计算机科学与探索 ›› 2022, Vol. 16 ›› Issue (6): 1362-1373.DOI: 10.3778/j.issn.1673-9418.2010049
收稿日期:
2020-10-19
修回日期:
2021-01-07
出版日期:
2022-06-01
发布日期:
2021-01-25
通讯作者:
+ E-mail: 17805058112@163.com作者简介:
何佩苑(1997—),女,江苏溧阳人,硕士研究生,主要研究方向为智能优化、系统工程。基金资助:
Received:
2020-10-19
Revised:
2021-01-07
Online:
2022-06-01
Published:
2021-01-25
About author:
HE Peiyuan, born in 1997, M.S. candidate. Her research interests include intelligent optimization and system engineering.Supported by:
摘要:
教与学优化算法(TLBO)是一种模拟教学过程的启发式优化算法。针对TLBO算法寻优精度低、稳定性差的特点,提出了基于社会心理学理论改进的教与学优化算法(SPTLBO)。该算法在改进中考虑了人的心理因素:在原TLBO算法的“教”阶段中结合社会心理学的“期望效应”理论,教师对高期望学生采取一对一教学策略,使得优秀学生更快向教师靠近;为了保留学生的多样性,学生依据认知风格可分为“场独立”与“场依存”两种类型,不同类型的学生将采取不同的交流方式进行学习;在“教”“学”阶段后,结合自我调节理论,学生进入学习方法调整阶段,从而增强了自我探索能力,提高学生整体水平。此外,引入自适应学生更新因子,模拟环境对学生学习效率的影响,增加算法的全局搜索能力,避免出现在初期迭代中陷入局部最优的情况。在25个标准测试函数上进行实验,结果表明SPTLBO算法相较基本TLBO算法和其他智能优化算法,在寻优精度和收敛速度方面都更具优势。
中图分类号:
何佩苑, 刘勇. 融入社会心理学理论的教与学优化算法[J]. 计算机科学与探索, 2022, 16(6): 1362-1373.
HE Peiyuan, LIU Yong. Teaching-Learning-Based Optimization Algorithm with Social Psychology Theory[J]. Journal of Frontiers of Computer Science and Technology, 2022, 16(6): 1362-1373.
函数 编号 | 函数名 | 表达式 | 最优值 |
---|---|---|---|
| Camel-Three Hump | | 0 |
| Rotated Ellipse 2 | | 0 |
| Scahffer 1 | | 0 |
| Rotated Ellipse | | 0 |
| Schumer Steiglitz | | 0 |
| Price 4 | | 0 |
| Freudenstein Roth | | 0 |
| Treccani | | 0 |
| Egg Crate | | 0 |
| Matyas | | 0 |
表1 低维测试函数
Table 1 Low-dimensional test functions
函数 编号 | 函数名 | 表达式 | 最优值 |
---|---|---|---|
| Camel-Three Hump | | 0 |
| Rotated Ellipse 2 | | 0 |
| Scahffer 1 | | 0 |
| Rotated Ellipse | | 0 |
| Schumer Steiglitz | | 0 |
| Price 4 | | 0 |
| Freudenstein Roth | | 0 |
| Treccani | | 0 |
| Egg Crate | | 0 |
| Matyas | | 0 |
函数编号 | 函数名 | 表达式 | 最优值 |
---|---|---|---|
| Chung Reynolds | | 0 |
| Sphere | | 0 |
| Schwefel2.22 | | 0 |
| Schwefel1.2 | | 0 |
| Schwefel2.21 | | 0 |
| Powell Sum | | 0 |
| W/Wavy | | 0 |
| Quartic | | 0 |
| Zakharov | | 0 |
| Alpine | | 0 |
| Cigar | | 0 |
| Schwefel2.23 | | 0 |
| Csendes | | 0 |
| Salomon | | 0 |
| Rastrigin | | 0 |
表2 高维测试函数
Table 2 High-dimensional test functions
函数编号 | 函数名 | 表达式 | 最优值 |
---|---|---|---|
| Chung Reynolds | | 0 |
| Sphere | | 0 |
| Schwefel2.22 | | 0 |
| Schwefel1.2 | | 0 |
| Schwefel2.21 | | 0 |
| Powell Sum | | 0 |
| W/Wavy | | 0 |
| Quartic | | 0 |
| Zakharov | | 0 |
| Alpine | | 0 |
