Journal of Computer Applications ›› 2022, Vol. 42 ›› Issue (9): 2788-2799.DOI: 10.11772/j.issn.1001-9081.2021071342
• Advanced computing • Previous Articles Next Articles
Dahai LI, Qingteng LIU(), Zhigang AI, Zhendong WANG
Received:
2021-07-27
Revised:
2021-09-17
Accepted:
2021-09-22
Online:
2021-09-27
Published:
2022-09-10
Contact:
Qingteng LIU
About author:
LI Dahai, born in 1975, Ph. D., associate professor. His research interests include intelligent optimization algorithm, reinforcement learning algorithm.Supported by:
通讯作者:
刘庆腾
作者简介:
李大海(1975—),男,山东乳山人,副教授,博士,CCF会员,主要研究方向:智能优化算法、强化学习算法;基金资助:
CLC Number:
Dahai LI, Qingteng LIU, Zhigang AI, Zhendong WANG. Yin-Yang-pair optimization algorithm based on dynamic D-way splitting and chaotic perturbation[J]. Journal of Computer Applications, 2022, 42(9): 2788-2799.
李大海, 刘庆腾, 艾志刚, 王振东. 基于动态D向分割和混沌扰动的阴阳对优化算法[J]. 《计算机应用》唯一官方网站, 2022, 42(9): 2788-2799.
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URL: https://www.joca.cn/EN/10.11772/j.issn.1001-9081.2021071342
函数类型 | 函数 | 函数名称 | 理论最优解 |
---|---|---|---|
单峰 函数 | f1 | Sphere Function | -1 400 |
f2 | Rotated High Conditioned Elliptic Function | -1 300 | |
f3 | Rotated Bent Cigar Function | -1 100 | |
f4 | Rotated Discus Function | -1 000 | |
多峰 函数 | f5 | Rastrigin’s Function | -400 |
f6 | Schwefel’s Function | -100 | |
f7 | Rotated Schwefel’s | 100 | |
f8 | Rotated Katsuura Function | 200 | |
f9 | Lunacek bi-Rastrigin Function | 300 | |
f10 | RotatedExpandedGriewank’splusRosenbrock | 500 | |
复合 函数 | f11 | Composition Function1 | 700 |
f12 | Composition Function2 | 800 | |
f13 | Composition Function3 | 900 | |
f14 | Composition Function6 | 1 200 | |
f15 | Composition Function8 | 1 400 |
Tab. 1 Test functions
函数类型 | 函数 | 函数名称 | 理论最优解 |
---|---|---|---|
单峰 函数 | f1 | Sphere Function | -1 400 |
f2 | Rotated High Conditioned Elliptic Function | -1 300 | |
f3 | Rotated Bent Cigar Function | -1 100 | |
f4 | Rotated Discus Function | -1 000 | |
多峰 函数 | f5 | Rastrigin’s Function | -400 |
f6 | Schwefel’s Function | -100 | |
f7 | Rotated Schwefel’s | 100 | |
f8 | Rotated Katsuura Function | 200 | |
f9 | Lunacek bi-Rastrigin Function | 300 | |
f10 | RotatedExpandedGriewank’splusRosenbrock | 500 | |
复合 函数 | f11 | Composition Function1 | 700 |
f12 | Composition Function2 | 800 | |
f13 | Composition Function3 | 900 | |
f14 | Composition Function6 | 1 200 | |
f15 | Composition Function8 | 1 400 |
函数 | 统计 | NYYPO | YYPO-SA1 | CSA | PSO | GWO | WOA | FPA | SSA | NYYPO1 | NYYPO2 |
---|---|---|---|---|---|---|---|---|---|---|---|
f1 | 均值 | 4.48E-28 | 1.02E-08 | 7.04E-13 | 1.39E-12 | 3.11E+02 | 8.63E-13 | 6.45E-09 | 9.14E+02 | 1.92E-10 | 1.90E-10 |
方差 | 7.92E-29 | 8.67E-09 | 8.84E-13 | 3.44E-12 | 1.90E+02 | 8.70E-13 | 6.17E-09 | 3.31E+02 | 1.76E-10 | 1.76E-10 | |
排名 | 1 | 8 | 2 | 4 | 9 | 3 | 7 | 10 | 6 | 5 | |
f2 | 均值 | 9.62E+05 | 5.88E+04 | 2.03E+04 | 1.39E+06 | 3.20E+06 | 3.48E+04 | 5.68E+01 | 6.09E+06 | 7.40E+04 | 7.41E+04 |
方差 | 9.04E+05 | 5.26E+04 | 1.68E+04 | 1.37E+06 | 1.61E+06 | 4.11E+04 | 4.01E+01 | 2.82E+06 | 5.19E+04 | 5.19E+04 | |
排名 | 7 | 4 | 2 | 8 | 9 | 3 | 1 | 10 | 5 | 6 | |
f3 | 均值 | 4.73E+03 | 6.15E+03 | 1.49E+02 | 2.47E+03 | 9.40E+03 | 1.31E+02 | 1.79E+02 | 4.67E+03 | 1.92E+02 | 1.90E+02 |
方差 | 2.57E+03 | 5.40E+03 | 1.48E+02 | 1.16E+03 | 3.27E+03 | 1.52E+02 | 9.52E+01 | 2.51E+03 | 2.42E+02 | 2.42E+02 | |
排名 | 8 | 9 | 2 | 6 | 10 | 1 | 3 | 7 | 5 | 4 | |
f4 | 均值 | 2.17E-06 | 5.94E-04 | 8.08E-04 | 1.30E-08 | 1.09E+02 | 6.51E-04 | 1.90E-06 | 2.01E+02 | 3.53E-06 | 3.90E-06 |
方差 | 8.88E-06 | 4.51E-04 | 3.95E-04 | 2.15E-08 | 9.71E+01 | 4.01E-04 | 1.02E-06 | 5.18E+01 | 1.99E-06 | 2.72E-06 | |
排名 | 3 | 6 | 8 | 1 | 9 | 7 | 2 | 10 | 4 | 5 | |
f5 | 均值 | 2.83E-01 | 1.45E+01 | 3.40E+01 | 1.73E+00 | 4.32E+01 | 3.15E+01 | 1.42E+01 | 6.05E+01 | 9.36E-01 | 1.24E+00 |
方差 | 4.48E-01 | 6.40E+00 | 1.14E+01 | 1.24E+00 | 1.03E+01 | 1.62E+01 | 3.69E+00 | 9.81E+00 | 7.00E-01 | 7.74E-01 | |
排名 | 1 | 5 | 8 | 6 | 9 | 7 | 4 | 10 | 2 | 3 | |
f6 | 均值 | 4.87E+00 | 1.01E+03 | 9.56E+02 | 2.26E+02 | 1.22E+03 | 9.49E+02 | 6.76E+02 | 1.62E+03 | 3.86E+00 | 2.37E+00 |
