系统工程与电子技术 ›› 2022, Vol. 44 ›› Issue (7): 2229-2240.doi: 10.12305/j.issn.1001-506X.2022.07.19
汤安迪1,2, 韩统1,*, 徐登武3, 周欢1, 谢磊2
收稿日期:
2021-02-09
出版日期:
2022-06-22
发布日期:
2022-06-28
通讯作者:
韩统
作者简介:
汤安迪(1996—), 男, 硕士研究生, 主要研究方向为无人机任务规划和优化算法|韩统(1980—), 男, 副教授, 博士, 主要研究方向为机载武器系统和无人机任务规划|徐登武(1980—), 男, 工程师, 博士, 主要研究方向为机载武器系统|周欢(1989—), 男, 讲师, 博士, 主要研究方向为多无人机协同控制技术|谢磊(1997—), 男, 硕士研究生, 主要研究方向为无人作战系统与技术
基金资助:
Andi TANG1,2, Tong HAN1,*, Dengwu XU3, Huan ZHOU1, lei XIE2
Received:
2021-02-09
Online:
2022-06-22
Published:
2022-06-28
Contact:
Tong HAN
摘要:
针对樽海鞘群算法在求解复杂优化问题时存在种群多样性减弱、易于陷入局部最优等不足, 提出了一种使用高斯分布估计策略的改进樽海鞘群算法(salp swarm algorithm using elite pool strategy and Gaussian distribution estimation strategy, GDESSA)。首先提出一种精英池选择策略, 领导者位置在每次更新时随机从精英池中选择一个个体作为食物源, 增强领导者的探索能力, 丰富种群多样性。其次利用高斯分布估计策略对追随者公式进行改进, 通过拟合优势群体信息, 修正种群进化方向, 增强算法的寻优能力。使用CEC2017测试函数对改进算法进行测试, 并通过统计分析、收敛性分析、稳定性分析、Wilcoxon检验、Friedman检验、Iman-Davenport检验评估改进算法性能。仿真结果表明: 本文提出的改进策略能有效提高算法性能; 提出的改进算法相比其他算法, 具有更快的收敛速度和更好的收敛精度。
中图分类号:
汤安迪, 韩统, 徐登武, 周欢, 谢磊. 使用高斯分布估计策略的改进樽海鞘群算法[J]. 系统工程与电子技术, 2022, 44(7): 2229-2240.
Andi TANG, Tong HAN, Dengwu XU, Huan ZHOU, lei XIE. An improved salp swarm algorithm using Gaussian distribution estimation strategy[J]. Systems Engineering and Electronics, 2022, 44(7): 2229-2240.
表1
不同改进策略对比结果"
函数 | SSA | SSA-1 | SSA-2 | GDESSA | |||||||
均值(排名) | 耗时(排名) | 均值(排名) | 耗时(排名) | 均值(排名) | 耗时(排名) | 均值(排名) | 耗时(排名) | ||||
F1 | 1.85E+00(3) | 6.49E+00(3) | 1.12E+04(4) | 6.69E+00(4) | 6.84E-08(2) | 2.64E+00(1) | 4.32E-08(1) | 2.77E+00(2) | |||
F2 | 9.49E+01(3) | 6.47E+00(3) | 1.00E+02(4) | 6.69E+00(4) | 5.70E+01(1) | 2.66E+00(1) | 6.80E+01(2) | 2.72E+00(2) | |||
F3 | 1.18E+02(4) | 6.65E+00(3) | 3.27E+01(2) | 6.91E+00(4) | 3.95E+01(3) | 2.90E+00(1) | 2.23E+01(1) | 3.01E+00(2) | |||
F4 | 2.65E+01(4) | 7.67E+00(3) | 8.17E-01(3) | 7.92E+00(4) | 2.75E-04(2) | 3.98E+00(1) | 2.72E-05(1) | 4.14E+00(2) | |||
F5 | 1.50E+02(4) | 6.73E+00(3) | 5.56E+01(2) | 6.99E+00(4) | 6.73E+01(3) | 2.96E+00(1) | 4.32E+01(1) | 3.07E+00(2) | |||
F6 | 1.16E+02(4) | 6.70E+00(3) | 2.67E+01(2) | 6.96E+00(4) | 4.03E+01(3) | 2.89E+00(1) | 1.98E+01(1) | 3.08E+00(2) | |||
F7 | 1.93E+03(4) | 6.77E+00(3) | 6.34E+00(3) | 7.00E+00(4) | 5.52E-09(2) | 2.93E+00(1) | 2.51E-09(1) | 3.04E+00(2) | |||
F8 | 3.85E+03(4) | 6.94E+00(3) | 2.42E+03(1) | 7.20E+00(4) | 3.50E+03(3) | 3.19E+00(1) | 2.56E+03(2) | 3.34E+00(2) | |||
F9 | 2.11E+02(4) | 6.54E+00(3) | 1.31E+02(3) | 6.81E+00(4) | 2.24E+01(2) | 2.73E+00(1) | 1.81E+01(1) | 2.89E+00(2) | |||
F10 | 9.30E+06(4) | 6.73E+00(3) | 5.61E+06(3) | 6.98E+00(4) | 3.80E+02(2) | 2.91E+00(1) | 3.72E+02(1) | 3.08E+00(2) | |||