| Cigar | | 0 |
| Schwefel2.23 | | 0 |
| Csendes | | 0 |
| Salomon | | 0 |
| Rastrigin | | 0 |
函数 | 算法 | 平均值 | 标准差 | 最劣值 | 最优值 |
---|---|---|---|---|---|
| TLBO | 1.512 6E-112 | 6.458 6E-112 | 2.894 4E-111 | 4.090 9E-118 |
PSO | 1.302 6E-20 | 1.933 7E-20 | 7.307 6E-20 | 5.395 1E-23 | |
IA | 6.657 7E-10 | 7.446 9E-10 | 2.787 7E-09 | 9.070 7E-12 | |
GA | 1.560 7E-12 | 5.808 1E-12 | 2.600 9E-11 | 0 | |
SPTLBO | 1.628 6E-214 | 0 | 3.250 7E-213 | 0 | |
| TLBO | 1.056 1E-112 | 2.719 4E-112 | 1.155 5E-111 | 1.288 2E-117 |
PSO | 1.020 7E-20 | 3.217 7E-20 | 1.456 8E-19 | 4.594 1E-23 | |
IA | 3.824 2E-10 | 3.938 7E-10 | 1.780 3E-09 | 4.599 2E-12 | |
GA | 4.112 9E-10 | 1.777 5E-09 | 7.959 9E-09 | 8.370 8E-19 | |
SPTLBO | 1.610 5E-211 | 0 | 1.400 5E-210 | 3.400 4E-220 | |
| TLBO | 2.155 9E-04 | 7.115 1E-04 | 3.189 3E-03 | 1.498 8E-14 |
PSO | 2.915 2E-03 | 4.567 9E-03 | 9.715 9E-03 | 0 | |
IA | 4.372 2E-03 | 4.959 2E-03 | 9.715 9E-03 | 4.118 4E-10 | |
GA | 9.809 7E-04 | 3.019 5E-03 | 9.903 5E-03 | 0 | |
SPTLBO | 1.901 6E-09 | 7.703 1E-09 | 3.452 9E-08 | 0 | |
| TLBO | 9.655 4E-110 | 3.400 5E-109 | 1.520 8E-108 | 1.460 6E-115 |
PSO | 7.982 6E-19 | 2.972 7E-18 | 1.330 5E-17 | 1.825 3E-22 | |
IA | 5.226 4E-09 | 6.151 1E-09 | 2.764 9E-08 | 2.662 5E-11 | |
GA | 5.343 2E-08 | 2.170 8E-07 | 9.737 5E-07 | 3.654 1E-17 | |
SPTLBO | 7.761 0E-209 | 0 | 7.794 1E-208 | 1.081 0E-218 | |
| TLBO | 2.393 1E-224 | 0 | 4.715 2E-223 | 6.769 0E-238 |
PSO | 7.593 2E-39 | 2.154 6E-38 | 9.311 5E-38 | 6.585 8E-49 | |
IA | 2.091 4E-18 | 2.775 6E-18 | 1.222 9E-17 | 1.285 3E-21 | |
GA | 1.080 7E-23 | 4.786 5E-23 | 2.141 6E-22 | 2.974 2E-31 | |
SPTLBO | 0 | 0 | 0 | 0 | |
| TLBO | 2.161 4E-11 | 5.273 3E-11 | 2.291 7E-10 | 7.999 7E-15 |
PSO | 1.442 7E-15 | 1.828 3E-15 | 6.864 7E-15 | 1.469 7E-19 | |
IA | 9.009 1E-10 | 1.169 8E-09 | 3.641 5E-09 | 1.764 4E-11 | |
GA | 3.219 7E-02 | 9.219 6E-02 | 3.995 9E-01 | 0 | |
SPTLBO | 1.412 2E-14 | 2.668 1E-14 | 1.024 9E-13 | 0 | |
| TLBO | 3.427 9E-176 | 0 | 6.850 8E-175 | 3.071 6E-190 |
PSO | 1.836 2E-19 | 5.306 3E-19 | 2.116 2E-18 | 2.905 8E-25 | |
IA | 1.067 6E-08 | 1.073 5E-08 | 3.676 8E-08 | 4.156 2E-11 | |
GA | 1.111 5E-07 | 4.970 8E-07 | 2.223 4E-06 | 0 | |
SPTLBO | 6.924 5E-310 | 0 | 1.372 2E-308 | 0 | |
| TLBO | 5.771 4E-223 | 0 | 1.154 2E-221 | 3.984 7E-237 |
PSO | 6.535 1E-40 | 2.623 2E-39 | 1.178 4E-38 | 1.064 0E-45 | |
