计算机科学与探索 ›› 2022, Vol. 16 ›› Issue (7): 1661-1672.DOI: 10.3778/j.issn.1673-9418.2012066
收稿日期:
2020-11-30
修回日期:
2021-01-25
出版日期:
2022-07-01
发布日期:
2021-01-28
作者简介:
李守玉(1996—),男,贵州安顺人,硕士研究生,主要研究方向为进化计算、深度学习。 基金资助:
LI Shouyu1, HE Qing1,+(), DU Nisuo2
Received:
2020-11-30
Revised:
2021-01-25
Online:
2022-07-01
Published:
2021-01-28
Supported by:
摘要:
针对蝴蝶优化算法(BOA)寻优精度低和易陷入局部最优等缺点,提出了混沌反馈共享和群体协同效应的蝴蝶优化算法(CFSBOA)。首先,利用Hénon混沌初始化种群,能够使种群尽可能地覆盖搜索盲区,增加种群多样性,提高算法寻优性能;其次,利用反馈控制电路中正负反馈作用机制的思想,构建蝴蝶之间的反馈共享交流网络,使得蝴蝶个体能够接收来自多个方向的信息,帮助种群定位最优解的位置并执行精细搜索,增强算法逃离局部最优的能力和加快算法收敛的速度;最后,利用群体协同效应机制,提高和平衡全局与局部搜索的能力,增强算法的全局和局部的寻优能力。使用不同维度的基准测试函数、统计检验、Wilcoxon检验及多类型的CEC2014部分函数验证改进蝴蝶优化算法的性能,并与新改进的蝴蝶算法及其他群智能算法进行对比,实验结果表明该算法具有明显优势。
中图分类号:
李守玉, 何庆, 杜逆索. 混沌反馈共享和群体协同效应的蝴蝶优化算法[J]. 计算机科学与探索, 2022, 16(7): 1661-1672.
LI Shouyu, HE Qing, DU Nisuo. Butterfly Optimization Algorithm for Chaotic Feedback Sharing and Group Synergy[J]. Journal of Frontiers of Computer Science and Technology, 2022, 16(7): 1661-1672.
函数 | 维度 | 特征 | 范围 | 最佳值 |
---|---|---|---|---|
| 10 | US | [-100,100] | 0 |
| 50 | UN | [-10,10] | 0 |
| 50 | UN | [-100,100] | 0 |
| 50 | US | [-100,100] | 0 |
| 2 | UN | [-10,10] | 0 |
| 2 | MN | [-100,100] | 0 |
| 10 | MS | [-5.12,5.12] | 0 |
| 50 | MN | [-32,32] | 0 |
| 100 | MN | [-600,600] | 0 |
| 2 | MN | [-65.56,65.56] | ≈1 |
| 100 | MN | [-10,10] | 0 |
| 200 | MN | [-100,100] | 0 |
表1 基准测试函数
Table 1 Benchmark functions
函数 | 维度 | 特征 | 范围 | 最佳值 |
---|---|---|---|---|
| 10 | US | [-100,100] | 0 |
| 50 | UN | [-10,10] | 0 |
| 50 | UN | [-100,100] | 0 |
| 50 | US | [-100,100] | 0 |
| 2 | UN | [-10,10] | 0 |
| 2 | MN | [-100,100] | 0 |
| 10 | MS | [-5.12,5.12] | 0 |
| 50 | MN | [-32,32] | 0 |
| 100 | MN | [-600,600] | 0 |
| 2 | MN | [-65.56,65.56] | ≈1 |
| 100 | MN | [-10,10] | 0 |
| 200 | MN | [-100,100] | 0 |
算法 | 主要参数 |
---|---|
CFSBOA | P=0.8,c=0.01, |
SBOA | P=0.8,c=0.01, |
FBOA | P=0.8,c=0.01, |
CBOA | P=0.8,c=0.01, |
BOA | P=0.8,c=0.01, |
MFO | — |
SSA | m=2 |
GWO | |
表2 主要参数
Table 2 Main parameters
算法 | 主要参数 |
---|---|
CFSBOA | P=0.8,c=0.01, |
SBOA | P=0.8,c=0.01, |
FBOA | P=0.8,c=0.01, |
CBOA | P=0.8,c=0.01, |
BOA | P=0.8,c=0.01, |
MFO | — |
SSA | m=2 |
GWO | |
函数 | 算法 | 最优值 | 平均值 | 标准差 | SR/% | T/s | 函数 | 算法 | 最优值 | 平均值 | 标准差 | SR/% | T/s |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| CFSBOA | 0.00E+00 | 0.00E+00 | 0.00E+00 | 100 | 0.40 | | CFSBOA | 0.00E+00 | 0.00E+00 | 0.00E+00 | 100 | 0.63 |
SBOA | 0.00E+00 | 0.00E+00 | 0.00E+00 | 100 | 0.25 | SBOA | 0.00E+00 | 0.00E+00 | 0.00E+00 | 100 | 0.46 | ||
FBOA | 6.51E-80 | 9.13E-79 | 9.00E-79 | 100 | 0.37 | FBOA | 0.00E+00 | 0.00E+00 | 0.00E+00 | 100 | 0.56 | ||
CBOA | 7.30E-13 | 1.09E-12 | 3.10E-13 | 100 | 0.23 | CBOA | 0.00E+00 | 5.68E-16 | 2.81E-15 | 100 | 0.40 | ||
BOA | 7.13E-12 | 1.01E-11 | 1.50E-12 | 100 | 0.22 | BOA | 2.84E-14 | 2.49E+01 | 2.11E+01 | 28 | 0.38 | ||
MFO | 3.91E-16 | 3.44E-13 | 5.72E-13 | 100 | 0.11 | MFO | 5.97E+00 | 2.47E+01 | 1.47E+01 | 0 | 0.16 | ||
SSA | 3.12E-10 | 9.43E-10 | 3.07E-10 | 100 | 0.14 | SSA | 2.98E+00 | 1.68E+01 | 8.34E+00 | 0 | 0.18 | ||
GWO | 7.01E-61 | 1.48E-56 | 7.76E-56 | 100 | 0.11 | GWO | 0.00E+00 | 4.25E-01 | 1.06E+00 | 88 | 0.16 | ||
| CFSBOA | 2.02E-225 | 2.53E-169 | 0.00E+00 | 100 | 0.47 | | CFSBOA | 8.88E-16 | 8.88E-16 | 0.00E+00 | 100 | 0.82 |
SBOA | 4.51E-149 | 2.81E-113 | 1.99E-112 | 100 | 0.28 | SBOA | 8.88E-16 | 8.88E-16 | 0.00E+00 | 100 | 0.54 | ||
FBOA | 2.68E-180 | 6.61E+23 | 3.85E+24 | 70 | 0.43 | FBOA | 8.88E-16 | 8.88E-16 | 0.00E+00 | 100 | 0.78 | ||
CBOA | 3.00E-12 | 1.73E-01 | 6.91E-01 | 92 | 0.27 | CBOA | 7.55E-14 | 5.62E-12 | 6.87E-12 | 100 | 0.49 | ||
BOA | 4.38E-13 | 5.40E+24 | 3.64E+25 | 68 | 0.26 | BOA | 5.15E-09 | 5.94E-09 | 3.51E-10 | 100 | 0.47 | ||