方差 | 4.23E+00 | 3.84E+02 | 2.27E+02 | 1.44E+02 | 2.85E+02 | 3.25E+02 | 1.28E+02 | 1.43E+02 | 3.41E+00 | 2.47E+00 | |
排名 | 3 | 8 | 7 | 4 | 9 | 6 | 5 | 10 | 2 | 1 | |
f7 | 均值 | 6.82E+02 | 7.89E+02 | 6.97E+02 | 1.04E+03 | 1.35E+03 | 6.58E+02 | 9.12E+02 | 1.48E+03 | 5.60E+02 | 7.26E+02 |
方差 | 2.18E+02 | 5.13E+02 | 2.25E+02 | 3.86E+02 | 2.64E+02 | 2.14E+02 | 1.11E+02 | 2.28E+02 | 2.63E+02 | 2.17E+02 | |
排名 | 3 | 6 | 4 | 8 | 9 | 2 | 7 | 10 | 1 | 5 | |
f8 | 均值 | 2.79E-01 | 1.01E+00 | 3.64E-01 | 9.43E-01 | 5.04E+01 | 3.01E-01 | 9.75E-01 | 1.22E+00 | 9.33E-01 | 7.52E-01 |
方差 | 1.67E-01 | 1.99E-01 | 2.29E-01 | 2.21E-01 | 9.19E+00 | 1.55E-01 | 1.90E-01 | 2.11E-01 | 8.07E-02 | 1.75E-01 | |
排名 | 1 | 8 | 3 | 6 | 10 | 2 | 7 | 9 | 5 | 4 | |
f9 | 均值 | 9.79E+00 | 2.42E+01 | 3.58E+01 | 2.16E+01 | 5.04E+01 | 3.40E+01 | 2.77E+01 | 9.51E+01 | 1.25E+01 | 1.17E+01 |
方差 | 2.94E+00 | 6.80E+00 | 1.36E+01 | 9.12E+00 | 9.19E+00 | 1.13E+01 | 5.34E+00 | 1.19E+01 | 1.08E+00 | 6.61E-01 | |
排名 | 1 | 5 | 8 | 4 | 9 | 7 | 6 | 10 | 3 | 2 | |
f10 | 均值 | 4.98E-01 | 9.78E-01 | 1.95E+00 | 1.24E+00 | 3.68E+01 | 1.79E+00 | 1.10E+00 | 1.29E+01 | 5.96E-01 | 6.14E-01 |
方差 | 2.21E-01 | 5.74E-01 | 1.08E+00 | 7.20E-01 | 1.28E+02 | 9.89E-01 | 2.41E-01 | 5.57E+00 | 1.86E-01 | 1.65E-01 | |
排名 | 1 | 4 | 9 | 6 | 10 | 8 | 5 | 7 | 2 | 3 | |
f11 | 均值 | 3.55E+02 | 4.00E+02 | 3.97E+02 | 3.60E+02 | 4.07E+02 | 3.94E+02 | 1.90E+02 | 4.71E+02 | 4.00E+02 | 4.00E+02 |
方差 | 7.17E+01 | 1.93E-08 | 1.83E+01 | 8.56E+01 | 2.35E+01 | 3.66E+01 | 9.23E+01 | 2.05E+01 | 1.06E-11 | 2.71E-11 | |
排名 | 2 | 7 | 5 | 3 | 9 | 4 | 1 | 10 | 6 | 8 | |
f12 | 均值 | 1.00E+02 | 9.87E+02 | 1.23E+03 | 3.08E+02 | 1.44E+03 | 1.34E+03 | 8.30E+02 | 1.72E+03 | 9.82E+01 | 5.82E+01 |
方差 | 7.68E+01 | 4.71E+02 | 3.58E+02 | 1.71E+02 | 2.40E+02 | 4.16E+02 | 1.19E+02 | 2.44E+02 | 8.53E+01 | 6.53E+01 | |
排名 | 3 | 6 | 7 | 4 | 9 | 8 | 5 | 10 | 2 | 1 | |
f13 | 均值 | 9.17E+02 | 9.34E+02 | 1.23E+03 | 1.04E+03 | 1.61E+03 | 1.16E+03 | 1.04E+03 | 1.65E+03 | 7.50E+02 | 6.83E+02 |
方差 | 2.95E+02 | 5.33E+02 | 3.60E+02 | 3.84E+02 | 2.24E+02 | 2.85E+02 | 1.37E+02 | 1.88E+02 | 4.52E+02 | 1.85E+02 | |
排名 | 3 | 4 | 8 | 6 | 9 | 7 | 5 | 10 | 2 | 1 | |
f14 | 均值 | 1.45E+02 | 1.72E+02 | 1.63E+02 | 2.30E+02 | 2.32E+02 | 1.71E+02 | 1.49E+02 | 1.94E+02 | 1.68E+02 | 1.58E+02 |
方差 | 3.57E+01 | 3.83E+01 | 3.54E+01 | 9.25E+01 | 7.83E+01 | 3.28E+01 | 3.70E+01 | 1.55E+01 | 3.47E+01 | 3.79E+01 | |
排名 | 1 | 7 | 4 | 9 | 10 | 6 | 2 | 8 | 5 | 3 | |
f15 | 均值 | 3.15E+02 | 2.60E+02 | 4.93E+02 | 3.45E+02 | 6.28E+02 | 5.11E+02 | 2.00E+02 | 8.44E+02 | 2.80E+02 | 2.60E+02 |
方差 | 1.16E+02 | 8.00E+01 | 2.47E+02 | 1.19E+02 | 1.09E+02 | 2.35E+02 | 1.02E+02 | 6.01E+01 | 6.32E+01 | 8.43E+01 | |
排名 | 5 | 2 | 7 | 6 | 9 | 8 | 1 | 10 | 4 | 3 | |
Count | 6 | 0 | 0 | 1 | 0 | 1 | 3 | 0 | 1 | 3 | |
Ave rank | 2.87 | 5.93 | 5.6 | 5.4 | 9.27 | 5.27 | 4.07 | 9.4 | 3.6 | 3.6 | |
Total rank | 1 | 8 | 7 | 6 | 9 | 5 | 4 | 10 | 3 | 2 |
Tab. 2 Experimental results of algorithms on 15 test functions with 10-dimension
函数 | 统计 | NYYPO | YYPO-SA1 | CSA | PSO | GWO | WOA | FPA | SSA | NYYPO1 | NYYPO2 |
---|---|---|---|---|---|---|---|---|---|---|---|
f1 | 均值 | 4.48E-28 | 1.02E-08 | 7.04E-13 | 1.39E-12 | 3.11E+02 | 8.63E-13 | 6.45E-09 | 9.14E+02 | 1.92E-10 | 1.90E-10 |
方差 | 7.92E-29 | 8.67E-09 | 8.84E-13 | 3.44E-12 | 1.90E+02 | 8.70E-13 | 6.17E-09 | 3.31E+02 | 1.76E-10 | 1.76E-10 | |
排名 | 1 | 8 | 2 | 4 | 9 | 3 | 7 | 10 | 6 | 5 | |
f2 | 均值 | 9.62E+05 | 5.88E+04 | 2.03E+04 | 1.39E+06 | 3.20E+06 | 3.48E+04 | 5.68E+01 | 6.09E+06 | 7.40E+04 | 7.41E+04 |
方差 | 9.04E+05 | 5.26E+04 | 1.68E+04 | 1.37E+06 | 1.61E+06 | 4.11E+04 | 4.01E+01 | 2.82E+06 | 5.19E+04 | 5.19E+04 | |
排名 | 7 | 4 | 2 | 8 | 9 | 3 | 1 | 10 | 5 | 6 | |
f3 | 均值 | 4.73E+03 | 6.15E+03 | 1.49E+02 | 2.47E+03 | 9.40E+03 | 1.31E+02 | 1.79E+02 | 4.67E+03 | 1.92E+02 | 1.90E+02 |
方差 | 2.57E+03 | 5.40E+03 | 1.48E+02 | 1.16E+03 | 3.27E+03 | 1.52E+02 | 9.52E+01 | 2.51E+03 | 2.42E+02 | 2.42E+02 | |
排名 | 8 | 9 | 2 | 6 | 10 | 1 | 3 | 7 | 5 | 4 | |