IA | 2.094 3E-19 | 3.927 9E-19 | 1.310 9E-18 | 3.685 9E-24 | |
GA | 1.930 7E-18 | 8.438 4E-18 | 3.777 3E-17 | 8.797 8E-32 | |
SPTLBO | 0 | 0 | 0 | 0 | |
| TLBO | 2.861 5E-110 | 1.132 5E-109 | 5.077 5E-109 | 3.366 4E-116 |
PSO | 1.921 2E-19 | 3.848 4E-19 | 1.206 2E-18 | 1.228 8E-22 | |
IA | 6.763 3E-09 | 7.252 5E-09 | 2.793 9E-08 | 7.046 8E-10 | |
GA | 7.111 1E-09 | 2.390 5E-08 | 1.054 3E-07 | 1.951 7E-18 | |
SPTLBO | 2.418 8E-213 | 0 | 4.100 5E-212 | 0 | |
| TLBO | 2.190 9E-81 | 7.402 1E-81 | 3.278 3E-80 | 3.535 1E-85 |
PSO | 4.075 1E-20 | 1.780 0E-19 | 7.969 4E-19 | 1.105 8E-26 | |
IA | 5.164 1E-10 | 5.077 0E-10 | 1.988 6E-09 | 1.900 2E-11 | |
GA | 4.275 8E-03 | 5.692 9E-03 | 1.709 7E-02 | 0 | |
SPTLBO | 5.109 4E-168 | 0 | 7.329 3E-167 | 0 |
表3 低维测数函数结果对比
Table 3 Comparison of experimental results of low-dimensional benchmark functions
函数 | 算法 | 平均值 | 标准差 | 最劣值 | 最优值 |
---|---|---|---|---|---|
| TLBO | 1.512 6E-112 | 6.458 6E-112 | 2.894 4E-111 | 4.090 9E-118 |
PSO | 1.302 6E-20 | 1.933 7E-20 | 7.307 6E-20 | 5.395 1E-23 | |
IA | 6.657 7E-10 | 7.446 9E-10 | 2.787 7E-09 | 9.070 7E-12 | |
GA | 1.560 7E-12 | 5.808 1E-12 | 2.600 9E-11 | 0 | |
SPTLBO | 1.628 6E-214 | 0 | 3.250 7E-213 | 0 | |
| TLBO | 1.056 1E-112 | 2.719 4E-112 | 1.155 5E-111 | 1.288 2E-117 |
PSO | 1.020 7E-20 | 3.217 7E-20 | 1.456 8E-19 | 4.594 1E-23 | |
IA | 3.824 2E-10 | 3.938 7E-10 | 1.780 3E-09 | 4.599 2E-12 | |
GA | 4.112 9E-10 | 1.777 5E-09 | 7.959 9E-09 | 8.370 8E-19 | |
SPTLBO | 1.610 5E-211 | 0 | 1.400 5E-210 | 3.400 4E-220 | |
| TLBO | 2.155 9E-04 | 7.115 1E-04 | 3.189 3E-03 | 1.498 8E-14 |
PSO | 2.915 2E-03 | 4.567 9E-03 | 9.715 9E-03 | 0 | |
IA | 4.372 2E-03 | 4.959 2E-03 | 9.715 9E-03 | 4.118 4E-10 | |
GA | 9.809 7E-04 | 3.019 5E-03 | 9.903 5E-03 | 0 | |
SPTLBO | 1.901 6E-09 | 7.703 1E-09 | 3.452 9E-08 | 0 | |
| TLBO | 9.655 4E-110 | 3.400 5E-109 | 1.520 8E-108 | 1.460 6E-115 |
PSO | 7.982 6E-19 | 2.972 7E-18 | 1.330 5E-17 | 1.825 3E-22 | |
IA | 5.226 4E-09 | 6.151 1E-09 | 2.764 9E-08 | 2.662 5E-11 | |
GA | 5.343 2E-08 | 2.170 8E-07 | 9.737 5E-07 | 3.654 1E-17 | |
SPTLBO | 7.761 0E-209 | 0 | 7.794 1E-208 | 1.081 0E-218 | |
| TLBO | 2.393 1E-224 | 0 | 4.715 2E-223 | 6.769 0E-238 |
PSO | 7.593 2E-39 | 2.154 6E-38 | 9.311 5E-38 | 6.585 8E-49 | |
IA | 2.091 4E-18 | 2.775 6E-18 | 1.222 9E-17 | 1.285 3E-21 | |
GA | 1.080 7E-23 | 4.786 5E-23 | 2.141 6E-22 | 2.974 2E-31 | |