F11 | 1.46E+05(4) | 6.60E+00(3) | 6.09E+04(3) | 6.85E+00(4) | 5.06E+01(1) | 2.78E+00(1) | 5.76E+01(2) | 2.93E+00(2) | |||
F12 | 1.18E+04(4) | 6.96E+00(3) | 8.87E+03(3) | 7.22E+00(4) | 4.12E+01(2) | 3.15E+00(1) | 4.08E+01(1) | 3.32E+00(2) | |||
F13 | 5.78E+04(4) | 6.55E+00(3) | 2.86E+04(3) | 6.83E+00(4) | 2.18E+01(1) | 2.72E+00(1) | 2.34E+01(2) | 2.86E+00(2) | |||
F14 | 8.67E+02(4) | 6.72E+00(3) | 5.10E+02(3) | 6.97E+00(4) | 4.05E+02(2) | 2.91E+00(1) | 2.82E+02(1) | 3.02E+00(2) | |||
F15 | 3.82E+02(4) | 7.52E+00(3) | 2.30E+02(3) | 7.73E+00(4) | 1.05E+02(2) | 3.70E+00(1) | 7.76E+01(1) | 3.87E+00(2) | |||
F16 | 2.15E+05(4) | 6.80E+00(3) | 1.38E+05(3) | 6.98E+00(4) | 2.71E+01(1) | 2.90E+00(1) | 2.72E+01(2) | 3.05E+00(2) | |||
F17 | 7.59E+05(4) | 1.17E+01(3) | 5.21E+05(3) | 1.19E+01(4) | 2.06E+01(2) | 7.91E+00(1) | 2.03E+01(1) | 8.35E+00(2) | |||
F18 | 4.29E+02(4) | 7.72E+00(3) | 2.52E+02(3) | 7.91E+00(4) | 1.81E+02(2) | 3.86E+00(1) | 1.01E+02(1) | 4.09E+00(2) | |||
F19 | 2.98E+02(4) | 8.19E+00(3) | 2.34E+02(2) | 8.38E+00(4) | 2.42E+02(3) | 4.37E+00(1) | 2.20E+02(1) | 4.61E+00(2) | |||
F20 | 4.21E+02(2) | 8.54E+00(3) | 1.00E+02(1) | 8.72E+00(4) | 9.67E+02(4) | 4.70E+00(1) | 7.63E+02(3) | 4.97E+00(2) | |||
F21 | 4.48E+02(4) | 9.00E+00(3) | 3.79E+02(2) | 9.19E+00(4) | 3.82E+02(3) | 5.18E+00(1) | 3.60E+02(1) | 5.50E+00(2) | |||
F22 | 5.12E+02(4) | 9.29E+00(3) | 4.45E+02(2) | 9.46E+00(4) | 4.54E+02(3) | 5.50E+00(1) | 4.38E+02(1) | 5.79E+00(2) | |||
F23 | 4.02E+02(3) | 8.94E+00(3) | 4.09E+02(4) | 9.15E+00(4) | 3.87E+02(2) | 5.11E+00(1) | 3.87E+02(1) | 5.40E+00(2) | |||
F24 | 1.53E+03(4) | 9.80E+00(3) | 1.28E+03(3) | 9.96E+00(4) | 1.25E+03(2) | 5.98E+00(1) | 1.04E+03(1) | 6.32E+00(2) | |||
F25 | 5.24E+02(4) | 1.04E+01(3) | 5.10E+02(3) | 1.06E+01(4) | 4.99E+02(2) | 6.64E+00(1) | 4.95E+02(1) | 7.06E+00(2) | |||
F26 | 4.36E+02(4) | 9.76E+00(3) | 4.33E+02(3) | 9.98E+00(4) | 3.73E+02(2) | 6.00E+00(1) | 3.68E+02(1) | 6.33E+00(2) | |||
F27 | 9.01E+02(4) | 8.85E+00(3) | 7.05E+02(3) | 9.05E+00(4) | 5.69E+02(2) | 5.07E+00(1) | 5.26E+02(1) | 5.34E+00(2) | |||
F28 | 2.85E+06(4) | 1.30E+01(3) | 2.68E+06(3) | 1.33E+01(4) | 2.16E+03(2) | 9.27E+00(1) | 2.14E+03(1) | 9.79E+00(2) | |||
平均排名 | 3.82 | 3.00 | 2.75 | 4.00 | 2.18 | 1.00 | 1.25 | 2.00 |
表3
CEC2017 30D测试中7种算法的结果统计"
函数 | 比较项 | HFPSO | GEDGWO | VCS | MPA | SMA | HHO | GDESSA | |
F1 | 均值 | 2.21E+02 | 4.79E-07 | 7.32E+03 | 2.73E-01 | 4.94E-01 | 1.68E+03 | 4.32E-08 | |
标准差 | 1.35E+02 | 1.83E-07 | 5.58E+03 | 3.30E-01 | 3.18E-01 | 7.95E+02 | 2.36E-08 | ||
排名 | 5 | 2 | 7 | 3 | 4 | 6 | 1 | ||
F2 | 均值 | 4.22E+01 | 4.25E+01 | 7.39E+01 | 8.68E+01 | 8.99E+01 | 1.23E+02 | 6.80E+01 | |