MFO | 7.42E+00 | 6.99E+01 | 3.45E+01 | 0 | 0.23 | MFO | 1.29E+01 | 1.93E+01 | 1.20E+00 | 0 | 0.31 | ||
SSA | 4.02E+00 | 1.08E+01 | 7.95E+00 | 0 | 0.21 | SSA | 2.87E+00 | 4.64E+00 | 1.13E+00 | 0 | 0.29 | ||
GWO | 6.80E-13 | 2.80E-12 | 2.12E-12 | 100 | 0.25 | GWO | 1.14E-11 | 3.57E-11 | 2.08E-11 | 100 | 0.34 | ||
| CFSBOA | 0.00E+00 | 0.00E+00 | 0.00E+00 | 100 | 4.55 | | CFSBOA | 0.00E+00 | 0.00E+00 | 0.00E+00 | 100 | 0.96 |
SBOA | 0.00E+00 | 0.00E+00 | 0.00E+00 | 100 | 2.31 | SBOA | 0.00E+00 | 0.00E+00 | 0.00E+00 | 100 | 0.62 | ||
FBOA | 2.94E-217 | 5.73E-198 | 0.00E+00 | 100 | 4.50 | FBOA | 0.00E+00 | 0.00E+00 | 0.00E+00 | 100 | 0.92 | ||
CBOA | 1.61E-16 | 1.38E-12 | 1.24E-12 | 100 | 2.29 | CBOA | 6.35E-13 | 1.36E-12 | 3.75E-13 | 100 | 0.57 | ||
BOA | 1.08E-11 | 1.32E-11 | 9.79E-13 | 100 | 2.31 | BOA | 1.98E-12 | 1.28E-11 | 4.12E-12 | 100 | 0.56 | ||
MFO | 3.27E+04 | 6.62E+04 | 2.13E+04 | 0 | 1.26 | MFO | 3.04E+02 | 5.42E+02 | 1.43E+02 | 0 | 0.49 | ||
SSA | 3.39E+03 | 9.13E+03 | 3.85E+03 | 0 | 1.23 | SSA | 7.20E+00 | 1.34E+01 | 3.20E+00 | 0 | 0.44 | ||
GWO | 3.05E-03 | 8.96E-01 | 5.13E+00 | 0 | 1.25 | GWO | 1.09E-13 | 1.94E-03 | 6.75E-03 | 88 | 0.52 | ||
| CFSBOA | 1.35E-193 | 2.08E-156 | 1.42E-155 | 100 | 0.56 | | CFSBOA | 9.98E-01 | 9.98E-01 | 1.84E-10 | 100 | 3.53 |
SBOA | 1.71E-164 | 4.69E-153 | 1.66E-152 | 100 | 0.33 | SBOA | 9.98E-01 | 5.02E+00 | 4.21E+00 | 8 | 1.91 | ||
FBOA | 1.11E-28 | 2.75E-28 | 9.52E-29 | 100 | 0.54 | FBOA | 9.98E-01 | 1.41E+00 | 6.41E-01 | 30 | 3.49 | ||
CBOA | 6.68E-14 | 2.89E-11 | 8.86E-11 | 100 | 0.32 | CBOA | 9.98E-01 | 9.98E-01 | 2.11E-10 | 100 | 1.86 | ||
BOA | 5.51E-09 | 6.20E-09 | 3.67E-10 | 100 | 0.31 | BOA | 9.98E-01 | 1.31E+00 | 5.06E-01 | 16 | 1.80 | ||
MFO | 6.74E+01 | 8.32E+01 | 5.17E+00 | 0 | 0.25 | MFO | 9.98E-01 | 1.99E+00 | 1.49E+00 | 32 | 0.85 | ||
SSA | 1.22E+01 | 2.00E+01 | 3.49E+00 | 0 | 0.23 | SSA | 9.98E-01 | 1.22E+00 | 6.43E-01 | 88 | 0.88 | ||
GWO | 2.92E-05 | 3.51E-04 | 3.50E-04 | 10 | 0.26 | GWO | 9.98E-01 | 4.42E+00 | 4.25E+00 | 42 | 0.86 | ||
| CFSBOA | 0.00E+00 | 2.55E-297 | 0.00E+00 | 100 | 0.61 | | CFSBOA | 2.17E-215 | 6.29E-165 | 0.00E+00 | 100 | 0.61 |
SBOA | 0.00E+00 | 0.00E+00 | 0.00E+00 | 100 | 0.41 | SBOA | 5.03E-165 | 1.76E-151 | 1.19E-150 | 100 | 0.45 | ||
FBOA | 3.41E-51 | 3.63E-49 | 8.70E-49 | 100 | 0.57 | FBOA | 1.41E-45 | 3.18E-44 | 3.64E-44 | 100 | 0.59 | ||
CBOA | 1.07E-18 | 6.74E-13 | 2.56E-13 | 100 | 0.37 | CBOA | 9.26E-12 | 3.79E-03 | 1.71E-02 | 76 | 0.44 | ||
BOA | 6.30E-17 | 9.28E-13 | 3.70E-13 | 100 | 0.37 | BOA | 3.24E-10 | 8.30E-10 | 3.61E-10 | 100 | 0.43 | ||
MFO | 1.34E-86 | 2.53E-22 | 1.79E-21 | 100 | 0.13 | MFO | 4.29E+01 | 6.64E+01 | 1.60E+01 | 0 | 0.39 | ||
SSA | 4.86E-18 | 1.29E-15 | 1.85E-15 | 100 | 0.16 | SSA | 1.93E+01 | 2.94E+01 | 5.58E+00 | 0 | 0.34 | ||
GWO | 5.97E-129 | 1.82E-102 | 9.01E-102 | 100 | 0.14 | GWO | 2.80E-08 | 3.39E-03 | 2.86E-03 | 6 | 0.43 | ||
| CFSBOA | 0.00E+00 | 0.00E+00 | 0.00E+00 | 100 | 0.66 | | CFSBOA | 0.00E+00 | 0.00E+00 | 0.00E+00 | 100 | 38.72 |
SBOA | 0.00E+00 | 0.00E+00 | 0.00E+00 | 100 | 0.44 | SBOA | 1.97E-305 | 3.16E-258 | 0.00E+00 | 100 | 19.41 | ||
FBOA | 0.00E+00 | 1.53E-02 | 1.10E-02 | 4 | 0.58 | FBOA | 0.00E+00 | 6.38E-106 | 4.51E-105 | 100 | 38.54 | ||
CBOA | 1.44E-15 | 1.94E-04 | 1.37E-03 | 96 | 0.37 | CBOA | 3.99E-14 | 7.45E-02 | 4.45E-02 | 18 | 19.47 | ||
BOA | 1.65E-05 | 1.28E-02 | 7.97E-03 | 0 | 0.36 | BOA | 1.52E-16 | 3.98E-03 | 1.97E-02 | 94 | 19.44 | ||
MFO | 0.00E+00 | 9.49E-03 | 4.81E-03 | 10 | 0.14 | MFO | 0.00E+00 | 5.56E-30 | 9.42E-30 | 100 | 10.08 | ||
SSA | 2.60E-14 | 5.05E-03 | 4.90E-03 | 46 | 0.17 | SSA | 1.12E-16 | 2.35E-12 | 3.52E-12 | 100 | 10.00 | ||