SPTLBO | 0 | 0 | 0 | 0 | |
| TLBO | 2.161 4E-11 | 5.273 3E-11 | 2.291 7E-10 | 7.999 7E-15 |
PSO | 1.442 7E-15 | 1.828 3E-15 | 6.864 7E-15 | 1.469 7E-19 | |
IA | 9.009 1E-10 | 1.169 8E-09 | 3.641 5E-09 | 1.764 4E-11 | |
GA | 3.219 7E-02 | 9.219 6E-02 | 3.995 9E-01 | 0 | |
SPTLBO | 1.412 2E-14 | 2.668 1E-14 | 1.024 9E-13 | 0 | |
| TLBO | 3.427 9E-176 | 0 | 6.850 8E-175 | 3.071 6E-190 |
PSO | 1.836 2E-19 | 5.306 3E-19 | 2.116 2E-18 | 2.905 8E-25 | |
IA | 1.067 6E-08 | 1.073 5E-08 | 3.676 8E-08 | 4.156 2E-11 | |
GA | 1.111 5E-07 | 4.970 8E-07 | 2.223 4E-06 | 0 | |
SPTLBO | 6.924 5E-310 | 0 | 1.372 2E-308 | 0 | |
| TLBO | 5.771 4E-223 | 0 | 1.154 2E-221 | 3.984 7E-237 |
PSO | 6.535 1E-40 | 2.623 2E-39 | 1.178 4E-38 | 1.064 0E-45 | |
IA | 2.094 3E-19 | 3.927 9E-19 | 1.310 9E-18 | 3.685 9E-24 | |
GA | 1.930 7E-18 | 8.438 4E-18 | 3.777 3E-17 | 8.797 8E-32 | |
SPTLBO | 0 | 0 | 0 | 0 | |
| TLBO | 2.861 5E-110 | 1.132 5E-109 | 5.077 5E-109 | 3.366 4E-116 |
PSO | 1.921 2E-19 | 3.848 4E-19 | 1.206 2E-18 | 1.228 8E-22 | |
IA | 6.763 3E-09 | 7.252 5E-09 | 2.793 9E-08 | 7.046 8E-10 | |
GA | 7.111 1E-09 | 2.390 5E-08 | 1.054 3E-07 | 1.951 7E-18 | |
SPTLBO | 2.418 8E-213 | 0 | 4.100 5E-212 | 0 | |
| TLBO | 2.190 9E-81 | 7.402 1E-81 | 3.278 3E-80 | 3.535 1E-85 |
PSO | 4.075 1E-20 | 1.780 0E-19 | 7.969 4E-19 | 1.105 8E-26 | |
IA | 5.164 1E-10 | 5.077 0E-10 | 1.988 6E-09 | 1.900 2E-11 | |
GA | 4.275 8E-03 | 5.692 9E-03 | 1.709 7E-02 | 0 | |
SPTLBO | 5.109 4E-168 | 0 | 7.329 3E-167 | 0 |
函数 | 算法 | 平均值 | 标准差 | 最劣值 | 最优值 |
---|---|---|---|---|---|
| TLBO | 1.972 4E-92 | 4.370 7E-92 | 1.996 9E-91 | 1.696 6E-95 |
PSO | 4.744 0E+04 | 1.543 1E+04 | 7.997 7E+04 | 2.079 8E+04 | |
IA | 5.107 2E+05 | 6.601 6E+05 | 6.440 1E+05 | 3.462 6E+05 | |
GA | 5.025 8E+02 | 4.270 5E+02 | 1.705 9E+02 | 1.382 8E+02 | |
SPTLBO | 1.991 5E-196 | 0 | 2.690 7E-195 | 0 | |
| TLBO | 4.987 2E-47 | 4.125 9E-47 | 1.528 9E-46 | 1.100 8E-47 |
PSO | 1.930 2E+02 | 2.928 0E+01 | 2.652 5E+02 | 1.530 2E+02 | |
IA | 6.909 6E+02 | 4.517 1E+01 | 7.592 7E+02 | 6.129 4E+02 | |
GA | 2.212 2E+01 | 1.011 3E+02 | 5.552 8E+02 | 1.095 1E+01 | |
SPTLBO | 8.184 0E-104 | 1.241 0E-103 | 4.326 4E-103 | 0 | |
| TLBO | 8.259 2E-23 | 4.310 6E-23 | 2.157 4E-22 | 3.647 1E-23 |
PSO | 1.133 2E+02 | 1.796 7E+02 | 1.762 4E+02 | 9.473 2E+01 | |
IA | 7.383 4E+08 | 3.301 5E+09 | 1.476 5E+10 | 3.053 7E+02 | |