f4 | 均值 | 2.17E-06 | 5.94E-04 | 8.08E-04 | 1.30E-08 | 1.09E+02 | 6.51E-04 | 1.90E-06 | 2.01E+02 | 3.53E-06 | 3.90E-06 |
方差 | 8.88E-06 | 4.51E-04 | 3.95E-04 | 2.15E-08 | 9.71E+01 | 4.01E-04 | 1.02E-06 | 5.18E+01 | 1.99E-06 | 2.72E-06 | |
排名 | 3 | 6 | 8 | 1 | 9 | 7 | 2 | 10 | 4 | 5 | |
f5 | 均值 | 2.83E-01 | 1.45E+01 | 3.40E+01 | 1.73E+00 | 4.32E+01 | 3.15E+01 | 1.42E+01 | 6.05E+01 | 9.36E-01 | 1.24E+00 |
方差 | 4.48E-01 | 6.40E+00 | 1.14E+01 | 1.24E+00 | 1.03E+01 | 1.62E+01 | 3.69E+00 | 9.81E+00 | 7.00E-01 | 7.74E-01 | |
排名 | 1 | 5 | 8 | 6 | 9 | 7 | 4 | 10 | 2 | 3 | |
f6 | 均值 | 4.87E+00 | 1.01E+03 | 9.56E+02 | 2.26E+02 | 1.22E+03 | 9.49E+02 | 6.76E+02 | 1.62E+03 | 3.86E+00 | 2.37E+00 |
方差 | 4.23E+00 | 3.84E+02 | 2.27E+02 | 1.44E+02 | 2.85E+02 | 3.25E+02 | 1.28E+02 | 1.43E+02 | 3.41E+00 | 2.47E+00 | |
排名 | 3 | 8 | 7 | 4 | 9 | 6 | 5 | 10 | 2 | 1 | |
f7 | 均值 | 6.82E+02 | 7.89E+02 | 6.97E+02 | 1.04E+03 | 1.35E+03 | 6.58E+02 | 9.12E+02 | 1.48E+03 | 5.60E+02 | 7.26E+02 |
方差 | 2.18E+02 | 5.13E+02 | 2.25E+02 | 3.86E+02 | 2.64E+02 | 2.14E+02 | 1.11E+02 | 2.28E+02 | 2.63E+02 | 2.17E+02 | |
排名 | 3 | 6 | 4 | 8 | 9 | 2 | 7 | 10 | 1 | 5 | |
f8 | 均值 | 2.79E-01 | 1.01E+00 | 3.64E-01 | 9.43E-01 | 5.04E+01 | 3.01E-01 | 9.75E-01 | 1.22E+00 | 9.33E-01 | 7.52E-01 |
方差 | 1.67E-01 | 1.99E-01 | 2.29E-01 | 2.21E-01 | 9.19E+00 | 1.55E-01 | 1.90E-01 | 2.11E-01 | 8.07E-02 | 1.75E-01 | |
排名 | 1 | 8 | 3 | 6 | 10 | 2 | 7 | 9 | 5 | 4 | |
f9 | 均值 | 9.79E+00 | 2.42E+01 | 3.58E+01 | 2.16E+01 | 5.04E+01 | 3.40E+01 | 2.77E+01 | 9.51E+01 | 1.25E+01 | 1.17E+01 |
方差 | 2.94E+00 | 6.80E+00 | 1.36E+01 | 9.12E+00 | 9.19E+00 | 1.13E+01 | 5.34E+00 | 1.19E+01 | 1.08E+00 | 6.61E-01 | |
排名 | 1 | 5 | 8 | 4 | 9 | 7 | 6 | 10 | 3 | 2 | |
f10 | 均值 | 4.98E-01 | 9.78E-01 | 1.95E+00 | 1.24E+00 | 3.68E+01 | 1.79E+00 | 1.10E+00 | 1.29E+01 | 5.96E-01 | 6.14E-01 |
方差 | 2.21E-01 | 5.74E-01 | 1.08E+00 | 7.20E-01 | 1.28E+02 | 9.89E-01 | 2.41E-01 | 5.57E+00 | 1.86E-01 | 1.65E-01 | |
排名 | 1 | 4 | 9 | 6 | 10 | 8 | 5 | 7 | 2 | 3 | |
f11 | 均值 | 3.55E+02 | 4.00E+02 | 3.97E+02 | 3.60E+02 | 4.07E+02 | 3.94E+02 | 1.90E+02 | 4.71E+02 | 4.00E+02 | 4.00E+02 |
方差 | 7.17E+01 | 1.93E-08 | 1.83E+01 | 8.56E+01 | 2.35E+01 | 3.66E+01 | 9.23E+01 | 2.05E+01 | 1.06E-11 | 2.71E-11 | |
排名 | 2 | 7 | 5 | 3 | 9 | 4 | 1 | 10 | 6 | 8 | |
f12 | 均值 | 1.00E+02 | 9.87E+02 | 1.23E+03 | 3.08E+02 | 1.44E+03 | 1.34E+03 | 8.30E+02 | 1.72E+03 | 9.82E+01 | 5.82E+01 |
方差 | 7.68E+01 | 4.71E+02 | 3.58E+02 | 1.71E+02 | 2.40E+02 | 4.16E+02 | 1.19E+02 | 2.44E+02 | 8.53E+01 | 6.53E+01 | |
排名 | 3 | 6 | 7 | 4 | 9 | 8 | 5 | 10 | 2 | 1 | |
f13 | 均值 | 9.17E+02 | 9.34E+02 | 1.23E+03 | 1.04E+03 | 1.61E+03 | 1.16E+03 | 1.04E+03 | 1.65E+03 | 7.50E+02 | 6.83E+02 |
方差 | 2.95E+02 | 5.33E+02 | 3.60E+02 | 3.84E+02 | 2.24E+02 | 2.85E+02 | 1.37E+02 | 1.88E+02 | 4.52E+02 | 1.85E+02 | |
排名 | 3 | 4 | 8 | 6 | 9 | 7 | 5 | 10 | 2 | 1 | |
f14 | 均值 | 1.45E+02 | 1.72E+02 | 1.63E+02 | 2.30E+02 | 2.32E+02 | 1.71E+02 | 1.49E+02 | 1.94E+02 | 1.68E+02 | 1.58E+02 |
方差 | 3.57E+01 | 3.83E+01 | 3.54E+01 | 9.25E+01 | 7.83E+01 | 3.28E+01 | 3.70E+01 | 1.55E+01 | 3.47E+01 | 3.79E+01 | |
排名 | 1 | 7 | 4 | 9 | 10 | 6 | 2 | 8 | 5 | 3 | |
f15 | 均值 | 3.15E+02 | 2.60E+02 | 4.93E+02 | 3.45E+02 | 6.28E+02 | 5.11E+02 | 2.00E+02 | 8.44E+02 | 2.80E+02 | 2.60E+02 |
方差 | 1.16E+02 | 8.00E+01 | 2.47E+02 | 1.19E+02 | 1.09E+02 | 2.35E+02 | 1.02E+02 | 6.01E+01 | 6.32E+01 | 8.43E+01 | |
排名 | 5 | 2 | 7 | 6 | 9 | 8 | 1 | 10 | 4 | 3 | |
Count | 6 | 0 | 0 | 1 | 0 | 1 | 3 | 0 | 1 | 3 | |
Ave rank | 2.87 | 5.93 | 5.6 | 5.4 | 9.27 | 5.27 | 4.07 | 9.4 | 3.6 | 3.6 | |
Total rank | 1 | 8 | 7 | 6 | 9 | 5 | 4 | 10 | 3 | 2 |
函数 | 统计 | NYYPO | YYPO-SA1 | CSA | PSO | GWO | WOA | FPA | SSA | NYYPO1 | NYYPO2 |
---|---|---|---|---|---|---|---|---|---|---|---|
f1 | 均值 | 2.10E-20 | 5.14E-08 | 1.50E-03 | 5.99E+01 | 7.73E+03 | 1.01E+02 | 7.49E+02 | 1.85E+04 | 4.00E-10 | 4.05E-10 |
方差 | 5.47E-20 | 5.14E-08 | 9.56E-04 | 4.47E+01 | 1.94E+03 | 1.14E+02 | 4.82E+02 | 3.73E+03 | 3.27E-10 | 3.27E-10 | |
排名 | 1 | 4 | 5 | 6 | 9 | 7 | 8 | 10 | 2 | 3 | |
f2 | 均值 | 1.03E+06 | 1.52E+06 | 8.74E+06 | 5.24E+07 | 7.81E+07 | 7.92E+07 | 1.60E+06 | 2.25E+08 | 8.91E+05 | 8.91E+05 |
