E-10 | 1.23E-102 | |
f6 | Best | 1.20E+01 | 1.52E+04 | 7.21E+04 | 5.40E+00 | 5.76E+00 | 1.12E+01 | 5.07E+00 |
Mean | 1.11E+02 | 2.13E+04 | 9.97E+04 | 5.94E+00 | 6.48E+00 | 1.20E+01 | 5.41E+00 | |
Std | 1.49E+02 | 4.51E+03 | 2.18E+04 | 4.29E-01 | 3.91E-01 | 3.49E-01 | 2.15E-01 | |
f7 | Best | 9.68E-02 | 7.88E+00 | 2.05E+02 | 1.25E-04 | 5.26E-04 | 3.26E-05 | 1.35E-05 |
Mean | 1.94E+00 | 1.35E+01 | 2.88E+02 | 9.93E-04 | 3.74E-03 | 5.43E-04 | 4.17E-05 | |
Std | 3.50E+00 | 4.77E+00 | 7.31E+01 | 7.39E-04 | 2.72E-03 | 5.43E-04 | 2.68E-05 | |
f8 | Best | 5.01E+00 | 3.31E+02 | 2.19E+02 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 |
Mean | 7.30E+01 | 4.15E+02 | 2.44E+02 | 5.68E-15 | 2.44E-13 | 3.90E-08 | 0.00E+00 | |
Std | 5.01E+01 | 4.59E+01 | 1.04E+01 | 1.80E-14 | 6.94E-13 | 7.99E-08 | 0.00E+00 | |
f9 | Best | 1.34E-01 | 8.64E+00 | 9.30E+00 | 7.79E-13 | 2.02E+01 | 6.93E-12 | 8.88E-16 |
Mean | 1.61E+01 | 8.86E+00 | 9.87E+00 | 1.02E+01 | 2.03E+01 | 1.38E-05 | 8.88E-16 | |
Std | 8.19E+00 | 3.23E-01 | 4.21E-01 | 1.08E+01 | 7.46E-02 | 3.56E-05 | 2.08E-31 | |
f10 | Best | 9.67E-01 | 1.45E+02 | 8.05E-01 | 6.53E-11 | 4.44E-16 | 1.11E-16 | 0.00E+00 |
Mean | 2.65E+00 | 1.96E+02 | 9.65E-01 | 5.78E-09 | 1.86E-14 | 5.49E-09 | 0.00E+00 | |
Std | 3.52E+00 | 5.31E+01 | 6.50E-02 | 1.59E-08 | 2.53E-14 | 1.48E-08 | 0.00E+00 | |
f11 | Best | 9.35E-02 | 3.68E+03 | 1.23E+04 | 8.60E-25 | 1.43E-18 | 2.42E-19 | 4.80E-195 |
Mean | 2.62E+00 | 5.06E+03 | 1.62E+04 | 1.62E-21 | 3.53E-15 | 1.24E-07 | 1.15E-162 | |
Std | 3.49E+00 | 9.61E+02 | 3.46E+03 | 4.61E-21 | 7.23E-15 | 3.91E-07 | 0.00E+00 | |
f12 | Best | 6.82E+02 | 6.54E+17 | 5.26E+34 | 4.12E-94 | 1.90E-63 | 7.23E-222 | 0.00E+00 |
Mean | 8.62E+10 | 3.21E+24 | 5.90E+43 | 1.47E-70 | 1.33E-47 | 1.21E-31 | 0.00E+00 | |
Std | 2.67E+11 | 8.84E+24 | 1.71E+44 | 3.77E-70 | 4.17E-47 | 3.82E-31 | 0.00E+00 | |
f13 | Best | 2.15E-02 | 3.43E+01 | 4.41E+01 | 4.59E-17 | 1.23E-13 | 7.22E-11 | 7.44E-223 |
Mean | 2.58E+00 | 5.01E+01 | 6.33E+01 | 8.78E-13 | 9.44E-05 | 1.16E-06 | 7.85E-201 | |
Std | 4.00E+00 | 9.25E+00 | 9.58E+00 | 1.64E-12 | 2.12E-04 | 2.14E-06 | 0.00E+00 | |
f14 | Best | 7.92E+00 | 4.52E+03 | 1.86E+04 | 1.51E-09 | 1.11E-08 | 7.06E-02 | 3.61E-44 |
Mean | 7.60E+01 | 1.05E+04 | 6.22E+04 | 1.84E-07 | 1.73E-07 | 1.17E+03 | 4.05E-15 | |
Std | 5.92E+01 | 4.55E+03 | 3.83E+04 | 1.40E-07 | 1.47E-07 | 3.58E+03 | 1.28E-14 | |
f15 | Best | -1.34E+01 | -1.13E+01 | -1.44E+01 | -1.50E+01 | -1.30E+01 | -1.03E+01 | -1.78E+01 |
Mean | -1.06E+01 | -1.05E+01 | -1.26E+01 | -1.28E+01 | -1.08E+01 | -9.04E+00 | -1.69E+01 | |
Std | 1.34E+00 | 6.58E-01 | 1.78E+00 | 1.27E+00 | 1.20E+00 | 7.58E-01 | 5.35E-01 |
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