GA | 6.070 5E+01 | 2.216 4E+01 | 9.080 5E+01 | 2.551 2E+01 | |
SPTLBO | 2.656 8E-53 | 4.009 8E-53 | 1.359 7E-52 | 9.473 3E-55 | |
| TLBO | 1.095 9E-03 | 1.192 3E-03 | 5.210 8E-03 | 6.265 2E-05 |
PSO | 5.466 4E+02 | 1.069 5E+02 | 7.502 4E+02 | 3.242 6E+02 | |
IA | 5.838 1E-13 | 9.582 4E-13 | 3.758 1E-12 | 5.186 2E-16 | |
GA | 7.471 5E+02 | 1.473 9E+02 | 1.086 8E+03 | 5.003 2E+02 | |
SPTLBO | 9.173 0E-58 | 3.389 2E-57 | 1.522 6E-56 | 3.479 6E-62 | |
| TLBO | 3.427 6E-19 | 1.397 4E-19 | 6.257 0E-19 | 1.382 9E-19 |
PSO | 4.539 6E-00 | 5.405 1E-01 | 5.665 1E-00 | 3.531 3E-00 | |
IA | 6.743 6E-00 | 1.487 3E-01 | 6.965 4E-00 | 6.332 7E-00 | |
GA | 3.869 5E-00 | 5.852 4E-01 | 5.213 1E-00 | 2.588 1E-00 | |
SPTLBO | 5.060 6E-46 | 4.956 8E-46 | 1.913 8E-45 | 1.196 5E-47 | |
| TLBO | 3.498 3E-111 | 1.413 2E-110 | 6.339 4E-110 | 7.358 1E-117 |
PSO | 5.331 3E+38 | 1.632 2E+39 | 5.954 1E+39 | 3.673 2E+27 | |
IA | 9.341 4E-13 | 1.930 6E-12 | 7.041 3E-12 | 1.218 1E-15 | |
GA | 7.742 0E+48 | 3.411 8E+49 | 1.526 8E+50 | 2.385 5E+26 | |
SPTLBO | 5.540 5E-210 | 0 | 4.912 8E-209 | 0 | |
| TLBO | 8.573 7E-01 | 1.658 3E-02 | 8.868 8E-01 | 8.271 3E-01 |
PSO | 7.645 3E-01 | 1.903 9E-02 | 8.100 8E-01 | 7.299 8E-01 | |
IA | 1.160 7E-11 | 1.588 2E-11 | 6.437 3E-11 | 2.101 7E-13 | |
GA | 6.381 7E-01 | 4.672 4E-02 | 7.147 6E-01 | 5.547 1E-01 | |
SPTLBO | 2.401 5E-10 | 9.335 4E-10 | 4.193 9E-09 | 0 | |
| TLBO | 8.059 8E-83 | 8.753 3E-83 | 2.864 8E-82 | 3.003 0E-84 |
PSO | 9.721 1E+09 | 3.768 2E+09 | 1.519 8E+10 | 3.853 7E+09 | |
IA | 6.301 0E-20 | 1.740 6E-19 | 6.073 9E-19 | 1.620 7E-27 | |
GA | 3.216 6E+08 | 2.418 8E+08 | 1.131 4E+09 | 1.403 2E+08 | |
SPTLBO | 3.628 8E-179 | 0 | 4.636 1E-178 | 1.628 2E-183 | |
| TLBO | 7.547 9E+02 | 1.776 6E+02 | 1.076 7E+03 | 4.076 1E+02 |
PSO | 6.936 6E+02 | 1.281 9E+02 | 9.561 3E+02 | 4.552 9E+02 | |
IA | 7.779 1E-13 | 1.771 2E-12 | 7.977 8E-12 | 2.557 6E-16 | |
GA | 2.183 0E+03 | 5.843 3E+02 | 3.494 3E+03 | 1.292 0E+03 | |
SPTLBO | 3.211 4E-07 | 1.410 2E-06 | 6.311 5E-06 | 0 | |
| TLBO | 1.007 5E-23 | 3.711 2E-24 | 1.791 7E-23 | 5.063 7E-24 |
PSO | 6.519 2E+01 | 6.349 6E-00 | 7.340 1E+01 | 5.095 1E+01 | |
IA | 4.929 2E+01 | 4.107 2E+00 | 5.772 0E+01 | 4.031 8E+01 | |
GA | 1.378 9E+01 | 1.819 3E+00 | 1.793 7E+01 | 1.139 9E+01 | |
SPTLBO | 2.142 9E-54 | 2.690 6E-54 | 1.104 4E-53 | 0 | |
函数 | 算法 | 平均值 | 标准差 | 最劣值 | 最优值 |
| TLBO | 1.249 1E-40 | 1.209 1E-40 | 3.885 7E-40 | 1.775 3E-41 |