方差 | 5.08E+06 | 9.94E+05 | 3.81E+06 | 1.39E+07 | 2.50E+07 | 2.80E+07 | 1.65E+06 | 7.74E+07 | 4.10E+05 | 4.15E+05 | |
排名 | 3 | 4 | 6 | 7 | 8 | 9 | 5 | 10 | 1 | 2 | |
f3 | 均值 | 2.42E+03 | 1.39E+04 | 1.24E+04 | 2.59E+04 | 4.30E+04 | 8.61E+04 | 2.79E+04 | 4.46E+04 | 3.17E+03 | 3.10E+03 |
方差 | 1.31E+03 | 1.64E+04 | 3.71E+03 | 7.71E+03 | 4.39E+03 | 2.81E+04 | 8.45E+03 | 1.08E+04 | 1.94E+03 | 1.94E+03 | |
排名 | 1 | 5 | 4 | 6 | 8 | 10 | 7 | 9 | 3 | 2 | |
f4 | 均值 | 1.24E-03 | 1.98E-03 | 6.33E+01 | 2.00E+01 | 2.34E+03 | 3.55E+02 | 1.33E+02 | 4.26E+03 | 7.12E-03 | 7.71E-03 |
方差 | 1.64E-03 | 2.75E-04 | 2.72E+01 | 1.05E+01 | 1.20E+03 | 1.88E+02 | 6.01E+01 | 1.01E+03 | 5.07E-04 | 5.07E-04 | |
排名 | 1 | 2 | 6 | 5 | 9 | 8 | 7 | 10 | 3 | 4 | |
f5 | 均值 | 6.52E-01 | 8.18E+01 | 3.09E+02 | 1.05E+02 | 3.28E+02 | 5.39E+02 | 2.00E+02 | 4.17E+02 | 3.31E+00 | 3.74E+00 |
方差 | 7.57E-01 | 2.58E+01 | 9.29E+01 | 2.44E+01 | 4.04E+01 | 1.14E+02 | 5.10E+01 | 2.95E+01 | 1.11E+00 | 1.45E+00 | |
排名 | 1 | 4 | 7 | 5 | 8 | 10 | 6 | 9 | 2 | 3 | |
f6 | 均值 | 1.79E+01 | 4.74E+03 | 4.04E+03 | 3.64E+03 | 7.21E+03 | 4.94E+03 | 4.67E+03 | 7.64E+03 | 7.46E+00 | 9.72E+00 |
方差 | 1.02E+01 | 2.02E+03 | 7.46E+02 | 1.05E+03 | 5.59E+02 | 9.83E+02 | 2.59E+02 | 3.04E+02 | 2.44E+00 | 5.90E+00 | |
排名 | 3 | 7 | 5 | 4 | 9 | 10 | 6 | 8 | 1 | 2 | |
f7 | 均值 | 4.04E+03 | 4.45E+03 | 4.00E+03 | 7.23E+03 | 7.72E+03 | 6.03E+03 | 5.65E+03 | 7.74E+03 | 4.00E+03 | 3.94E+03 |
方差 | 5.99E+02 | 2.15E+03 | 7.02E+02 | 3.61E+02 | 3.02E+02 | 7.03E+02 | 2.53E+02 | 3.19E+02 | 4.86E+02 | 6.75E+02 | |
排名 | 4 | 5 | 3 | 8 | 9 | 7 | 6 | 10 | 2 | 1 | |
f8 | 均值 | 5.31E-01 | 2.44E+00 | 8.70E-01 | 2.59E+00 | 3.18E+00 | 1.88E+00 | 2.69E+00 | 2.80E+00 | 7.88E-01 | 1.28E+00 |
方差 | 2.26E-01 | 2.83E-01 | 3.44E-01 | 4.40E-01 | 4.30E-01 | 5.35E-01 | 4.09E-01 | 3.27E-01 | 1.21E-01 | 4.11E-01 | |
排名 | 1 | 6 | 3 | 7 | 10 | 5 | 8 | 9 | 2 | 4 | |
f9 | 均值 | 3.22E+01 | 1.16E+02 | 2.77E+02 | 2.59E+02 | 3.99E+02 | 6.59E+02 | 3.83E+02 | 7.19E+02 | 3.94E+01 | 3.85E+01 |
方差 | 9.00E-01 | 2.44E+01 | 8.03E+01 | 3.73E+01 | 4.62E+01 | 1.14E+02 | 7.43E+01 | 6.11E+01 | 1.78E+00 | 1.85E+00 | |
排名 | 1 | 4 | 6 | 5 | 8 | 9 | 7 | 10 | 3 | 2 | |
f10 | 均值 | 1.47E+00 | 4.21E+00 | 2.66E+01 | 2.29E+01 | 5.11E+03 | 8.47E+01 | 7.83E+01 | 4.71E+04 | 2.23E+00 | 2.22E+00 |
方差 | 3.25E-01 | 9.75E-01 | 1.08E+01 | 3.71E+00 | 8.34E+03 | 3.63E+01 | 3.92E+01 | 4.64E+04 | 3.70E-01 | 5.53E-01 | |
排名 | 1 | 4 | 6 | 5 | 9 | 8 | 7 | 10 | 3 | 2 | |
f11 | 均值 | 3.19E+02 | 3.21E+02 | 3.28E+02 | 3.90E+02 | 1.72E+03 | 5.25E+02 | 6.02E+02 | 2.51E+03 | 2.99E+02 | 2.90E+02 |
方差 | 8.24E+01 | 7.88E+01 | 1.19E+02 | 6.68E+01 | 2.76E+02 | 1.91E+02 | 9.98E+01 | 1.61E+02 | 1.01E+02 | 3.16E+01 | |
排名 | 3 | 4 | 5 | 6 | 7 | 9 | 8 | 10 | 2 | 1 | |
f12 | 均值 | 1.19E+02 | 3.34E+03 | 4.99E+03 | 4.06E+03 | 7.23E+03 | 6.77E+03 | 5.37E+03 | 8.31E+03 | 1.28E+02 | 1.21E+02 |
方差 | 5.95E+01 | 1.39E+03 | 9.05E+02 | 7.02E+02 | 6.14E+02 | 9.38E+02 | 3.40E+02 | 4.35E+02 | 6.37E+00 | 3.23E+01 | |
排名 | 1 | 4 | 6 | 5 | 9 | 8 | 7 | 10 | 3 | 2 | |
f13 | 均值 | 4.91E+03 | 3.47E+03 | 5.60E+03 | 7.34E+03 | 7.97E+03 | 6.93E+03 | 6.13E+03 | 8.15E+03 | 4.02E+03 | 4.19E+03 |
方差 | 8.60E+02 | 9.21E+02 | 8.05E+02 | 3.91E+02 | 4.47E+02 | 9.00E+02 | 4.24E+02 | 3.86E+02 | 7.07E+02 | 5.50E+02 | |
排名 | 4 | 1 | 5 | 8 | 9 | 7 | 6 | 10 | 2 | 3 | |
f14 | 均值 | 2.00E+02 | 2.00E+02 | 2.09E+02 | 3.22E+02 | 3.58E+02 | 3.71E+02 | 2.12E+02 | 2.35E+02 | 2.00E+02 | 2.00E+02 |
方差 | 1.90E-01 | 2.18E-02 | 3.90E+01 | 7.97E+01 | 6.47E+01 | 7.24E+01 | 4.20E+01 | 4.20E+01 | 3.44E-01 | 2.46E-01 | |
排名 | 1 | 2 | 5 | 8 | 9 | 10 | 6 | 7 | 4 | 3 | |
f15 | 均值 | 3.08E+02 | 3.00E+02 | 3.15E+03 | 8.28E+02 | 2.55E+03 | 4.60E+03 | 1.60E+03 | 3.58E+03 | 2.80E+02 | 3.00E+02 |
方差 | 1.78E+02 | 8.94E-03 | 8.74E+02 | 3.38E+02 | 3.91E+02 | 9.25E+02 | 5.20E+02 | 4.19E+02 | 6.32E+01 | 2.13E-04 | |
排名 | 4 | 3 | 8 | 5 | 7 | 10 | 6 | 9 | 1 | 2 | |
Count | 9 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 2 | |
Ave rank | 2.0 | 3.93 | 5.33 | 6.0 | 8.53 | 8.47 | 6.67 | 9.4 | 2.27 | 2.40 | |