标准差 | 2.87E+01 | 2.64E+01 | 3.48E+01 | 6.25E+00 | 5.12E+00 | 3.33E+01 | 3.36E+01 | ||
排名 | 1 | 2 | 4 | 5 | 6 | 7 | 3 | ||
F3 | 均值 | 7.42E+01 | 4.53E+01 | 1.09E+02 | 6.89E+01 | 8.17E+01 | 2.05E+02 | 2.23E+01 | |
标准差 | 1.82E+01 | 1.24E+01 | 2.56E+01 | 1.86E+01 | 1.99E+01 | 3.62E+01 | 1.01E+01 | ||
排名 | 4 | 2 | 6 | 3 | 5 | 7 | 1 | ||
F4 | 均值 | 9.20E-01 | 7.22E-03 | 8.72E-01 | 1.92E+00 | 7.35E-01 | 5.62E+01 | 2.72E-05 | |
标准差 | 1.29E+00 | 1.47E-02 | 8.88E-01 | 1.10E+00 | 3.21E-01 | 5.92E+00 | 3.06E-06 | ||
排名 | 5 | 2 | 4 | 6 | 3 | 7 | 1 | ||
F5 | 均值 | 8.74E+01 | 7.18E+01 | 1.79E+02 | 1.00E+02 | 1.18E+02 | 4.98E+02 | 4.32E+01 | |
标准差 | 2.05E+01 | 1.30E+01 | 1.20E+02 | 1.68E+01 | 2.40E+01 | 6.57E+01 | 7.56E+00 | ||
排名 | 3 | 2 | 6 | 4 | 5 | 7 | 1 | ||
F6 | 均值 | 7.06E+01 | 4.50E+01 | 9.19E+01 | 7.05E+01 | 9.39E+01 | 1.40E+02 | 1.98E+01 | |
标准差 | 2.31E+01 | 1.17E+01 | 2.25E+01 | 1.44E+01 | 2.03E+01 | 2.13E+01 | 9.77E+00 | ||
排名 | 4 | 2 | 5 | 3 | 6 | 7 | 1 | ||
F7 | 均值 | 8.99E+00 | 1.76E-03 | 5.22E+02 | 8.87E+01 | 9.95E+02 | 4.69E+03 | 2.51E-09 | |
标准差 | 1.11E+01 | 1.25E-02 | 1.44E+03 | 4.60E+01 | 1.22E+03 | 8.28E+02 | 5.04E-10 | ||
排名 | 3 | 2 | 5 | 4 | 6 | 7 | 1 | ||
F8 | 均值 | 2.87E+03 | 3.01E+03 | 4.00E+03 | 2.50E+03 | 3.04E+03 | 4.35E+03 | 2.56E+03 | |
标准差 | 6.39E+02 | 4.30E+02 | 1.03E+03 | 4.10E+02 | 5.06E+02 | 7.25E+02 | 7.00E+02 | ||
排名 | 3 | 4 | 6 | 1 | 5 | 7 | 2 | ||
F9 | 均值 | 9.43E+01 | 1.56E+01 | 1.25E+02 | 4.59E+01 | 1.16E+02 | 1.61E+02 | 1.81E+01 | |
标准差 | 3.12E+01 | 1.54E+01 | 2.42E+01 | 2.30E+01 | 4.33E+01 | 4.86E+01 | 1.60E+01 | ||
排名 | 4 | 1 | 6 | 3 | 5 | 7 | 2 | ||
F10 | 均值 | 1.04E+05 | 7.75E+02 | 3.51E+06 | 9.82E+04 | 1.31E+06 | 7.61E+06 | 3.72E+02 | |
标准差 | 8.70E+04 | 5.82E+02 | 1.89E+06 | 7.77E+04 | 1.09E+06 | 4.21E+06 | 2.53E+02 | ||
排名 | 4 | 2 | 6 | 3 | 5 | 7 | 1 | ||
F11 | 均值 | 1.83E+04 | 5.80E+01 | 9.00E+04 | 1.39E+03 | 2.71E+04 | 1.51E+05 | 5.76E+01 | |
标准差 | 2.99E+04 | 1.90E+01 | 4.08E+04 | 3.80E+02 | 2.64E+04 | 9.05E+04 | 2.82E+01 | ||
排名 | 4 | 2 | 6 | 3 | 5 | 7 | 1 | ||
F12 | 均值 | 1.05E+04 | 3.66E+01 | 1.49E+04 | 4.57E+01 | 4.71E+04 | 3.82E+04 | 4.08E+01 | |
标准差 | 1.06E+04 | 1.32E+01 | 1.80E+04 | 1.08E+01 | 2.84E+04 | 4.25E+04 | 7.05E+00 | ||
排名 | 4 | 1 | 5 | 3 | 7 | 6 | 2 | ||
F13 | 均值 | 9.39E+03 | 2.49E+01 | 1.59E+04 | 9.26E+01 | 1.99E+04 | 6.86E+04 | 2.34E+01 | |
标准差 | 1.12E+04 | 1.56E+01 | 1.82E+04 | 2.60E+01 | 1.57E+04 | 4.86E+04 | 6.31E+00 | ||
排名 | 4 | 2 | 5 | 3 | 6 | 7 | 1 | ||
F14 | 均值 | 7.09E+02 | 5.90E+02 | 8.28E+02 | 3.40E+02 | 8.18E+02 | 1.55E+03 | 2.82E+02 | |
标准差 | 2.30E+02 | 2.89E+02 | 2.45E+02 | 1.84E+02 | 2.83E+02 | 3.56E+02 | 2.08E+02 | ||