PSO | 2.076 1E+08 | 2.832 2E+07 | 2.603 1E+08 | 1.359 8E+08 | |
IA | 7.482 2E-13 | 1.499 5E-12 | 5.304 2E-12 | 2.420 7E-16 | |
GA | 1.669 7E+07 | 5.665 2E+06 | 3.528 1E+07 | 1.012 2E+07 | |
SPTLBO | 2.199 9E-97 | 4.073 2E-97 | 1.517 8E-96 | 2.772 3E-100 | |
| TLBO | 5.901 4E-201 | 0 | 5.807 8E-200 | 4.946 7E-207 |
PSO | 1.860 8E+06 | 1.147 9E+06 | 4.062 5E+06 | 3.991 8E+06 | |
IA | 1.458 3E+08 | 3.891 2E+08 | 2.203 8E+08 | 8.836 9E+08 | |
GA | 3.765 2E+03 | 3.027 1E+03 | 1.016 1E+04 | 4.084 1E+02 | |
SPTLBO | 0 | 0 | 0 | 0 | |
| TLBO | 2.187 3E-124 | 4.547 6E-124 | 2.044 6E-123 | 9.101 1E-127 |
PSO | 3.429 1E+04 | 1.319 9E+04 | 6.479 9E+04 | 1.054 2E+04 | |
IA | 4.333 5E+05 | 7.887 6E+04 | 5.710 3E+05 | 2.766 5E+05 | |
GA | 5.824 2E+02 | 8.617 2E+02 | 3.723 2E+03 | 3.864 4E+01 | |
SPTLBO | 2.149 9E-249 | 0 | 3.229 2E-248 | 6.968 4E-256 | |
| TLBO | 1.998 7E-01 | 4.723 4E-07 | 1.998 8E-01 | 1.998 7E-01 |
PSO | 2.094 9E-00 | 1.234 4E-01 | 2.399 9E-00 | 1.899 9E-00 | |
IA | 9.486 7E-08 | 9.731 1E-08 | 3.177 6E-07 | 1.193 2E-09 | |
GA | 2.609 9E+00 | 3.582 1E-01 | 3.299 9E+00 | 1.999 9E+00 | |
SPTLBO | 8.795 7E-02 | 3.003 2E-02 | 9.987 3E-02 | 0 | |
| TLBO | 8.410 8E-00 | 3.761 4E+01 | 1.682 1E+02 | 0 |
PSO | 1.000 5E+03 | 7.620 1E+03 | 1.147 3E+03 | 8.488 1E+03 | |
IA | 2.220 7E-10 | 3.770 1E-10 | 1.457 1E-09 | 1.659 1E-12 | |
GA | 4.110 5E+02 | 4.757 3E+01 | 5.280 3E+02 | 3.345 0E+02 | |
SPTLBO | 0 | 0 | 0 | 0 |
表4 高维测试函数结果对比
Table 4 Comparison of experimental results of high-dimensional benchmark functions
函数 | 算法 | 平均值 | 标准差 | 最劣值 | 最优值 |
---|---|---|---|---|---|
| TLBO | 1.972 4E-92 | 4.370 7E-92 | 1.996 9E-91 | 1.696 6E-95 |
PSO | 4.744 0E+04 | 1.543 1E+04 | 7.997 7E+04 | 2.079 8E+04 | |
IA | 5.107 2E+05 | 6.601 6E+05 | 6.440 1E+05 | 3.462 6E+05 | |
GA | 5.025 8E+02 | 4.270 5E+02 | 1.705 9E+02 | 1.382 8E+02 | |
SPTLBO | 1.991 5E-196 | 0 | 2.690 7E-195 | 0 | |
| TLBO | 4.987 2E-47 | 4.125 9E-47 | 1.528 9E-46 | 1.100 8E-47 |
PSO | 1.930 2E+02 | 2.928 0E+01 | 2.652 5E+02 | 1.530 2E+02 | |
IA | 6.909 6E+02 | 4.517 1E+01 | 7.592 7E+02 | 6.129 4E+02 | |
GA | 2.212 2E+01 | 1.011 3E+02 | 5.552 8E+02 | 1.095 1E+01 | |
SPTLBO | 8.184 0E-104 | 1.241 0E-103 | 4.326 4E-103 | 0 | |
| TLBO | 8.259 2E-23 | 4.310 6E-23 | 2.157 4E-22 | 3.647 1E-23 |
PSO | 1.133 2E+02 | 1.796 7E+02 | 1.762 4E+02 | 9.473 2E+01 | |