Total rank | 1 | 4 | 5 | 6 | 9 | 8 | 7 | 10 | 2 | 3 |
Tab. 3 Experimental results of algorithms on 15 test functions with 30-dimension
函数 | 统计 | NYYPO | YYPO-SA1 | CSA | PSO | GWO | WOA | FPA | SSA | NYYPO1 | NYYPO2 |
---|---|---|---|---|---|---|---|---|---|---|---|
f1 | 均值 | 2.10E-20 | 5.14E-08 | 1.50E-03 | 5.99E+01 | 7.73E+03 | 1.01E+02 | 7.49E+02 | 1.85E+04 | 4.00E-10 | 4.05E-10 |
方差 | 5.47E-20 | 5.14E-08 | 9.56E-04 | 4.47E+01 | 1.94E+03 | 1.14E+02 | 4.82E+02 | 3.73E+03 | 3.27E-10 | 3.27E-10 | |
排名 | 1 | 4 | 5 | 6 | 9 | 7 | 8 | 10 | 2 | 3 | |
f2 | 均值 | 1.03E+06 | 1.52E+06 | 8.74E+06 | 5.24E+07 | 7.81E+07 | 7.92E+07 | 1.60E+06 | 2.25E+08 | 8.91E+05 | 8.91E+05 |
方差 | 5.08E+06 | 9.94E+05 | 3.81E+06 | 1.39E+07 | 2.50E+07 | 2.80E+07 | 1.65E+06 | 7.74E+07 | 4.10E+05 | 4.15E+05 | |
排名 | 3 | 4 | 6 | 7 | 8 | 9 | 5 | 10 | 1 | 2 | |
f3 | 均值 | 2.42E+03 | 1.39E+04 | 1.24E+04 | 2.59E+04 | 4.30E+04 | 8.61E+04 | 2.79E+04 | 4.46E+04 | 3.17E+03 | 3.10E+03 |
方差 | 1.31E+03 | 1.64E+04 | 3.71E+03 | 7.71E+03 | 4.39E+03 | 2.81E+04 | 8.45E+03 | 1.08E+04 | 1.94E+03 | 1.94E+03 | |
排名 | 1 | 5 | 4 | 6 | 8 | 10 | 7 | 9 | 3 | 2 | |
f4 | 均值 | 1.24E-03 | 1.98E-03 | 6.33E+01 | 2.00E+01 | 2.34E+03 | 3.55E+02 | 1.33E+02 | 4.26E+03 | 7.12E-03 | 7.71E-03 |
方差 | 1.64E-03 | 2.75E-04 | 2.72E+01 | 1.05E+01 | 1.20E+03 | 1.88E+02 | 6.01E+01 | 1.01E+03 | 5.07E-04 | 5.07E-04 | |
排名 | 1 | 2 | 6 | 5 | 9 | 8 | 7 | 10 | 3 | 4 | |
f5 | 均值 | 6.52E-01 | 8.18E+01 | 3.09E+02 | 1.05E+02 | 3.28E+02 | 5.39E+02 | 2.00E+02 | 4.17E+02 | 3.31E+00 | 3.74E+00 |
方差 | 7.57E-01 | 2.58E+01 | 9.29E+01 | 2.44E+01 | 4.04E+01 | 1.14E+02 | 5.10E+01 | 2.95E+01 | 1.11E+00 | 1.45E+00 | |
排名 | 1 | 4 | 7 | 5 | 8 | 10 | 6 | 9 | 2 | 3 | |
f6 | 均值 | 1.79E+01 | 4.74E+03 | 4.04E+03 | 3.64E+03 | 7.21E+03 | 4.94E+03 | 4.67E+03 | 7.64E+03 | 7.46E+00 | 9.72E+00 |
方差 | 1.02E+01 | 2.02E+03 | 7.46E+02 | 1.05E+03 | 5.59E+02 | 9.83E+02 | 2.59E+02 | 3.04E+02 | 2.44E+00 | 5.90E+00 | |
排名 | 3 | 7 | 5 | 4 | 9 | 10 | 6 | 8 | 1 | 2 | |
f7 | 均值 | 4.04E+03 | 4.45E+03 | 4.00E+03 | 7.23E+03 | 7.72E+03 | 6.03E+03 | 5.65E+03 | 7.74E+03 | 4.00E+03 | 3.94E+03 |
方差 | 5.99E+02 | 2.15E+03 | 7.02E+02 | 3.61E+02 | 3.02E+02 | 7.03E+02 | 2.53E+02 | 3.19E+02 | 4.86E+02 | 6.75E+02 | |
排名 | 4 | 5 | 3 | 8 | 9 | 7 | 6 | 10 | 2 | 1 | |
f8 | 均值 | 5.31E-01 | 2.44E+00 | 8.70E-01 | 2.59E+00 | 3.18E+00 | 1.88E+00 | 2.69E+00 | 2.80E+00 | 7.88E-01 | 1.28E+00 |
方差 | 2.26E-01 | 2.83E-01 | 3.44E-01 | 4.40E-01 | 4.30E-01 | 5.35E-01 | 4.09E-01 | 3.27E-01 | 1.21E-01 | 4.11E-01 | |
排名 | 1 | 6 | 3 | 7 | 10 | 5 | 8 | 9 | 2 | 4 | |
f9 | 均值 | 3.22E+01 | 1.16E+02 | 2.77E+02 | 2.59E+02 | 3.99E+02 | 6.59E+02 | 3.83E+02 | 7.19E+02 | 3.94E+01 | 3.85E+01 |
方差 | 9.00E-01 | 2.44E+01 | 8.03E+01 | 3.73E+01 | 4.62E+01 | 1.14E+02 | 7.43E+01 | 6.11E+01 | 1.78E+00 | 1.85E+00 | |
排名 | 1 | 4 | 6 | 5 | 8 | 9 | 7 | 10 | 3 | 2 | |
f10 | 均值 | 1.47E+00 | 4.21E+00 | 2.66E+01 | 2.29E+01 | 5.11E+03 | 8.47E+01 | 7.83E+01 | 4.71E+04 | 2.23E+00 | 2.22E+00 |
方差 | 3.25E-01 | 9.75E-01 | 1.08E+01 | 3.71E+00 | 8.34E+03 | 3.63E+01 | 3.92E+01 | 4.64E+04 | 3.70E-01 | 5.53E-01 | |
排名 | 1 | 4 | 6 | 5 | 9 | 8 | 7 | 10 | 3 | 2 | |
f11 | 均值 | 3.19E+02 | 3.21E+02 | 3.28E+02 | 3.90E+02 | 1.72E+03 | 5.25E+02 | 6.02E+02 | 2.51E+03 | 2.99E+02 | 2.90E+02 |
方差 | 8.24E+01 | 7.88E+01 | 1.19E+02 | 6.68E+01 | 2.76E+02 | 1.91E+02 | 9.98E+01 | 1.61E+02 | 1.01E+02 | 3.16E+01 | |
排名 | 3 | 4 | 5 | 6 | 7 | 9 | 8 | 10 | 2 | 1 | |
f12 | 均值 | 1.19E+02 | 3.34E+03 | 4.99E+03 | 4.06E+03 | 7.23E+03 | 6.77E+03 | 5.37E+03 | 8.31E+03 | 1.28E+02 | 1.21E+02 |
方差 | 5.95E+01 | 1.39E+03 | 9.05E+02 | 7.02E+02 | 6.14E+02 | 9.38E+02 | 3.40E+02 | 4.35E+02 | 6.37E+00 | 3.23E+01 | |
排名 | 1 | 4 | 6 | 5 | 9 | 8 | 7 | 10 | 3 | 2 | |
f13 | 均值 | 4.91E+03 | 3.47E+03 | 5.60E+03 | 7.34E+03 | 7.97E+03 | 6.93E+03 | 6.13E+03 | 8.15E+03 | 4.02E+03 | 4.19E+03 |
方差 | 8.60E+02 | 9.21E+02 | 8.05E+02 | 3.91E+02 | 4.47E+02 | 9.00E+02 | 4.24E+02 | 3.86E+02 | 7.07E+02 | 5.50E+02 | |
排名 | 4 | 1 | 5 | 8 | 9 | 7 | 6 | 10 | 2 | 3 | |
f14 | 均值 | 2.00E+02 | 2.00E+02 | 2.09E+02 | 3.22E+02 | 3.58E+02 | 3.71E+02 | 2.12E+02 | 2.35E+02 | 2.00E+02 | 2.00E+02 |