排名 | 4 | 3 | 6 | 2 | 5 | 7 | 1 | ||
F15 | 均值 | 2.11E+02 | 9.90E+01 | 2.56E+02 | 7.97E+01 | 4.34E+02 | 7.48E+02 | 7.76E+01 | |
标准差 | 8.26E+01 | 7.71E+01 | 1.22E+02 | 3.97E+01 | 1.64E+02 | 2.19E+02 | 3.09E+01 | ||
排名 | 4 | 3 | 5 | 2 | 6 | 7 | 1 | ||
F16 | 均值 | 1.67E+05 | 3.31E+01 | 2.30E+05 | 1.11E+02 | 3.75E+05 | 6.90E+05 | 2.72E+01 | |
标准差 | 1.45E+05 | 7.76E+00 | 1.74E+05 | 2.67E+01 | 3.55E+05 | 8.77E+05 | 2.36E+00 | ||
排名 | 4 | 2 | 5 | 3 | 6 | 7 | 1 | ||
F17 | 均值 | 6.60E+03 | 2.73E+01 | 1.49E+04 | 4.38E+01 | 3.00E+04 | 1.46E+05 | 2.03E+01 | |
标准差 | 8.00E+03 | 8.80E+00 | 1.87E+04 | 8.44E+00 | 2.11E+04 | 1.42E+05 | 2.80E+00 | ||
排名 | 4 | 2 | 5 | 3 | 6 | 7 | 1 | ||
F18 | 均值 | 2.70E+02 | 1.60E+02 | 2.22E+02 | 1.11E+02 | 3.59E+02 | 6.71E+02 | 1.01E+02 | |
标准差 | 1.03E+02 | 6.87E+01 | 6.41E+01 | 5.76E+01 | 1.59E+02 | 2.01E+02 | 6.61E+01 | ||
排名 | 5 | 3 | 4 | 2 | 6 | 7 | 1 | ||
F19 | 均值 | 2.69E+02 | 2.41E+02 | 2.78E+02 | 1.40E+02 | 2.93E+02 | 4.06E+02 | 2.20E+02 | |
标准差 | 1.94E+01 | 1.40E+01 | 2.98E+01 | 7.03E+01 | 2.17E+01 | 3.51E+01 | 8.73E+00 | ||
排名 | 4 | 3 | 5 | 1 | 6 | 7 | 2 | ||
F20 | 均值 | 9.77E+02 | 1.00E+02 | 1.07E+02 | 1.04E+02 | 2.90E+03 | 2.39E+03 | 7.63E+02 | |
标准差 | 1.53E+03 | 6.36E-06 | 6.10E+00 | 4.14E+00 | 1.36E+03 | 2.37E+03 | 1.17E+03 | ||
排名 | 5 | 1 | 3 | 2 | 7 | 6 | 4 | ||
F21 | 均值 | 4.52E+02 | 3.93E+02 | 4.62E+02 | 3.82E+02 | 4.35E+02 | 7.05E+02 | 3.60E+02 | |
标准差 | 2.90E+01 | 1.61E+01 | 2.35E+01 | 2.39E+01 | 1.95E+01 | 7.35E+01 | 1.32E+01 | ||
排名 | 5 | 3 | 6 | 2 | 4 | 7 | 1 | ||
F22 | 均值 | 5.34E+02 | 4.58E+02 | 5.32E+02 | 4.83E+02 | 5.30E+02 | 8.26E+02 | 4.38E+02 | |
标准差 | 3.47E+01 | 1.28E+01 | 3.20E+01 | 1.79E+01 | 2.95E+01 | 7.42E+01 | 1.07E+01 | ||
排名 | 6 | 2 | 5 | 3 | 4 | 7 | 1 | ||
F23 | 均值 | 3.79E+02 | 3.87E+02 | 3.78E+02 | 3.87E+02 | 3.88E+02 | 4.11E+02 | 3.87E+02 | |
标准差 | 4.73E+00 | 1.49E-02 | 3.35E+00 | 1.71E+00 | 1.69E+00 | 1.87E+01 | 7.58E-01 | ||
排名 | 2 | 4 | 1 | 3 | 6 | 7 | 5 | ||
F24 | 均值 | 1.50E+03 | 1.25E+03 | 1.55E+03 | 3.00E+02 | 1.98E+03 | 3.94E+03 | 1.04E+03 | |
标准差 | 8.58E+02 | 3.15E+02 | 9.39E+02 | 5.84E-02 | 3.42E+02 | 1.10E+03 | 1.17E+02 | ||
排名 | 4 | 3 | 5 | 1 | 6 | 7 | 2 | ||
F25 | 均值 | 4.45E+02 | 4.92E+02 | 5.00E+02 | 5.03E+02 | 5.11E+02 | 6.05E+02 | 4.95E+02 | |
标准差 | 1.01E+01 | 1.33E+01 | 1.51E-04 | 7.53E+00 | 1.17E+01 | 4.00E+01 | 1.52E+01 | ||
排名 | 1 | 2 | 4 | 5 | 6 | 7 | 3 | ||
F26 | 均值 | 4.05E+02 | 3.13E+02 | 4.96E+02 | 4.08E+02 | 4.46E+02 | 4.62E+02 | 368.3704 | |
标准差 | 4.98E+01 | 3.48E+01 | 5.05E+00 | 6.99E+00 | 2.89E+01 | 2.60E+01 | 43.01458 | ||
排名 | 3 | 1 | 7 | 4 | 5 | 6 | 2 | ||