GWO | 0.00E+00 | 5.64E-03 | 4.84E-03 | 42 | 0.14 | GWO | 7.21E-08 | 3.75E-04 | 7.36E-04 | 30 | 10.19 |
表3 基准测试函数结果对比
Table 3 Results comparison of benchmark test functions
函数 | 算法 | 最优值 | 平均值 | 标准差 | SR/% | T/s | 函数 | 算法 | 最优值 | 平均值 | 标准差 | SR/% | T/s |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| CFSBOA | 0.00E+00 | 0.00E+00 | 0.00E+00 | 100 | 0.40 | | CFSBOA | 0.00E+00 | 0.00E+00 | 0.00E+00 | 100 | 0.63 |
SBOA | 0.00E+00 | 0.00E+00 | 0.00E+00 | 100 | 0.25 | SBOA | 0.00E+00 | 0.00E+00 | 0.00E+00 | 100 | 0.46 | ||
FBOA | 6.51E-80 | 9.13E-79 | 9.00E-79 | 100 | 0.37 | FBOA | 0.00E+00 | 0.00E+00 | 0.00E+00 | 100 | 0.56 | ||
CBOA | 7.30E-13 | 1.09E-12 | 3.10E-13 | 100 | 0.23 | CBOA | 0.00E+00 | 5.68E-16 | 2.81E-15 | 100 | 0.40 | ||
BOA | 7.13E-12 | 1.01E-11 | 1.50E-12 | 100 | 0.22 | BOA | 2.84E-14 | 2.49E+01 | 2.11E+01 | 28 | 0.38 | ||
MFO | 3.91E-16 | 3.44E-13 | 5.72E-13 | 100 | 0.11 | MFO | 5.97E+00 | 2.47E+01 | 1.47E+01 | 0 | 0.16 | ||
SSA | 3.12E-10 | 9.43E-10 | 3.07E-10 | 100 | 0.14 | SSA | 2.98E+00 | 1.68E+01 | 8.34E+00 | 0 | 0.18 | ||
GWO | 7.01E-61 | 1.48E-56 | 7.76E-56 | 100 | 0.11 | GWO | 0.00E+00 | 4.25E-01 | 1.06E+00 | 88 | 0.16 | ||
| CFSBOA | 2.02E-225 | 2.53E-169 | 0.00E+00 | 100 | 0.47 | | CFSBOA | 8.88E-16 | 8.88E-16 | 0.00E+00 | 100 | 0.82 |
SBOA | 4.51E-149 | 2.81E-113 | 1.99E-112 | 100 | 0.28 | SBOA | 8.88E-16 | 8.88E-16 | 0.00E+00 | 100 | 0.54 | ||
FBOA | 2.68E-180 | 6.61E+23 | 3.85E+24 | 70 | 0.43 | FBOA | 8.88E-16 | 8.88E-16 | 0.00E+00 | 100 | 0.78 | ||
CBOA | 3.00E-12 | 1.73E-01 | 6.91E-01 | 92 | 0.27 | CBOA | 7.55E-14 | 5.62E-12 | 6.87E-12 | 100 | 0.49 | ||
BOA | 4.38E-13 | 5.40E+24 | 3.64E+25 | 68 | 0.26 | BOA | 5.15E-09 | 5.94E-09 | 3.51E-10 | 100 | 0.47 | ||
MFO | 7.42E+00 | 6.99E+01 | 3.45E+01 | 0 | 0.23 | MFO | 1.29E+01 | 1.93E+01 | 1.20E+00 | 0 | 0.31 | ||
SSA | 4.02E+00 | 1.08E+01 | 7.95E+00 | 0 | 0.21 | SSA | 2.87E+00 | 4.64E+00 | 1.13E+00 | 0 | 0.29 | ||
GWO | 6.80E-13 | 2.80E-12 | 2.12E-12 | 100 | 0.25 | GWO | 1.14E-11 | 3.57E-11 | 2.08E-11 | 100 | 0.34 | ||
| CFSBOA | 0.00E+00 | 0.00E+00 | 0.00E+00 | 100 | 4.55 | | CFSBOA | 0.00E+00 | 0.00E+00 | 0.00E+00 | 100 | 0.96 |
SBOA | 0.00E+00 | 0.00E+00 | 0.00E+00 | 100 | 2.31 | SBOA | 0.00E+00 | 0.00E+00 | 0.00E+00 | 100 | 0.62 | ||
FBOA | 2.94E-217 | 5.73E-198 | 0.00E+00 | 100 | 4.50 | FBOA | 0.00E+00 | 0.00E+00 | 0.00E+00 | 100 | 0.92 | ||
CBOA | 1.61E-16 | 1.38E-12 | 1.24E-12 | 100 | 2.29 | CBOA | 6.35E-13 | 1.36E-12 | 3.75E-13 | 100 | 0.57 | ||
BOA | 1.08E-11 | 1.32E-11 | 9.79E-13 | 100 | 2.31 | BOA | 1.98E-12 | 1.28E-11 | 4.12E-12 | 100 | 0.56 | ||
MFO | 3.27E+04 | 6.62E+04 | 2.13E+04 | 0 | 1.26 | MFO | 3.04E+02 | 5.42E+02 | 1.43E+02 | 0 | 0.49 | ||
SSA | 3.39E+03 | 9.13E+03 | 3.85E+03 | 0 | 1.23 | SSA | 7.20E+00 | 1.34E+01 | 3.20E+00 | 0 | 0.44 | ||
GWO | 3.05E-03 | 8.96E-01 | 5.13E+00 | 0 | 1.25 | GWO | 1.09E-13 | 1.94E-03 | 6.75E-03 | 88 | 0.52 | ||
| CFSBOA | 1.35E-193 | 2.08E-156 | 1.42E-155 | 100 | 0.56 | | CFSBOA | 9.98E-01 | 9.98E-01 | 1.84E-10 | 100 | 3.53 |
SBOA | 1.71E-164 | 4.69E-153 | 1.66E-152 | 100 | 0.33 | SBOA | 9.98E-01 | 5.02E+00 | 4.21E+00 | 8 | 1.91 | ||
FBOA | 1.11E-28 | 2.75E-28 | 9.52E-29 | 100 | 0.54 | FBOA | 9.98E-01 | 1.41E+00 | 6.41E-01 | 30 | 3.49 | ||
CBOA | 6.68E-14 | 2.89E-11 | 8.86E-11 | 100 | 0.32 | CBOA | 9.98E-01 | 9.98E-01 | 2.11E-10 | 100 | 1.86 | ||
BOA | 5.51E-09 | 6.20E-09 | 3.67E-10 | 100 | 0.31 | BOA | 9.98E-01 | 1.31E+00 | 5.06E-01 | 16 | 1.80 | ||
MFO | 6.74E+01 | 8.32E+01 | 5.17E+00 | 0 | 0.25 | MFO | 9.98E-01 | 1.99E+00 | 1.49E+00 | 32 | 0.85 | ||
SSA | 1.22E+01 | 2.00E+01 | 3.49E+00 | 0 | 0.23 | SSA | 9.98E-01 | 1.22E+00 | 6.43E-01 | 88 | 0.88 | ||