方差 | 1.90E-01 | 2.18E-02 | 3.90E+01 | 7.97E+01 | 6.47E+01 | 7.24E+01 | 4.20E+01 | 4.20E+01 | 3.44E-01 | 2.46E-01 | |
排名 | 1 | 2 | 5 | 8 | 9 | 10 | 6 | 7 | 4 | 3 | |
f15 | 均值 | 3.08E+02 | 3.00E+02 | 3.15E+03 | 8.28E+02 | 2.55E+03 | 4.60E+03 | 1.60E+03 | 3.58E+03 | 2.80E+02 | 3.00E+02 |
方差 | 1.78E+02 | 8.94E-03 | 8.74E+02 | 3.38E+02 | 3.91E+02 | 9.25E+02 | 5.20E+02 | 4.19E+02 | 6.32E+01 | 2.13E-04 | |
排名 | 4 | 3 | 8 | 5 | 7 | 10 | 6 | 9 | 1 | 2 | |
Count | 9 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 2 | |
Ave rank | 2.0 | 3.93 | 5.33 | 6.0 | 8.53 | 8.47 | 6.67 | 9.4 | 2.27 | 2.40 | |
Total rank | 1 | 4 | 5 | 6 | 9 | 8 | 7 | 10 | 2 | 3 |
函数 | 统计 | NYYPO | YYPO-SA1 | CSA | PSO | GWO | WOA | FPA | SSA | NYYPO1 | NYYPO2 |
---|---|---|---|---|---|---|---|---|---|---|---|
f1 | 均值 | 2.40E-09 | 3.42E-06 | 1.35E+00 | 1.34E+03 | 1.83E+04 | 6.60E+02 | 7.65E+03 | 5.03E+04 | 2.85E-09 | 2.85E-09 |
方差 | 2.02E-09 | 7.39E-06 | 1.29E+00 | 4.22E+02 | 4.22E+03 | 2.33E+02 | 2.86E+03 | 4.71E+03 | 3.98E-09 | 6.18E-09 | |
排名 | 1 | 4 | 5 | 7 | 9 | 6 | 8 | 10 | 2 | 3 | |
f2 | 均值 | 2.31E+06 | 2.56E+07 | 2.71E+07 | 1.77E+08 | 2.14E+08 | 1.11E+08 | 1.30E+07 | 7.89E+08 | 2.49E+06 | 2.46E+06 |
方差 | 7.38E+05 | 8.93E+06 | 9.47E+06 | 5.09E+07 | 4.22E+07 | 3.18E+07 | 5.34E+06 | 1.93E+08 | 9.21E+05 | 9.21E+05 | |
排名 | 1 | 5 | 6 | 8 | 9 | 7 | 4 | 10 | 3 | 2 | |
f3 | 均值 | 9.35E+03 | 3.10E+04 | 4.25E+04 | 7.00E+04 | 6.48E+04 | 7.83E+04 | 5.84E+04 | 8.79E+04 | 1.16E+04 | 1.12E+04 |
方差 | 8.75E+03 | 4.95E+03 | 7.71E+03 | 1.39E+04 | 5.81E+03 | 5.53E+03 | 6.66E+03 | 1.10E+04 | 1.21E+04 | 1.07E+04 | |
排名 | 1 | 4 | 5 | 8 | 7 | 9 | 6 | 10 | 3 | 2 | |
f4 | 均值 | 3.90E-03 | 2.51E+00 | 1.72E+02 | 2.81E+02 | 3.07E+03 | 7.32E+02 | 9.26E+02 | 1.04E+04 | 3.61E-03 | 3.56E-03 |
方差 | 4.74E-04 | 6.72E-01 | 3.42E+01 | 7.23E+01 | 1.33E+03 | 2.05E+02 | 4.77E+02 | 2.26E+03 | 4.75E-04 | 5.69E-04 | |
排名 | 3 | 4 | 5 | 6 | 9 | 7 | 8 | 10 | 2 | 1 | |
f5 | 均值 | 5.52E+00 | 7.14E+00 | 5.81E+02 | 3.54E+02 | 5.78E+02 | 8.84E+02 | 5.09E+02 | 9.48E+02 | 6.51E+00 | 5.86E+00 |
方差 | 1.71E+00 | 2.22E+00 | 7.84E+01 | 3.82E+01 | 7.49E+01 | 7.81E+01 | 6.09E+01 | 8.25E+01 | 2.16E+00 | 2.21E+00 | |
排名 | 1 | 4 | 8 | 5 | 7 | 9 | 6 | 10 | 3 | 2 | |
f6 | 均值 | 1.40E+01 | 1.85E+01 | 7.31E+03 | 9.25E+03 | 1.35E+04 | 1.05E+04 | 9.85E+03 | 1.43E+04 | 1.64E+01 | 1.56E+01 |
方差 | 4.35E+00 | 4.26E+00 | 9.13E+02 | 1.19E+03 | 5.18E+02 | 1.11E+03 | 3.86E+02 | 4.41E+02 | 4.40E+00 | 6.81E+00 | |
排名 | 1 | 4 | 5 | 6 | 9 | 8 | 7 | 10 | 3 | 2 | |
f7 | 均值 | 7.96E+03 | 7.63E+03 | 7.88E+03 | 1.43E+04 | 1.49E+04 | 1.23E+04 | 1.17E+04 | 1.47E+04 | 7.84E+03 | 8.16E+03 |
方差 | 1.16E+03 | 8.63E+02 | 1.08E+03 | 5.88E+02 | 4.49E+02 | 1.11E+03 | 4.30E+02 | 4.58E+02 | 7.71E+02 | 1.13E+03 | |
排名 | 4 | 1 | 3 | 8 | 10 | 7 | 6 | 9 | 2 | 5 | |
f8 | 均值 | 4.22E-01 | 5.04E-01 | 1.65E+00 | 3.76E+00 | 4.05E+00 | 2.75E+00 | 3.82E+00 | 3.84E+00 | 3.00E-01 | 1.72E+00 |
方差 | 1.98E-01 | 2.36E-01 | 4.42E-01 | 3.37E-01 | 5.10E-01 | 4.90E-01 | 2.73E-01 | 3.58E-01 | 1.37E-01 | 5.54E-01 | |
排名 | 2 | 3 | 4 | 7 | 10 | 6 | 8 | 9 | 1 | 5 | |
f9 | 均值 | 6.45E+01 | 6.95E+01 | 6.88E+02 | 6.86E+02 | 7.80E+02 | 1.16E+03 | 8.46E+02 | 1.72E+03 | 6.47E+01 | 6.43E+01 |
方差 | 2.09E+00 | 2.96E+00 | 1.58E+02 | 6.91E+01 | 6.01E+01 | 1.46E+02 | 1.03E+02 | 1.32E+02 | 2.40E+00 | 2.39E+00 | |
排名 | 2 | 4 | 6 | 5 | 7 | 9 | 8 | 10 | 3 | 1 | |
f10 | 均值 | 3.66E+00 | 4.83E+00 | 8.60E+01 | 1.33E+02 | 3.27E+04 | 2.74E+02 | 6.43E+03 | 3.31E+05 | 3.98E+00 | 3.85E+00 |
方差 | 4.48E-01 | 8.53E-01 | 3.38E+01 | 6.78E+01 | 8.35E+04 | 1.00E+02 | 7.12E+03 | 2.05E+05 | 3.60E-01 | 8.00E-01 | |
排名 | 1 | 4 | 5 | 6 | 9 | 7 | 8 | 10 | 3 | 2 | |
f11 | 均值 | 7.62E+02 | 9.73E+02 | 9.39E+02 | 1.46E+03 | 3.62E+03 | 2.05E+03 | 2.17E+03 | 5.10E+03 | 7.25E+02 | 8.59E+02 |
方差 | 3.73E+02 | 2.88E+02 | 2.20E+02 | 4.91E+02 | 1.33E+02 | 6.45E+02 | 3.79E+02 | 2.00E+02 | 4.60E+02 | 2.68E+02 | |
排名 | 2 | 5 | 4 | 6 | 9 | 7 | 8 | 10 | 1 | 3 | |
f12 | 均值 | 6.19E+01 | 8.37E+01 | 1.08E+04 | 9.93E+03 | 1.39E+04 | 1.28E+04 | 1.13E+04 | 1.51E+04 | 3.81E+01 | 3.70E+01 |