F27 | 均值 | 5.53E+02 | 5.11E+02 | 5.69E+02 | 5.32E+02 | 7.75E+02 | 1.32E+03 | 5.26E+02 | |
标准差 | 1.13E+02 | 6.00E+01 | 1.43E+02 | 6.92E+01 | 1.83E+02 | 2.56E+02 | 7.14E+01 | ||
排名 | 4 | 1 | 5 | 3 | 6 | 7 | 2 | ||
F28 | 均值 | 2.96E+03 | 1.98E+03 | 9.38E+03 | 4.46E+03 | 1.27E+04 | 1.01E+06 | 2.14E+03 | |
标准差 | 3.54E+03 | 2.30E+01 | 7.22E+03 | 1.42E+03 | 5.29E+03 | 6.08E+05 | 1.09E+02 | ||
排名 | 3 | 1 | 5 | 4 | 6 | 7 | 2 | ||
平均排名 | 3.79 | 2.14 | 5.07 | 3.00 | 5.46 | 6.86 | 1.68 |
表4
Wilcoxon符号秩检验结果(α=0.05)"
函数 | HFPSO | GEDGWO | VCS | |||||||||||
P-value | R+ | R- | Win | P-value | R+ | R- | Win | P-value | R+ | R- | Win | |||
F1 | 5.15E-10 | 1 326 | 0 | + | 5.15E-10 | 1 326 | 0 | + | 5.15E-10 | 1 326 | 0 | + | ||
F2 | 1.41E-04 | 257 | 1 069 | - | 8.58E-05 | 244 | 1 082 | - | 5.42E-01 | 728 | 598 | = | ||
F3 | 5.80E-10 | 1 324 | 2 | + | 4.17E-09 | 1 290 | 36 | + | 5.15E-10 | 1 326 | 0 | + | ||
F4 | 5.15E-10 | 1 326 | 0 | + | 5.15E-10 | 1 326 | 0 | + | 5.15E-10 | 1 326 | 0 | + | ||
F5 | 5.15E-10 | 1 326 | 0 | + | 1.05E-09 | 1 314 | 12 | + | 5.15E-10 | 1 326 | 0 | + | ||
F6 | 5.15E-10 | 1 326 | 0 | + | 7.35E-10 | 1 320 | 6 | + | 5.15E-10 | 1 326 | 0 | + | ||
F7 | 5.15E-10 | 1 326 | 0 | + | 9.66E-09 | 51 | 1 275 | - | 5.15E-10 | 1 326 | 0 | + | ||
F8 | 4.01E-02 | 882 | 444 | + | 1.04E-03 | 1 013 | 313 | + | 7.74E-09 | 1 279 | 47 | + | ||
F9 | 5.15E-10 | 1 326 | 0 | + | 1.39E-01 | 505 | 821 | = | 5.15E-10 | 1 326 | 0 | + | ||
F10 | 5.15E-10 | 1 326 | 0 | + | 2.57E-04 | 1 053 | 273 | + | 5.15E-10 | 1 326 | 0 | + | ||
F11 | 5.15E-10 | 1 326 | 0 | + | 5.30E-01 | 730 | 596 | = | 5.15E-10 | 1 326 | 0 | + | ||
F12 | 5.15E-10 | 1 326 | 0 | + | 5.69E-03 | 368 | 958 | + | 5.15E-10 | 1 326 | 0 | - | ||
F13 | 5.15E-10 | 1 326 | 0 | + | 4.76E-01 | 739 | 587 | = | 5.15E-10 | 1 326 | 0 | + | ||
F14 | 2.97E-09 | 1 296 | 30 | + | 1.52E-06 | 1 176 | 150 | + | 7.80E-10 | 1 319 | 7 | + | ||
F15 | 5.23E-09 | 1 286 | 40 | + | 3.73E-01 | 758 | 568 | = | 6.53E-10 | 1 322 | 4 | + | ||
F16 | 5.15E-10 | 1 326 | 0 | + | 3.43E-05 | 1 105 | 221 | + | 5.15E-10 | 1 326 | 0 | + | ||
F17 | 5.15E-10 | 1 326 | 0 | + | 1.49E-05 | 1 125 | 201 | + | 5.15E-10 | 1 326 | 0 | + | ||
F18 | 2.50E-09 | 1 299 | 27 | + | 2.76E-04 | 1 051 | 275 | + | 2.32E-08 | 1 259 | 67 | + | ||
F19 | 5.15E-10 | 1 326 | 0 | + | 4.17E-09 | 1 290 | 36 | + | 9.66E-09 | 1 275 | 51 | + | ||
F20 | 6.80E-01 | 619 | 707 | = | 5.15E-10 | 0 | 1 326 | - | 4.65E-01 | 741 | 585 | = | ||
F21 | 5.15E-10 | 1 326 | 0 | + | 2.23E-09 | 1 301 | 25 | + | 5.15E-10 | 1 326 | 0 | + | ||
F22 | 5.15E-10 | 1 326 | 0 | + | 1.58E-08 | 1 266 | 60 | + | 5.15E-10 | 1 326 | 0 | + | ||