GWO | 2.92E-05 | 3.51E-04 | 3.50E-04 | 10 | 0.26 | GWO | 9.98E-01 | 4.42E+00 | 4.25E+00 | 42 | 0.86 | ||
| CFSBOA | 0.00E+00 | 2.55E-297 | 0.00E+00 | 100 | 0.61 | | CFSBOA | 2.17E-215 | 6.29E-165 | 0.00E+00 | 100 | 0.61 |
SBOA | 0.00E+00 | 0.00E+00 | 0.00E+00 | 100 | 0.41 | SBOA | 5.03E-165 | 1.76E-151 | 1.19E-150 | 100 | 0.45 | ||
FBOA | 3.41E-51 | 3.63E-49 | 8.70E-49 | 100 | 0.57 | FBOA | 1.41E-45 | 3.18E-44 | 3.64E-44 | 100 | 0.59 | ||
CBOA | 1.07E-18 | 6.74E-13 | 2.56E-13 | 100 | 0.37 | CBOA | 9.26E-12 | 3.79E-03 | 1.71E-02 | 76 | 0.44 | ||
BOA | 6.30E-17 | 9.28E-13 | 3.70E-13 | 100 | 0.37 | BOA | 3.24E-10 | 8.30E-10 | 3.61E-10 | 100 | 0.43 | ||
MFO | 1.34E-86 | 2.53E-22 | 1.79E-21 | 100 | 0.13 | MFO | 4.29E+01 | 6.64E+01 | 1.60E+01 | 0 | 0.39 | ||
SSA | 4.86E-18 | 1.29E-15 | 1.85E-15 | 100 | 0.16 | SSA | 1.93E+01 | 2.94E+01 | 5.58E+00 | 0 | 0.34 | ||
GWO | 5.97E-129 | 1.82E-102 | 9.01E-102 | 100 | 0.14 | GWO | 2.80E-08 | 3.39E-03 | 2.86E-03 | 6 | 0.43 | ||
| CFSBOA | 0.00E+00 | 0.00E+00 | 0.00E+00 | 100 | 0.66 | | CFSBOA | 0.00E+00 | 0.00E+00 | 0.00E+00 | 100 | 38.72 |
SBOA | 0.00E+00 | 0.00E+00 | 0.00E+00 | 100 | 0.44 | SBOA | 1.97E-305 | 3.16E-258 | 0.00E+00 | 100 | 19.41 | ||
FBOA | 0.00E+00 | 1.53E-02 | 1.10E-02 | 4 | 0.58 | FBOA | 0.00E+00 | 6.38E-106 | 4.51E-105 | 100 | 38.54 | ||
CBOA | 1.44E-15 | 1.94E-04 | 1.37E-03 | 96 | 0.37 | CBOA | 3.99E-14 | 7.45E-02 | 4.45E-02 | 18 | 19.47 | ||
BOA | 1.65E-05 | 1.28E-02 | 7.97E-03 | 0 | 0.36 | BOA | 1.52E-16 | 3.98E-03 | 1.97E-02 | 94 | 19.44 | ||
MFO | 0.00E+00 | 9.49E-03 | 4.81E-03 | 10 | 0.14 | MFO | 0.00E+00 | 5.56E-30 | 9.42E-30 | 100 | 10.08 | ||
SSA | 2.60E-14 | 5.05E-03 | 4.90E-03 | 46 | 0.17 | SSA | 1.12E-16 | 2.35E-12 | 3.52E-12 | 100 | 10.00 | ||
GWO | 0.00E+00 | 5.64E-03 | 4.84E-03 | 42 | 0.14 | GWO | 7.21E-08 | 3.75E-04 | 7.36E-04 | 30 | 10.19 |
F | p-value win | ||||||
---|---|---|---|---|---|---|---|
BOA | CBOA | FBOA | SBOA | MFO | SSA | GWO | |
| 3.31E-20+ | 3.31E-20+ | 3.31E-20+ | N/A= | 3.31E-20+ | 3.31E-20+ | 3.31E-20+ |
| 7.07E-18+ | 7.07E-18+ | 2.78E-17+ | 7.07E-18+ | 7.07E-18+ | 7.07E-18+ | 7.07E-18+ |
| 3.31E-20+ | 3.31E-20+ | 3.31E-20+ | N/A= | 3.31E-20+ | 3.31E-20+ | 3.31E-20+ |
| 7.07E-18+ | 7.07E-18+ | 7.07E-18+ | 2.39E-13+ | 7.07E-18+ | 7.07E-18+ | 7.07E-18+ |
| 1.12E-18+ | 1.12E-18+ | 1.12E-18+ | 6.50E-05+ | 1.12E-18+ | 1.12E-18+ | 1.12E-18+ |
| 3.31E-20+ | 3.31E-20+ | 3.31E-20+ | N/A= | 7.55E-21+ | 3.28E-20+ | 5.25E-13+ |
| 3.31E-20+ | 1.59E-01- | N/A= | N/A= | 3.31E-20+ | 3.31E-20+ | 1.82E-03+ |
| 3.31E-20+ | 3.31E-20+ | N/A= | N/A= | 3.31E-20+ | 3.31E-20+ | 3.31E-20+ |
| 3.31E-20+ | 3.31E-20+ | N/A= | N/A= | 3.31E-20+ | 3.31E-20+ | 3.31E-20+ |
| 7.07E-18+ | 5.74E-01- | 7.07E-18+ | 7.07E-18+ | 2.38E-12+ | 3.59E-12+ | 1.27E-12+ |
| 7.07E-18+ | 7.07E-18+ | 7.07E-18+ | 7.07E-18+ | 7.07E-18+ | 7.07E-18+ | 7.07E-18+ |
| 3.31E-20+ | 3.31E-20+ | N/A= | 3.31E-20+ | 1.75E-06+ | 3.31E-20+ | 3.31E-20+ |
+/=/- | 12/0/0 | 10/0/2 | 8/4/0 | 6/6/0 | 12/0/0 | 12/0/0 | 12/0/0 |
表4 基准函数Wilcoxon秩和检验的 p值
Table 4 p value for Wilcoxon’s rank-sum test on benchmark functions
F | p-value win | ||||||
---|---|---|---|---|---|---|---|
BOA | CBOA | FBOA | SBOA | MFO | SSA | GWO | |
| 3.31E-20+ | 3.31E-20+ | 3.31E-20+ | N/A= | 3.31E-20+ | 3.31E-20+ | 3.31E-20+ |
| 7.07E-18+ | 7.07E-18+ | 2.78E-17+ | 7.07E-18+ | 7.07E-18+ | 7.07E-18+ | 7.07E-18+ |
| 3.31E-20+ | 3.31E-20+ | 3.31E-20+ | N/A= | 3.31E-20+ | 3.31E-20+ | 3.31E-20+ |
| 7.07E-18+ | 7.07E-18+ | 7.07E-18+ | 2.39E-13+ | 7.07E-18+ | 7.07E-18+ | 7.07E-18+ |
| 1.12E-18+ | 1.12E-18+ | 1.12E-18+ | 6.50E-05+ | 1.12E-18+ | 1.12E-18+ | 1.12E-18+ |
| 3.31E-20+ | 3.31E-20+ | 3.31E-20+ | N/A= | 7.55E-21+ | 3.28E-20+ | 5.25E-13+ |