方差 | 6.49E+01 | 7.29E+01 | 1.51E+03 | 1.27E+03 | 9.22E+02 | 1.19E+03 | 4.98E+02 | 4.63E+02 | 7.58E+00 | 8.37E+00 | |
排名 | 3 | 4 | 6 | 5 | 9 | 8 | 7 | 10 | 2 | 1 | |
f13 | 均值 | 8.02E+03 | 9.30E+03 | 1.14E+04 | 1.48E+04 | 1.55E+04 | 1.36E+04 | 1.23E+04 | 1.53E+04 | 8.40E+03 | 9.45E+03 |
方差 | 6.74E+02 | 8.26E+02 | 1.12E+03 | 5.18E+02 | 5.95E+02 | 1.52E+03 | 6.23E+02 | 4.93E+02 | 7.92E+02 | 8.43E+02 | |
排名 | 1 | 3 | 5 | 8 | 10 | 7 | 6 | 9 | 2 | 4 | |
f14 | 均值 | 2.12E+02 | 2.03E+02 | 3.93E+02 | 4.18E+02 | 4.22E+02 | 4.58E+02 | 2.78E+02 | 4.86E+02 | 2.01E+02 | 2.01E+02 |
方差 | 3.96E+01 | 1.91E+00 | 1.28E+02 | 8.96E+01 | 9.97E+01 | 8.58E+01 | 1.15E+02 | 4.48E+01 | 1.53E+00 | 1.60E+00 | |
排名 | 4 | 3 | 6 | 7 | 8 | 9 | 5 | 10 | 1 | 2 | |
f15 | 均值 | 6.09E+02 | 7.29E+02 | 4.82E+03 | 2.53E+03 | 4.08E+03 | 8.04E+03 | 3.77E+03 | 6.73E+03 | 4.00E+02 | 7.10E+02 |
方差 | 8.10E+02 | 1.01E+03 | 2.72E+03 | 1.78E+03 | 9.41E+02 | 1.76E+03 | 1.79E+03 | 7.71E+02 | 9.22E-05 | 9.81E+02 | |
排名 | 2 | 4 | 8 | 5 | 7 | 10 | 6 | 9 | 1 | 3 | |
Count | 7 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 4 | 3 | |
Ave rank | 1.93 | 3.73 | 5.4 | 6.47 | 8.6 | 7.73 | 6.73 | 9.73 | 2.13 | 2.53 | |
Total rank | 1 | 4 | 5 | 6 | 9 | 8 | 7 | 10 | 2 | 3 |
Tab. 4 Experimental results of algorithms on 15 test functions with 50-dimension
函数 | 统计 | NYYPO | YYPO-SA1 | CSA | PSO | GWO | WOA | FPA | SSA | NYYPO1 | NYYPO2 |
---|---|---|---|---|---|---|---|---|---|---|---|
f1 | 均值 | 2.40E-09 | 3.42E-06 | 1.35E+00 | 1.34E+03 | 1.83E+04 | 6.60E+02 | 7.65E+03 | 5.03E+04 | 2.85E-09 | 2.85E-09 |
方差 | 2.02E-09 | 7.39E-06 | 1.29E+00 | 4.22E+02 | 4.22E+03 | 2.33E+02 | 2.86E+03 | 4.71E+03 | 3.98E-09 | 6.18E-09 | |
排名 | 1 | 4 | 5 | 7 | 9 | 6 | 8 | 10 | 2 | 3 | |
f2 | 均值 | 2.31E+06 | 2.56E+07 | 2.71E+07 | 1.77E+08 | 2.14E+08 | 1.11E+08 | 1.30E+07 | 7.89E+08 | 2.49E+06 | 2.46E+06 |
方差 | 7.38E+05 | 8.93E+06 | 9.47E+06 | 5.09E+07 | 4.22E+07 | 3.18E+07 | 5.34E+06 | 1.93E+08 | 9.21E+05 | 9.21E+05 | |
排名 | 1 | 5 | 6 | 8 | 9 | 7 | 4 | 10 | 3 | 2 | |
f3 | 均值 | 9.35E+03 | 3.10E+04 | 4.25E+04 | 7.00E+04 | 6.48E+04 | 7.83E+04 | 5.84E+04 | 8.79E+04 | 1.16E+04 | 1.12E+04 |
方差 | 8.75E+03 | 4.95E+03 | 7.71E+03 | 1.39E+04 | 5.81E+03 | 5.53E+03 | 6.66E+03 | 1.10E+04 | 1.21E+04 | 1.07E+04 | |
排名 | 1 | 4 | 5 | 8 | 7 | 9 | 6 | 10 | 3 | 2 | |
f4 | 均值 | 3.90E-03 | 2.51E+00 | 1.72E+02 | 2.81E+02 | 3.07E+03 | 7.32E+02 | 9.26E+02 | 1.04E+04 | 3.61E-03 | 3.56E-03 |
方差 | 4.74E-04 | 6.72E-01 | 3.42E+01 | 7.23E+01 | 1.33E+03 | 2.05E+02 | 4.77E+02 | 2.26E+03 | 4.75E-04 | 5.69E-04 | |
排名 | 3 | 4 | 5 | 6 | 9 | 7 | 8 | 10 | 2 | 1 | |
f5 | 均值 | 5.52E+00 | 7.14E+00 | 5.81E+02 | 3.54E+02 | 5.78E+02 | 8.84E+02 | 5.09E+02 | 9.48E+02 | 6.51E+00 | 5.86E+00 |
方差 | 1.71E+00 | 2.22E+00 | 7.84E+01 | 3.82E+01 | 7.49E+01 | 7.81E+01 | 6.09E+01 | 8.25E+01 | 2.16E+00 | 2.21E+00 | |
排名 | 1 | 4 | 8 | 5 | 7 | 9 | 6 | 10 | 3 | 2 | |
f6 | 均值 | 1.40E+01 | 1.85E+01 | 7.31E+03 | 9.25E+03 | 1.35E+04 | 1.05E+04 | 9.85E+03 | 1.43E+04 | 1.64E+01 | 1.56E+01 |
方差 | 4.35E+00 | 4.26E+00 | 9.13E+02 | 1.19E+03 | 5.18E+02 | 1.11E+03 | 3.86E+02 | 4.41E+02 | 4.40E+00 | 6.81E+00 | |
排名 | 1 | 4 | 5 | 6 | 9 | 8 | 7 | 10 | 3 | 2 | |
f7 | 均值 | 7.96E+03 | 7.63E+03 | 7.88E+03 | 1.43E+04 | 1.49E+04 | 1.23E+04 | 1.17E+04 | 1.47E+04 | 7.84E+03 | 8.16E+03 |
方差 | 1.16E+03 | 8.63E+02 | 1.08E+03 | 5.88E+02 | 4.49E+02 | 1.11E+03 | 4.30E+02 | 4.58E+02 | 7.71E+02 | 1.13E+03 | |
排名 | 4 | 1 | 3 | 8 | 10 | 7 | 6 | 9 | 2 | 5 | |
f8 | 均值 | 4.22E-01 | 5.04E-01 | 1.65E+00 | 3.76E+00 | 4.05E+00 | 2.75E+00 | 3.82E+00 | 3.84E+00 | 3.00E-01 | 1.72E+00 |
方差 | 1.98E-01 | 2.36E-01 | 4.42E-01 | 3.37E-01 | 5.10E-01 | 4.90E-01 | 2.73E-01 | 3.58E-01 | 1.37E-01 | 5.54E-01 | |
排名 | 2 | 3 | 4 | 7 | 10 | 6 | 8 | 9 | 1 | 5 | |
f9 | 均值 | 6.45E+01 | 6.95E+01 | 6.88E+02 | 6.86E+02 | 7.80E+02 | 1.16E+03 | 8.46E+02 | 1.72E+03 | 6.47E+01 | 6.43E+01 |
方差 | 2.09E+00 | 2.96E+00 | 1.58E+02 | 6.91E+01 | 6.01E+01 | 1.46E+02 | 1.03E+02 | 1.32E+02 | 2.40E+00 | 2.39E+00 | |
排名 | 2 | 4 | 6 | 5 | 7 | 9 | 8 | 10 | 3 | 1 | |