F23 | 5.57E-07 | 129 | 1 197 | + | 1.45E-07 | 102 | 1 224 | - | 3.94E-09 | 35 | 1 291 | - | ||
F24 | 5.24E-04 | 1 033 | 293 | + | 1.31E-05 | 1 128 | 198 | + | 1.26E-04 | 1 072 | 254 | + | ||
F25 | 5.15E-10 | 0 | 1 326 | + | 3.88E-01 | 571 | 755 | = | 4.10E-02 | 881 | 445 | + | ||
F26 | 1.58E-04 | 1 066 | 260 | + | 5.15E-08 | 82 | 1244 | - | 5.15E-10 | 1 326 | 0 | + | ||
F27 | 1.34E-01 | 823 | 503 | = | 3.11E-01 | 555 | 771 | = | 1.20E-01 | 829 | 497 | = | ||
F28 | 9.78E-01 | 666 | 660 | = | 5.15E-10 | 0 | 1 326 | - | 5.15E-10 | 1 326 | 0 | + | ||
+/-/= | 24/1/3 | 16/6/6 | 23/2/3 | |||||||||||
函数 | MPA | SMA | HHO | |||||||||||
P-value | R+ | R- | Win | P-value | R+ | R- | Win | P-value | R+ | R- | Win | |||
F1 | 5.15E-10 | 1 326 | 0 | + | 5.15E-10 | 1 326 | 0 | + | 5.15E-10 | 1 326 | 0 | + | ||
F2 | 8.26E-05 | 1 083 | 243 | + | 8.49E-06 | 1 138 | 188 | + | 7.74E-09 | 1 279 | 47 | + | ||
F3 | 6.15E-10 | 1 323 | 3 | + | 5.15E-10 | 1 326 | 0 | + | 5.15E-10 | 1 326 | 0 | + | ||
F4 | 5.15E-10 | 1 326 | 0 | + | 5.15E-10 | 1 326 | 0 | + | 5.15E-10 | 1 326 | 0 | + | ||
F5 | 5.15E-10 | 1 326 | 0 | + | 5.15E-10 | 1 326 | 0 | + | 5.15E-10 | 1 326 | 0 | + | ||
F6 | 5.15E-10 | 1 326 | 0 | + | 5.15E-10 | 1 326 | 0 | + | 5.15E-10 | 1 326 | 0 | + | ||
F7 | 5.15E-10 | 1 326 | 0 | + | 5.15E-10 | 1 326 | 0 | + | 5.15E-10 | 1 326 | 0 | = | ||
F8 | 7.43E-01 | 628 | 698 | = | 2.86E-04 | 1 050 | 276 | + | 1.18E-09 | 1 312 | 14 | + | ||
F9 | 2.53E-07 | 1 213 | 113 | + | 5.80E-10 | 1 324 | 2 | + | 5.15E-10 | 1 326 | 0 | + | ||
F10 | 5.15E-10 | 1 326 | 0 | + | 5.15E-10 | 1 326 | 0 | + | 5.15E-10 | 1 326 | 0 | + | ||
F11 | 5.15E-10 | 1 326 | 0 | + | 5.15E-10 | 1 326 | 0 | + | 5.15E-10 | 1 326 | 0 | + | ||
F12 | 7.14E-03 | 950 | 376 | + | 5.15E-10 | 1 326 | 0 | + | 5.15E-10 | 1 326 | 0 | + | ||
F13 | 5.15E-10 | 1 326 | 0 | + | 5.15E-10 | 1 326 | 0 | + | 5.15E-10 | 1 326 | 0 | + | ||
F14 | 2.19E-01 | 794 | 532 | = | 1.67E-09 | 1 306 | 20 | + | 5.15E-10 | 1 326 | 0 | + | ||
F15 | 7.22E-01 | 625 | 701 | = | 5.15E-10 | 1 326 | 0 | + | 5.15E-10 | 1 326 | 0 | + | ||
F16 | 5.15E-10 | 1 326 | 0 | + | 5.15E-10 | 1 326 | 0 | + | 5.15E-10 | 1 326 | 0 | + | ||
F17 | 5.15E-10 | 1 326 | 0 | + | 5.15E-10 | 1 326 | 0 | + | 5.15E-10 | 1 326 | 0 | + | ||
F18 | 2.30E-01 | 791 | 535 | = | 1.99E-09 | 1303 | 23 | + | 5.15E-10 | 1 326 | 0 | + | ||
F19 | 4.17E-08 | 78 | 1 248 | - | 5.15E-10 | 1 326 | 0 | + | 5.15E-10 | 1 326 | 0 | + | ||
F20 | 4.65E-01 | 741 | 585 | = | 8.69E-08 | 1 234 | 92 | + | 8.87E-06 | 1 137 | 189 | + | ||
F21 | 5.57E-07 | 1 197 | 129 | + | 5.15E-10 | 1 326 | 0 | + | 5.15E-10 | 1 326 | 0 | + | ||