| 3.31E-20+ | 1.59E-01- | N/A= | N/A= | 3.31E-20+ | 3.31E-20+ | 1.82E-03+ |
| 3.31E-20+ | 3.31E-20+ | N/A= | N/A= | 3.31E-20+ | 3.31E-20+ | 3.31E-20+ |
| 3.31E-20+ | 3.31E-20+ | N/A= | N/A= | 3.31E-20+ | 3.31E-20+ | 3.31E-20+ |
| 7.07E-18+ | 5.74E-01- | 7.07E-18+ | 7.07E-18+ | 2.38E-12+ | 3.59E-12+ | 1.27E-12+ |
| 7.07E-18+ | 7.07E-18+ | 7.07E-18+ | 7.07E-18+ | 7.07E-18+ | 7.07E-18+ | 7.07E-18+ |
| 3.31E-20+ | 3.31E-20+ | N/A= | 3.31E-20+ | 1.75E-06+ | 3.31E-20+ | 3.31E-20+ |
+/=/- | 12/0/0 | 10/0/2 | 8/4/0 | 6/6/0 | 12/0/0 | 12/0/0 | 12/0/0 |
算法 | MAE | Rank |
---|---|---|
CFSBOA | 1.66E-04 | 1 |
CBOA | 1.04E-02 | 2 |
SBOA | 2.98E-01 | 3 |
GWO | 3.52E-01 | 4 |
SSA | 8.46E+02 | 5 |
MFO | 5.38E+03 | 6 |
FBOA | 2.93E+22 | 7 |
BOA | 5.38E+22 | 8 |
表5 各算法MAE排名
Table 5 MAE ranking of each algorithm
算法 | MAE | Rank |
---|---|---|
CFSBOA | 1.66E-04 | 1 |
CBOA | 1.04E-02 | 2 |
SBOA | 2.98E-01 | 3 |
GWO | 3.52E-01 | 4 |
SSA | 8.46E+02 | 5 |
MFO | 5.38E+03 | 6 |
FBOA | 2.93E+22 | 7 |
BOA | 5.38E+22 | 8 |
函数 | 特征 | 定义域 | 最佳值 |
---|---|---|---|
CEC03 | UF | [-100,100] | 300 |
CEC05 | MF | [-100,100] | 500 |
CEC16 | HF | [-100,100] | 1 600 |
CEC25 | CF | [-100,100] | 2 500 |
CEC27 | CF | [-100,100] | 2 700 |
CEC30 | CF | [-100,100] | 3 000 |
表6 CEC2014函数(部分)
Table 6 CEC2014 function (part)
函数 | 特征 | 定义域 | 最佳值 |
---|---|---|---|
CEC03 | UF | [-100,100] | 300 |
CEC05 | MF | [-100,100] | 500 |
CEC16 | HF | [-100,100] | 1 600 |
CEC25 | CF | [-100,100] | 2 500 |
CEC27 | CF | [-100,100] | 2 700 |
CEC30 | CF | [-100,100] | 3 000 |
函数 | 指标 | CFSBOA | BOA | MFO | SSA | GWO | PSO |
---|---|---|---|---|---|---|---|
CEC03 | Mean | 8.951 0E+04 | 1.077 5E+10 | 9.546 7E+04 | 1.026 6E+05 | 5.368 9E+04 | 2.799 2E+04 |
Std | 4.765 1E+02 | 0.000 0E+00 | 5.072 7E+04 | 2.751 8E+04 | 1.387 3E+04 | 2.221 6E+04 | |
CEC05 | Mean | 5.211 5E+02 | 5.217 6E+02 | 5.203 2E+02 | 5.200 6E+02 | 5.210 8E+02 | 5.210 0E+02 |
Std | 8.644 2E-03 | 3.468 9E-13 | 1.530 4E-01 | 9.554 9E-02 | 4.418 3E-02 | 7.922 0E-02 | |
CEC16 | Mean | 1.613 4E+03 | 1.614 9E+03 | 1.612 8E+03 | 1.612 6E+03 | 1.612 2E+03 | 1.612 5E+03 |
Std | 2.494 5E-04 | 2.312 6E-13 | 5.504 8E-01 | 3.771 0E-01 | 5.385 8E-01 | 4.627 2E-01 | |
CEC25 | Mean | 2.700 0E+03 | 5.125 0E+03 | 2.719 0E+03 | 2.718 6E+03 | 2.713 9E+03 | 2.714 9E+03 |
Std | 0.000 0E+00 | 0.000 0E+00 | 1.021 0E+01 | 4.834 9E+00 | 6.214 1E+00 | 3.990 2E+00 | |
CEC27 | Mean | 2.900 0E+03 | 1.933 9E+04 | 3.627 7E+03 | 3.558 1E+03 | 3.464 5E+03 | 3.412 5E+03 |
Std | 0.000 0E+00 | 1.110 1E-11 | 1.995 7E+02 | 2.412 9E+02 | 1.317 1E+02 | 1.711 3E+02 | |
CEC30 | Mean | 3.200 0E+03 | 3.236 5E+07 | 4.084 2E+04 | 6.971 4E+04 | 1.222 8E+05 | 1.806 6E+04 |
Std | 0.000 0E+00 | 1.515 6E-08 | 3.337 1E+04 | 3.733 2E+04 | 7.403 6E+04 | 8.312 1E+03 |
表7 CEC2014测试函数的结果对比
Table 7 Comparison of CEC2014 test function results
函数 | 指标 | CFSBOA | BOA | MFO | SSA | GWO | PSO |
---|---|---|---|---|---|---|---|
CEC03 | Mean | 8.951 0E+04 | 1.077 5E+10 | 9.546 7E+04 | 1.026 6E+05 | 5.368 9E+04 | 2.799 2E+04 |
Std | 4.765 1E+02 | 0.000 0E+00 | 5.072 7E+04 | 2.751 8E+04 | 1.387 3E+04 | 2.221 6E+04 | |
CEC05 | Mean | 5.211 5E+02 | 5.217 6E+02 | 5.203 2E+02 | 5.200 6E+02 | 5.210 8E+02 | 5.210 0E+02 |
Std | 8.644 2E-03 | 3.468 9E-13 | 1.530 4E-01 | 9.554 9E-02 | 4.418 3E-02 | 7.922 0E-02 | |
CEC16 | Mean | 1.613 4E+03 | 1.614 9E+03 | 1.612 8E+03 | 1.612 6E+03 | 1.612 2E+03 | 1.612 5E+03 |
Std | 2.494 5E-04 | 2.312 6E-13 | 5.504 8E-01 | 3.771 0E-01 | 5.385 8E-01 | 4.627 2E-01 | |
CEC25 | Mean | 2.700 0E+03 | 5.125 0E+03 | 2.719 0E+03 | 2.718 6E+03 | 2.713 9E+03 | 2.714 9E+03 |
Std | 0.000 0E+00 | 0.000 0E+00 | 1.021 0E+01 | 4.834 9E+00 | 6.214 1E+00 | 3.990 2E+00 | |