f10 | 均值 | 3.66E+00 | 4.83E+00 | 8.60E+01 | 1.33E+02 | 3.27E+04 | 2.74E+02 | 6.43E+03 | 3.31E+05 | 3.98E+00 | 3.85E+00 |
方差 | 4.48E-01 | 8.53E-01 | 3.38E+01 | 6.78E+01 | 8.35E+04 | 1.00E+02 | 7.12E+03 | 2.05E+05 | 3.60E-01 | 8.00E-01 | |
排名 | 1 | 4 | 5 | 6 | 9 | 7 | 8 | 10 | 3 | 2 | |
f11 | 均值 | 7.62E+02 | 9.73E+02 | 9.39E+02 | 1.46E+03 | 3.62E+03 | 2.05E+03 | 2.17E+03 | 5.10E+03 | 7.25E+02 | 8.59E+02 |
方差 | 3.73E+02 | 2.88E+02 | 2.20E+02 | 4.91E+02 | 1.33E+02 | 6.45E+02 | 3.79E+02 | 2.00E+02 | 4.60E+02 | 2.68E+02 | |
排名 | 2 | 5 | 4 | 6 | 9 | 7 | 8 | 10 | 1 | 3 | |
f12 | 均值 | 6.19E+01 | 8.37E+01 | 1.08E+04 | 9.93E+03 | 1.39E+04 | 1.28E+04 | 1.13E+04 | 1.51E+04 | 3.81E+01 | 3.70E+01 |
方差 | 6.49E+01 | 7.29E+01 | 1.51E+03 | 1.27E+03 | 9.22E+02 | 1.19E+03 | 4.98E+02 | 4.63E+02 | 7.58E+00 | 8.37E+00 | |
排名 | 3 | 4 | 6 | 5 | 9 | 8 | 7 | 10 | 2 | 1 | |
f13 | 均值 | 8.02E+03 | 9.30E+03 | 1.14E+04 | 1.48E+04 | 1.55E+04 | 1.36E+04 | 1.23E+04 | 1.53E+04 | 8.40E+03 | 9.45E+03 |
方差 | 6.74E+02 | 8.26E+02 | 1.12E+03 | 5.18E+02 | 5.95E+02 | 1.52E+03 | 6.23E+02 | 4.93E+02 | 7.92E+02 | 8.43E+02 | |
排名 | 1 | 3 | 5 | 8 | 10 | 7 | 6 | 9 | 2 | 4 | |
f14 | 均值 | 2.12E+02 | 2.03E+02 | 3.93E+02 | 4.18E+02 | 4.22E+02 | 4.58E+02 | 2.78E+02 | 4.86E+02 | 2.01E+02 | 2.01E+02 |
方差 | 3.96E+01 | 1.91E+00 | 1.28E+02 | 8.96E+01 | 9.97E+01 | 8.58E+01 | 1.15E+02 | 4.48E+01 | 1.53E+00 | 1.60E+00 | |
排名 | 4 | 3 | 6 | 7 | 8 | 9 | 5 | 10 | 1 | 2 | |
f15 | 均值 | 6.09E+02 | 7.29E+02 | 4.82E+03 | 2.53E+03 | 4.08E+03 | 8.04E+03 | 3.77E+03 | 6.73E+03 | 4.00E+02 | 7.10E+02 |
方差 | 8.10E+02 | 1.01E+03 | 2.72E+03 | 1.78E+03 | 9.41E+02 | 1.76E+03 | 1.79E+03 | 7.71E+02 | 9.22E-05 | 9.81E+02 | |
排名 | 2 | 4 | 8 | 5 | 7 | 10 | 6 | 9 | 1 | 3 | |
Count | 7 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 4 | 3 | |
Ave rank | 1.93 | 3.73 | 5.4 | 6.47 | 8.6 | 7.73 | 6.73 | 9.73 | 2.13 | 2.53 | |
Total rank | 1 | 4 | 5 | 6 | 9 | 8 | 7 | 10 | 2 | 3 |
算法 | 维度 | ||
---|---|---|---|
10 | 30 | 50 | |
P-value | 3.38E-12 | 6.41E-20 | 8.55E-15 |
NYYPO | 2.87 | 2.00 | 1.93 |
YYPO-SA1 | 5.93 | 3.93 | 3.73 |
CSA | 5.60 | 5.33 | 5.40 |
PSO | 5.40 | 6.00 | 6.47 |
GWO | 9.27 | 8.53 | 8.60 |
WOA | 5.27 | 8.47 | 6.67 |
FPA | 4.07 | 6.67 | 6.73 |
SSA | 9.40 | 9.40 | 9.73 |
NYYPO1 | 3.60 | 2.27 | 2.13 |
NYYPO2 | 3.60 | 3.40 | 2.53 |
Tab. 5 Results of Friedman test
算法 | 维度 | ||
---|---|---|---|
10 | 30 | 50 | |
P-value | 3.38E-12 | 6.41E-20 | 8.55E-15 |
NYYPO | 2.87 | 2.00 | 1.93 |
YYPO-SA1 | 5.93 | 3.93 | 3.73 |
CSA | 5.60 | 5.33 | 5.40 |
PSO | 5.40 | 6.00 | 6.47 |
GWO | 9.27 | 8.53 | 8.60 |
WOA | 5.27 | 8.47 | 6.67 |
FPA | 4.07 | 6.67 | 6.73 |
SSA | 9.40 | 9.40 | 9.73 |
NYYPO1 | 3.60 | 2.27 | 2.13 |
NYYPO2 | 3.60 | 3.40 | 2.53 |
海拔 | 算法 | 半径R/m | 高度H/m | 功率 | COE/ ($·kWh-1) |
---|---|---|---|---|---|
2 000 | N⁃YYPO | 20.5644 | 61.6720 | 0.4115 | 0.016639 |
3D-YYPO | 36.832 6 | 65.719 0 | 1.194 7 | 0.049 163 | |
3 000 | N⁃YYPO | 20.5427 | 60.5744 | 0.4219 | 0.019132 |
3D-YYPO | 37.271 2 | 64.515 7 | 1.141 8 | 0.052 408 | |
4 000 | N⁃YYPO | 20.5428 | 60.5745 | 0.4219 | 0.021218 |
3D-YYPO | 37.658 0 | 63.249 5 | 1.086 0 | 0.055 921 |
Tab. 6 Optimal results achieved by algorithms at different altitudes
海拔 | 算法 | 半径R/m | 高度H/m | 功率 | COE/ ($·kWh-1) |
---|---|---|---|---|---|
2 000 | N⁃YYPO | 20.5644 | 61.6720 | 0.4115 | 0.016639 |
3D-YYPO | 36.832 6 | 65.719 0 | 1.194 7 | 0.049 163 | |
3 000 | N⁃YYPO | 20.5427 | 60.5744 | 0.4219 | 0.019132 |
3D-YYPO | 37.271 2 | 64.515 7 | 1.141 8 | 0.052 408 | |
4 000 | N⁃YYPO | 20.5428 | 60.5745 | 0.4219 | 0.021218 |
3D-YYPO | 37.658 0 | 63.249 5 | 1.086 0 | 0.055 921 |
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[1] | XU Qiuyan, MA Liang, LIU Yong. Yin-Yang-pair optimization algorithm based on chaos search and intricate operator [J]. Journal of Computer Applications, 2020, 40(8): 2305-2312. |
[2] | CHEN Chuang, Ryad CHELLALI, XING Yin. Improved grey wolf optimizer algorithm using dynamic weighting and probabilistic disturbance strategy [J]. Journal of Computer Applications, 2017, 37(12): 3493-3497. |
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