F22 | 5.46E-10 | 1 325 | 1 | + | 5.15E-10 | 1 326 | 0 | + | 5.15E-10 | 1 326 | 0 | - | ||
F23 | 9.03E-01 | 676 | 650 | = | 1.00E-04 | 1 078 | 248 | + | 7.80E-10 | 1 319 | 7 | + | ||
F24 | 5.15E-10 | 0 | 1 326 | - | 7.35E-10 | 1 320 | 6 | + | 6.93E-10 | 1 321 | 5 | + | ||
F25 | 2.04E-03 | 992 | 334 | + | 4.37E-07 | 1 202 | 124 | + | 5.15E-10 | 1 326 | 0 | - | ||
F26 | 1.26E-06 | 1 180 | 146 | + | 5.80E-10 | 1324 | 2 | + | 5.15E-10 | 1 326 | 0 | + | ||
F27 | 6.87E-01 | 706 | 620 | = | 1.50E-08 | 1 267 | 59 | + | 5.15E-10 | 1 326 | 0 | + | ||
F28 | 5.15E-10 | 1 326 | 0 | + | 5.15E-10 | 1 326 | 0 | + | 5.15E-10 | 1 326 | 0 | + | ||
+/-/= | 19/2/7 | 28/0/0 | 27/2/1 |
表5
在均值、标准差和耗时3个方面的Friedman测试结果"
测试项目 | HFPSO | GEDGWO | VCS | MPA | SMA | HHO | GDESSA | 检验结果 |
均值排名 | 3.79 | 2.14 | 5.07 | 3.00 | 5.46 | 6.86 | 1.68 | Friedman测试的显著概率3.330 7E-25 卡方分布值128.04 6×168自由度的F分布值86.501 3 Iman-Davenport测试的显著概率2.220 4E-16 |
标准差排名 | 4.57 | 2.39 | 5.00 | 2.86 | 4.54 | 6.50 | 2.14 | Friedman测试的显著概率1.699 0E-17 卡方分布值91.21 6×168自由度的F分布值32.069 6 Iman-Davenport测试的显著概率4.584 2E-11 |
时间排名 | 1.00 | 2.00 | 3.86 | 5.00 | 7.00 | 6.00 | 3.14 | Friedman测试的显著概率2.441 9E-33 卡方分布值166.53 6×168自由度的F分布值3.05E+03 Iman-Davenport测试的显著概率0 |
1 |
HOLLAND J H . Genetic algorithms[J]. Scientific American, 1992, 267, 66- 73.
doi: 10.1038/scientificamerican0792-66 |
2 |
STORN R , PRICE K . Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces[J]. Journal of Global Optimization, 1997, 11 (4): 341- 359.
doi: 10.1023/A:1008202821328 |
3 |
HWANG C R . Simulated annealing: theory and applications[J]. Acta Applicandae Mathematica, 1988, 12 (1): 108- 111.
doi: 10.1007/BF00047572 |
4 |
RASHEDI E , NEZAMABADI P H , SARYAZDI S . GSA: a gravitational search algorithm[J]. Information Sciences, 2009, 179 (13): 2232- 2248.
doi: 10.1016/j.ins.2009.03.004 |
5 |
WEI Z , HUANG C Q , WANG X F , et al. Nuclear reaction optimization: a novel and powerful physics-based algorithm for global optimization[J]. IEEE Access, 2019, 7, 66084- 66109.
doi: 10.1109/ACCESS.2019.2918406 |
6 |
MIRJALILI S , MIRJALILI S M , LEWIS A . Grey wolf optimizer[J]. Advances in Engineering Software, 2014, 69, 46- 61.
doi: 10.1016/j.advengsoft.2013.12.007 |
7 | KARABOGA D , AKAY B . A comparative study of artificial bee colony algorithm[J]. Applied Mathematics & Computation, 2009, 214 (1): 108- 132. |
8 |
MIRJALILI S , LEWIS A . The whale optimization algorithm[J]. Advances in Engineering Software, 2016, 95, 51- 67.
doi: 10.1016/j.advengsoft.2016.01.008 |
9 |
WOLPERT D H , MACREADY W G . No free lunch theorems for optimization[J]. IEEE Trans.on Evolutionary Computation, 1997, 1 (1): 67- 82.