IA | 7.383 4E+08 | 3.301 5E+09 | 1.476 5E+10 | 3.053 7E+02 | |
GA | 6.070 5E+01 | 2.216 4E+01 | 9.080 5E+01 | 2.551 2E+01 | |
SPTLBO | 2.656 8E-53 | 4.009 8E-53 | 1.359 7E-52 | 9.473 3E-55 | |
| TLBO | 1.095 9E-03 | 1.192 3E-03 | 5.210 8E-03 | 6.265 2E-05 |
PSO | 5.466 4E+02 | 1.069 5E+02 | 7.502 4E+02 | 3.242 6E+02 | |
IA | 5.838 1E-13 | 9.582 4E-13 | 3.758 1E-12 | 5.186 2E-16 | |
GA | 7.471 5E+02 | 1.473 9E+02 | 1.086 8E+03 | 5.003 2E+02 | |
SPTLBO | 9.173 0E-58 | 3.389 2E-57 | 1.522 6E-56 | 3.479 6E-62 | |
| TLBO | 3.427 6E-19 | 1.397 4E-19 | 6.257 0E-19 | 1.382 9E-19 |
PSO | 4.539 6E-00 | 5.405 1E-01 | 5.665 1E-00 | 3.531 3E-00 | |
IA | 6.743 6E-00 | 1.487 3E-01 | 6.965 4E-00 | 6.332 7E-00 | |
GA | 3.869 5E-00 | 5.852 4E-01 | 5.213 1E-00 | 2.588 1E-00 | |
SPTLBO | 5.060 6E-46 | 4.956 8E-46 | 1.913 8E-45 | 1.196 5E-47 | |
| TLBO | 3.498 3E-111 | 1.413 2E-110 | 6.339 4E-110 | 7.358 1E-117 |
PSO | 5.331 3E+38 | 1.632 2E+39 | 5.954 1E+39 | 3.673 2E+27 | |
IA | 9.341 4E-13 | 1.930 6E-12 | 7.041 3E-12 | 1.218 1E-15 | |
GA | 7.742 0E+48 | 3.411 8E+49 | 1.526 8E+50 | 2.385 5E+26 | |
SPTLBO | 5.540 5E-210 | 0 | 4.912 8E-209 | 0 | |
| TLBO | 8.573 7E-01 | 1.658 3E-02 | 8.868 8E-01 | 8.271 3E-01 |
PSO | 7.645 3E-01 | 1.903 9E-02 | 8.100 8E-01 | 7.299 8E-01 | |
IA | 1.160 7E-11 | 1.588 2E-11 | 6.437 3E-11 | 2.101 7E-13 | |
GA | 6.381 7E-01 | 4.672 4E-02 | 7.147 6E-01 | 5.547 1E-01 | |
SPTLBO | 2.401 5E-10 | 9.335 4E-10 | 4.193 9E-09 | 0 | |
| TLBO | 8.059 8E-83 | 8.753 3E-83 | 2.864 8E-82 | 3.003 0E-84 |
PSO | 9.721 1E+09 | 3.768 2E+09 | 1.519 8E+10 | 3.853 7E+09 | |
IA | 6.301 0E-20 | 1.740 6E-19 | 6.073 9E-19 | 1.620 7E-27 | |
GA | 3.216 6E+08 | 2.418 8E+08 | 1.131 4E+09 | 1.403 2E+08 | |
SPTLBO | 3.628 8E-179 | 0 | 4.636 1E-178 | 1.628 2E-183 | |
| TLBO | 7.547 9E+02 | 1.776 6E+02 | 1.076 7E+03 | 4.076 1E+02 |
PSO | 6.936 6E+02 | 1.281 9E+02 | 9.561 3E+02 | 4.552 9E+02 | |
IA | 7.779 1E-13 | 1.771 2E-12 | 7.977 8E-12 | 2.557 6E-16 | |
GA | 2.183 0E+03 | 5.843 3E+02 | 3.494 3E+03 | 1.292 0E+03 | |
SPTLBO | 3.211 4E-07 | 1.410 2E-06 | 6.311 5E-06 | 0 | |
| TLBO | 1.007 5E-23 | 3.711 2E-24 | 1.791 7E-23 | 5.063 7E-24 |
PSO | 6.519 2E+01 | 6.349 6E-00 | 7.340 1E+01 | 5.095 1E+01 | |
IA | 4.929 2E+01 | 4.107 2E+00 | 5.772 0E+01 | 4.031 8E+01 | |
GA | 1.378 9E+01 | 1.819 3E+00 | 1.793 7E+01 | 1.139 9E+01 | |
SPTLBO | 2.142 9E-54 | 2.690 6E-54 | 1.104 4E-53 | 0 | |