CEC27 | Mean | 2.900 0E+03 | 1.933 9E+04 | 3.627 7E+03 | 3.558 1E+03 | 3.464 5E+03 | 3.412 5E+03 |
Std | 0.000 0E+00 | 1.110 1E-11 | 1.995 7E+02 | 2.412 9E+02 | 1.317 1E+02 | 1.711 3E+02 | |
CEC30 | Mean | 3.200 0E+03 | 3.236 5E+07 | 4.084 2E+04 | 6.971 4E+04 | 1.222 8E+05 | 1.806 6E+04 |
Std | 0.000 0E+00 | 1.515 6E-08 | 3.337 1E+04 | 3.733 2E+04 | 7.403 6E+04 | 8.312 1E+03 |
算法 | 指标 | | | | | | | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
CFSBOA | Mean | 0.00E+00 | 3.40E-170 | 0.00E+00 | 1.13E-155 | 2.83E-296 | 0.00E+00 | |||||||
Std | 0.00E+00 | 0.00E+00 | 0.00E+00 | 6.18E-155 | 0.00E+00 | 0.00E+00 | ||||||||
HPSOBOA[ | Mean | 3.74E-104 | 2.63E-22 | 3.04E-71 | 3.61E-46 | — | — | |||||||
Std | 2.05E-103 | 1.44E-21 | 1.67E-70 | 1.97E-45 | — | — | ||||||||
LBOA[ | Mean | 3.92E-12 | 1.39E-09 | 2.74E-12 | 2.30E-09 | — | — | |||||||
Std | 4.46E-12 | 2.08E-09 | 2.44E-12 | 2.36E-09 | — | — | ||||||||
IBOA[ | Mean | 1.61E-30 | 5.11E-19 | 6.15E-31 | 1.36E-19 | — | — | |||||||
Std | 3.90E-30 | 1.73E-18 | 1.16E-30 | 1.97E-19 | — | — | ||||||||
CWBOA[ | Mean | 0.00E+00 | 3.86E-134 | — | 3.29E-134 | 0.00E+00 | 0.00E+00 | |||||||
Std | 0.00E+00 | 1.52E-133 | — | 1.80E-133 | 0.00E+00 | 0.00E+00 | ||||||||
BOA-CE[ | Mean | 1.26E-95 | 3.60E-47 | 2.44E-09 | 8.82E-07 | — | — | |||||||
Std | 9.78E-96 | 2.50E-47 | 1.83E-10 | 1.51E-07 | — | — | ||||||||
CSO[ | Mean | 3.50E-14 | 2.68E-08 | 7.17E-09 | 1.04E-02 | — | — | |||||||
Std | 6.34E-14 | 2.61E-08 | 1.16E-08 | 7.96E-03 | — | — | ||||||||
MPA[ | Mean | 4.51E-23 | 3.01E-13 | 1.27E-04 | 3.26E-09 | 2.97E-51 | 3.84E-13 | |||||||
Std | 3.56E-23 | 3.07E-13 | 2.19E-04 | 2.22E-09 | 1.57E-50 | 2.10E-12 | ||||||||
MSIWOA[ | Mean | 0.00E+00 | 7.17E-203 | 0.00E+00 | 4.59E-139 | — | — | |||||||
Std | 0.00E+00 | 1.64E-203 | 0.00E+00 | 2.51E-138 | — | — | ||||||||
QOWOA-CS[ | Mean | 1.01E-232 | 2.23E-125 | 2.61E-201 | 3.58E-103 | — | — | |||||||
Std | 0.00E+00 | 5.85E-125 | 0.00E+00 | 6.47E-103 | — | — | ||||||||
算法 | 指标 | | | | | | | |||||||
CFSBOA | Mean | 0.00E+00 | 8.88E-16 | 0.00E+00 | 9.98E-01 | 1.27E-166 | 0.00E+00 | |||||||
Std | 0.00E+00 | 0.00E+00 | 0.00E+00 | 1.20E-10 | 0.00E+00 | 0.00E+00 | ||||||||
HPSOBOA[ | Mean | 0.00E+00 | 8.96E-11 | 0.00E+00 | — | 2.54E-45 | 2.53E-08 | |||||||
Std | 0.00E+00 | 4.73E-10 | 0.00E+00 | — | 1.39E-44 | 1.38E-07 | ||||||||
LBOA[ | Mean | 0.00E+00 | 2.34E-12 | 3.48E-13 | — | 6.32E-14 | 3.65E-02 | |||||||
Std | 0.00E+00 | 7.87E-12 | 8.78E-13 | — | 1.73E-13 | 4.88E-02 | ||||||||
IBOA[ | Mean | 0.00E+00 | 8.88E-16 | 0.00E+00 | — | 8.93E-20 | 2.25E-32 | |||||||
Std | 0.00E+00 | 0.00E+00 | 0.00E+00 | — | 1.19E-19 | 5.88E-32 | ||||||||
CWBOA[ | Mean | 0.00E+00 | 8.88E-16 | 0.00E+00 | — | 2.13E-137 | — | |||||||
Std | 0.00E+00 | 0.00E+00 | 0.00E+00 | — | 8.15E-137 | — | ||||||||
BOA-CE[ | Mean | 1.01E+01 | 4.44E-15 | 0.00E+00 | — | — | — | |||||||
Std | 3.46E+01 | 0.00E+00 | 0.00E+00 | — | — | — | ||||||||
CSO[ | Mean | 2.40E+01 | 3.75E+00 | 3.56E-01 | 9.98E-01 | — | — | |||||||
Std | 6.48E+00 | 1.68E+00 | 1.91E-01 | 3.39E-07 | — | — | ||||||||
MPA[ | Mean | 0.00E+00 | 1.59E-12 | 0.00E+00 | 9.98E-01 | 9.12E-14 | 5.58E-17 | |||||||
Std | 0.00E+00 | 9.87E-13 | 0.00E+00 | 1.62E-16 | 8.01E-14 | 1.40E-16 | ||||||||
MSIWOA[ | Mean | 0.00E+00 | 0.00E+00 | 0.00E+00 | — | — | — | |||||||
Std | 0.00E+00 | 0.00E+00 | 0.00E+00 | — | — | — | ||||||||
QOWOA-CS[ | Mean | 0.00E+00 | 8.88E-16 | 0.00E+00 | — | — | — | |||||||
Std | 0.00E+00 | 0.00E+00 | 0.00E+00 | — | — | — |
表8 与参考文献中算法平均值和标准差的结果对比
Table 8 Results comparison of mean and standard deviation of algorithms in references
算法 | 指标 | | | | | | | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