doi: 10.1109/4235.585893 |
10 |
MIRJALILI S , GANDOMI A H , MIRJALILI S Z , et al. Salp swarm algorithm: a bio-inspired optimizer for engineering design problems[J]. Advances in Engineering Software, 2017, 114, 163- 169.
doi: 10.1016/j.advengsoft.2017.07.002 |
11 | TOLBA M , REZK H , DIAB A , et al. A novel robust methodology based salp swarm algorithm for allocation and capacity of renewable distributed generators on distribution grids[J]. Energies, 2018, 11 (10): 1- 34. |
12 | 陈涛, 王梦馨, 黄湘松. 基于樽海鞘群算法的无源时差定位[J]. 电子与信息学报, 2018, 40 (7): 1591- 1597. |
CHEN T , WANG M X , HUANG X S . Time difference of arrival passive location based on salp swarm algorithm[J]. Journal of Electronics & Information Technology, 2018, 40 (7): 1591- 1597. | |
13 |
GOUDOS S , ATHANASIADOU G E . Application of an ensemble method to uav power modeling for cellular communications[J]. IEEE Antennas and Wireless Propagation Letters, 2019, 18 (11): 2340- 2344.
doi: 10.1109/LAWP.2019.2926784 |
14 | SINGH N , SINGH S B , HOUSSEIN E H . Hybridizing salp swarm algorithm with particle swarm optimization algorithm for recent optimization functions[J]. Evolutionary Intelligence, 2020, 22, 468- 476. |
15 | ZHANG H L , WANG Z Y , CHEN W B , et al. Ensemble mutation-driven salp swarm algorithm with restart mechanism: framework and fundamental analysis[J]. Expert Systems with Applications, 2020, 165, 113897. |
16 |
ZHANG Q , CHEN H , HEIDARI A A , et al. Chaos-induced and mutation-driven schemes boosting salp chains-inspired optimizers[J]. IEEE Access, 2019, 7, 31243- 31261.
doi: 10.1109/ACCESS.2019.2902306 |
17 | 张铸, 张仕杰, 饶盛华, 等. 基于自适应正态云模型的引力樽海鞘群算法[J]. 控制与决策, 2022, 37 (2): 344- 352. |
ZHANG Z , ZHANG S J , RAO S H , et al. Gravity salp swarm algorithm based on adaptive normal cloud model[J]. Control and Decision, 2022, 37 (2): 344- 352. | |
18 | 白钰, 彭珍瑞. 基于自适应惯性权重的樽海鞘群算法[J]. 控制与决策, 2022, 37 (1): 237- 246. |
BAI Y , PENG Z R . Salp swarm algorithm based on adaptive inertia weight[J]. Control and Decision, 2022, 37 (1): 237- 246. | |
19 | IBRAHIM B A . A hybrid firefly and particle swarm optimization algorithm for computationally expensive numerical problems[J]. Applied Soft Computing, 2018, 6, 232- 249. |
20 |
WANG X F , ZHAO H , HAN T , et al. A grey wolf optimizer using Gaussian estimation of distribution and its application in the multi-UAV multi-target urban tracking problem[J]. Applied Soft Computing, 2019, 78, 240- 260.
doi: 10.1016/j.asoc.2019.02.037 |
21 |
LI M D , ZHAO H , WENG X W , et al. A novel nature-inspired algorithm for optimization: virus colony search[J]. Advances in Engineering Software, 2016, 92, 65- 88.
doi: 10.1016/j.advengsoft.2015.11.004 |
22 |
FARAMARZI A , HEIDARINEJAD M , MIRJALILI S , et al. Marine predators algorithm: a nature-inspired metaheuristic[J]. Expert Systems with Applications, 2020, 152, 113377.
doi: 10.1016/j.eswa.2020.113377 |
23 |
LI S M , CHEN H L , WANG M J , et al. Slime mould algorithm: a new method for stochastic optimization[J]. Future Generation Computer Systems, 2020, 111, 300- 323.
doi: 10.1016/j.future.2020.03.055 |
24 |
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 |
25 |
SALVADOR G , MOLINA D , LOZANO M , et al. A study on the use of non-parametric tests for analyzing the evolutionary algorithms'behaviour: a case study on the CEC'2005 special session on real parameter optimization[J]. Journal of Heuristics, 2009, 15 (6): 617- 644.
doi: 10.1007/s10732-008-9080-4 |
26 |
GARCÍA S , MOLINA D , LOZANO M , et al. A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms[J]. Journal of Heuristics, 2009, 15 (6): 617- 644.
doi: 10.1007/s10732-008-9080-4 |
27 |
DERRAC J , GARCIA S , MOLINA D , et al. A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms[J]. Swarm and Evolutionary Computation, 2011, 1 (1): 3- 18.
doi: 10.1016/j.swevo.2011.02.002 |
28 |
VECEK N , MERNIK M , CREPINSEK M . A chess rating system for evolutionary algorithms: a new method for the comparison and ranking of evolutionary algorithms[J]. Information Sciences, 2014, 277, 154- 177.
doi: 10.1016/j.ins.2014.02.014 |
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