CFSBOA | Mean | 0.00E+00 | 3.40E-170 | 0.00E+00 | 1.13E-155 | 2.83E-296 | 0.00E+00 | |||||||
Std | 0.00E+00 | 0.00E+00 | 0.00E+00 | 6.18E-155 | 0.00E+00 | 0.00E+00 | ||||||||
HPSOBOA[ | Mean | 3.74E-104 | 2.63E-22 | 3.04E-71 | 3.61E-46 | — | — | |||||||
Std | 2.05E-103 | 1.44E-21 | 1.67E-70 | 1.97E-45 | — | — | ||||||||
LBOA[ | Mean | 3.92E-12 | 1.39E-09 | 2.74E-12 | 2.30E-09 | — | — | |||||||
Std | 4.46E-12 | 2.08E-09 | 2.44E-12 | 2.36E-09 | — | — | ||||||||
IBOA[ | Mean | 1.61E-30 | 5.11E-19 | 6.15E-31 | 1.36E-19 | — | — | |||||||
Std | 3.90E-30 | 1.73E-18 | 1.16E-30 | 1.97E-19 | — | — | ||||||||
CWBOA[ | Mean | 0.00E+00 | 3.86E-134 | — | 3.29E-134 | 0.00E+00 | 0.00E+00 | |||||||
Std | 0.00E+00 | 1.52E-133 | — | 1.80E-133 | 0.00E+00 | 0.00E+00 | ||||||||
BOA-CE[ | Mean | 1.26E-95 | 3.60E-47 | 2.44E-09 | 8.82E-07 | — | — | |||||||
Std | 9.78E-96 | 2.50E-47 | 1.83E-10 | 1.51E-07 | — | — | ||||||||
CSO[ | Mean | 3.50E-14 | 2.68E-08 | 7.17E-09 | 1.04E-02 | — | — | |||||||
Std | 6.34E-14 | 2.61E-08 | 1.16E-08 | 7.96E-03 | — | — | ||||||||
MPA[ | Mean | 4.51E-23 | 3.01E-13 | 1.27E-04 | 3.26E-09 | 2.97E-51 | 3.84E-13 | |||||||
Std | 3.56E-23 | 3.07E-13 | 2.19E-04 | 2.22E-09 | 1.57E-50 | 2.10E-12 | ||||||||
MSIWOA[ | Mean | 0.00E+00 | 7.17E-203 | 0.00E+00 | 4.59E-139 | — | — | |||||||
Std | 0.00E+00 | 1.64E-203 | 0.00E+00 | 2.51E-138 | — | — | ||||||||
QOWOA-CS[ | Mean | 1.01E-232 | 2.23E-125 | 2.61E-201 | 3.58E-103 | — | — | |||||||
Std | 0.00E+00 | 5.85E-125 | 0.00E+00 | 6.47E-103 | — | — | ||||||||
算法 | 指标 | | | | | | | |||||||
CFSBOA | Mean | 0.00E+00 | 8.88E-16 | 0.00E+00 | 9.98E-01 | 1.27E-166 | 0.00E+00 | |||||||
Std | 0.00E+00 | 0.00E+00 | 0.00E+00 | 1.20E-10 | 0.00E+00 | 0.00E+00 | ||||||||
HPSOBOA[ | Mean | 0.00E+00 | 8.96E-11 | 0.00E+00 | — | 2.54E-45 | 2.53E-08 | |||||||
Std | 0.00E+00 | 4.73E-10 | 0.00E+00 | — | 1.39E-44 | 1.38E-07 | ||||||||
LBOA[ | Mean | 0.00E+00 | 2.34E-12 | 3.48E-13 | — | 6.32E-14 | 3.65E-02 | |||||||
Std | 0.00E+00 | 7.87E-12 | 8.78E-13 | — | 1.73E-13 | 4.88E-02 | ||||||||
IBOA[ | Mean | 0.00E+00 | 8.88E-16 | 0.00E+00 | — | 8.93E-20 | 2.25E-32 | |||||||
Std | 0.00E+00 | 0.00E+00 | 0.00E+00 | — | 1.19E-19 | 5.88E-32 | ||||||||
CWBOA[ | Mean | 0.00E+00 | 8.88E-16 | 0.00E+00 | — | 2.13E-137 | — | |||||||
Std | 0.00E+00 | 0.00E+00 | 0.00E+00 | — | 8.15E-137 | — | ||||||||
BOA-CE[ | Mean | 1.01E+01 | 4.44E-15 | 0.00E+00 | — | — | — | |||||||
Std | 3.46E+01 | 0.00E+00 | 0.00E+00 | — | — | — | ||||||||
CSO[ | Mean | 2.40E+01 | 3.75E+00 | 3.56E-01 | 9.98E-01 | — | — | |||||||
Std | 6.48E+00 | 1.68E+00 | 1.91E-01 | 3.39E-07 | — | — | ||||||||
MPA[ | Mean | 0.00E+00 | 1.59E-12 | 0.00E+00 | 9.98E-01 | 9.12E-14 | 5.58E-17 | |||||||
Std | 0.00E+00 | 9.87E-13 | 0.00E+00 | 1.62E-16 | 8.01E-14 | 1.40E-16 | ||||||||
MSIWOA[ | Mean | 0.00E+00 | 0.00E+00 | 0.00E+00 | — | — | — | |||||||
Std | 0.00E+00 | 0.00E+00 | 0.00E+00 | — | — | — | ||||||||
QOWOA-CS[ | Mean | 0.00E+00 | 8.88E-16 | 0.00E+00 | — | — | — | |||||||
Std | 0.00E+00 | 0.00E+00 | 0.00E+00 | — | — | — |
[1] | 周蓉, 李俊, 王浩. 基于灰狼优化的反向学习粒子群算法[J]. 计算机工程与应用, 2020, 56(7): 48-56. |
ZHOU R, LI J, WANG H. Reverse learning particle swarm optimization based on grey wolf optimization[J]. Computer Engineering and Applications, 2020, 56(7): 48-56. | |
[2] | 张明伟, 李波, 屈晓龙, 等. 基于混合蚁群算法的异质车队低碳VRP研究[J]. 计算机工程与应用, 2020, 56(14): 240-249. |
ZHANG M W, LI B, QU X L, et al. Research on low carbon VRP of heterogeneous fleet based on hybrid ant colony algo-rithm[J]. Computer Engineering and Applications, 2020, 56(14): 240-249. | |
[3] |
ARORA S, SINGH S. Butterfly optimization algorithm: a novel approach for global optimization[J]. Soft Computing, 2019, 23(3): 715-734.
DOI URL |
[4] |
FATHY A. Butterfly optimization algorithm based methodo-logy for enhancing the shaded photovoltaic array extracted power via reconfiguration process[J]. Energy Conversion and Management, 2020, 220: 113115.
DOI URL |
[5] |
MAHESHWARI P, SHARMA A K, VERMA K. Energy effi-cient cluster based routing protocol for WSN using butter-fly optimization algorithm and ant colony optimization[J]. Ad Hoc Networks, 2021, 110: 102317.
DOI URL |
[6] |
TAN L S, ZAINUDDIN Z, ONG P. Wavelet neural networks based solutions for elliptic partial differential equations with improved butterfly optimization algorithm training[J]. Applied Soft Computing, 2020, 95: 106518.
DOI URL |
[7] |
WEN L, CAO Y. A hybrid intelligent predicting model for exploring household CO2 emissions mitigation strategies derived from butterfly optimization algorithm[J]. Science of the Total Environment, 2020, 727: 138572.
DOI URL |
[8] | 张达敏, 王依柔, 徐航, 等. 认知智能电网中基于能效优化的频谱分配策略[J]. 控制与决策, 2021, 36(8): 1901-1910. |
ZHANG D M, WANG Y R, XU H, et al. Spectrum allocation strategy based on energy efficiency optimization in cognitive smart grid[J]. Control and Decision, 2021, 36(8): 1901-1910. | |
[9] | 高文欣, 刘升, 肖子雅, 等. 柯西变异和自适应权重优化的蝴蝶算法[J]. 计算机工程与应用, 2020, 56(15): 43-50. |
GAO W X, LIU S, XIAO Z Y, et al. Butterfly optimization algorithm based on Cauchy variation and adaptive weight[J]. Computer Engineering and Applications, 2020, 56(15): 43-50. | |
[10] |
王依柔, 张达敏. 融合正弦余弦和无限折叠迭代混沌映射的蝴蝶优化算法[J]. 模式识别与人工智能, 2020, 33(7): 660-669.
DOI |
WANG Y R, ZHANG D M. Butterfly optimization algori-thm combining sine cosine and iterative chaotic map with infinite collapses[J]. Pattern Recognition and A.pngicial Inte-lligence, 2020, 33(7): 660-669. | |
[11] |
LI G C, SHUANG F, ZHAO P, et al. An improved butterfly optimization algorithm for engineering design problems using the cross-entropy method[J]. Symmetry, 2019, 11(8): 1049.
DOI URL |
[12] | 高文欣, 刘升, 肖子雅, 等. 全局优化的蝴蝶优化算法[J]. 计算机应用研究, 2020, 37(10): 2966-2970. |
GAO W X, LIU S, XIAO Z Y, et al. Butterfly optimization algorithm for global optimization[J]. Application Research of Computers, 2020, 37(10): 2966-2970. | |
[13] | 王依柔, 张达敏, 徐航, 等. 基于自适应扰动的疯狂蝴蝶算法[J]. 计算机应用研究, 2020, 37(11): 3276-3280. |
WANG Y R, ZHANG D M, XU H, et al. Crazy butterfly algorithm based on adaptive perturbation[J]. Application Research of Computers, 2020, 37(11): 3276-3280. | |
[14] | 张达敏, 陈忠云, 辛梓芸, 等. 基于疯狂自适应的樽海鞘群算法[J]. 控制与决策, 2020, 35(9): 2112-2120. |
ZHANG D M, CHEN Z Y, XIN Z Y, et al. Salp swarm algorithm based on craziness and adaptive[J]. Control and Decision, 2020, 35(9): 2112-2120. | |
[15] | 谭光兴, 朱燕飞, 毛宗源. 基于Hénon映射的自适应克隆选择优化算法[J]. 计算机工程与应用, 2006, 42(9): 73-76. |
TAN G X, ZHU Y F, MAO Z Y. Adaptive clone selection optimization algorithm based on Hénon map[J]. Computer Engineering and Applications, 2006, 42(9): 73-76. | |
[16] | TANYILDIZI E, DEMIR G. Golden sine algorithm: a novel math-inspired algorithm[J]. Advances in Electrical and Com-puter Engineering, 2017, 17(2): 71-78. |
[17] | 周新, 邹海. 融合黄金正弦混合变异的自适应樽海鞘群算法[J]. 计算机工程与应用, 2021, 57(12): 75-85. |
ZHOU X, ZOU H. Adaptive salp swarm algorithm with gol-den sine algorithm and hybrid mutation[J]. Computer Engi-neering and Applications, 2021, 57(12): 75-85. | |
[18] | MIRJALILI S. Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm[J]. Knowledge-Based Sys-tems, 2015, 89: 228-249. |
[19] |
MIRJALILI S, GANDOMI A H, MIRJALILI S Z, et al. Salp swarm algorithm: a bio-inspired optimizer for enginee-ring design problems[J]. Advances in Engineering Software, 2017, 114: 163-191.
DOI URL |
[20] |
MIRJALILI S, MIRJALILI S M, LEWIS A. Grey wolf opti-mizer[J]. Advances in Engineering Software, 2014, 69: 46-61.
DOI URL |
[21] |
DERRAC J, GARCÍA S, MOLINA D, et al. A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelli-gence algorithms[J]. Swarm and Evolutionary Computation, 2011, 1(1): 3-18.
DOI URL |
[22] |
NABIL E. A modified flower pollination algorithm for global optimization[J]. Expert Systems with Applications, 2016, 57: 192-203.
DOI URL |
[23] | ZHANG M J, LONG D Y, QIN T, et al. A chaotic hybrid butterfly optimization algorithm with particle swarm optimi-zation for high-dimensional optimization problems[J]. Sym-metry, 2020, 12(11): 1800. |
[24] | AHMED A M, RASHID T A, SAEED S A M, et al. Cat swarm optimization algorithm: a survey and performance evaluation[J]. Computational Intelligence and Neuroscience, 2020(1): 20. |
[25] |
FARAMARZI A, HEIDARINEJAD M, MIRJALILI S, et al. Marine predators algorithm: a nature-inspired metaheuristic[J]. Expert Systems with Applications, 2020, 152: 113377.
DOI URL |
[26] | 郝晓弘, 宋吉祥, 周强, 等. 混合策略改进的鲸鱼优化算法[J]. 计算机应用研究, 2020, 37(12): 3622-3626. |
HAO X H, SONG J X, ZHOU Q, et al. Improved whale optimization algorithm based on hybrid strategy[J]. Applica-tion Research of Computers, 2020, 37(12): 3622-3626. | |
[27] | 冯文涛, 邓兵. 一种基于交叉选择的柯西反向鲸鱼优化算法[J]. 兵器装备工程学报, 2020, 41(8): 131-137. |
FENG W T, DENG B. Quasi-oppositional whale optimiza-tion algorithm based on crossover and selection strategy[J]. Journal of Ordnance Equipment Engineering, 2020, 41(8): 131-137. |
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