函数 | 算法 | 平均值 | 标准差 | 最劣值 | 最优值 |
| TLBO | 1.249 1E-40 | 1.209 1E-40 | 3.885 7E-40 | 1.775 3E-41 |
PSO | 2.076 1E+08 | 2.832 2E+07 | 2.603 1E+08 | 1.359 8E+08 | |
IA | 7.482 2E-13 | 1.499 5E-12 | 5.304 2E-12 | 2.420 7E-16 | |
GA | 1.669 7E+07 | 5.665 2E+06 | 3.528 1E+07 | 1.012 2E+07 | |
SPTLBO | 2.199 9E-97 | 4.073 2E-97 | 1.517 8E-96 | 2.772 3E-100 | |
| TLBO | 5.901 4E-201 | 0 | 5.807 8E-200 | 4.946 7E-207 |
PSO | 1.860 8E+06 | 1.147 9E+06 | 4.062 5E+06 | 3.991 8E+06 | |
IA | 1.458 3E+08 | 3.891 2E+08 | 2.203 8E+08 | 8.836 9E+08 | |
GA | 3.765 2E+03 | 3.027 1E+03 | 1.016 1E+04 | 4.084 1E+02 | |
SPTLBO | 0 | 0 | 0 | 0 | |
| TLBO | 2.187 3E-124 | 4.547 6E-124 | 2.044 6E-123 | 9.101 1E-127 |
PSO | 3.429 1E+04 | 1.319 9E+04 | 6.479 9E+04 | 1.054 2E+04 | |
IA | 4.333 5E+05 | 7.887 6E+04 | 5.710 3E+05 | 2.766 5E+05 | |
GA | 5.824 2E+02 | 8.617 2E+02 | 3.723 2E+03 | 3.864 4E+01 | |
SPTLBO | 2.149 9E-249 | 0 | 3.229 2E-248 | 6.968 4E-256 | |
| TLBO | 1.998 7E-01 | 4.723 4E-07 | 1.998 8E-01 | 1.998 7E-01 |
PSO | 2.094 9E-00 | 1.234 4E-01 | 2.399 9E-00 | 1.899 9E-00 | |
IA | 9.486 7E-08 | 9.731 1E-08 | 3.177 6E-07 | 1.193 2E-09 | |
GA | 2.609 9E+00 | 3.582 1E-01 | 3.299 9E+00 | 1.999 9E+00 | |
SPTLBO | 8.795 7E-02 | 3.003 2E-02 | 9.987 3E-02 | 0 | |
| TLBO | 8.410 8E-00 | 3.761 4E+01 | 1.682 1E+02 | 0 |
PSO | 1.000 5E+03 | 7.620 1E+03 | 1.147 3E+03 | 8.488 1E+03 | |
IA | 2.220 7E-10 | 3.770 1E-10 | 1.457 1E-09 | 1.659 1E-12 | |
GA | 4.110 5E+02 | 4.757 3E+01 | 5.280 3E+02 | 3.345 0E+02 | |
SPTLBO | 0 | 0 | 0 | 0 |
[1] |
RAO R V, SAVSANI V J, VAKHARIA D P. Teaching-learning-based optimization: a novel method for constrained mechanical design optimization problems[J]. Computer-Aided Design, 2011, 43(3): 303-315.
DOI URL |
[2] | 邓志诚, 孙辉, 赵嘉, 等. 具有动态子空间的随机单维变异粒子群算法[J]. 计算机科学与探索, 2020, 14(8): 1409-1426. |
DENG Z C, SUN H, ZHAO J, et al. Stochastic single-dimensional mutated particle swarm optimization with dyna-mic subspace[J]. Journal of Frontiers of Computer Science and Technology, 2020, 14(8): 1409-1426. | |
[3] | 张海南, 游晓明, 刘升, 等. 交互式学习的布谷鸟搜索算法[J]. 计算机工程与应用, 2020, 56(7): 147-154. |
ZHANG H N, YOU X M, LIU S, et al. Interactive learning cuckoo search algorithm[J]. Computer Engineering and App-lications, 2020, 56(7): 147-154. | |
[4] | DONG B, WU X J, SUN Y F. A collaborative learning model in teaching-learning-based optimization: some numerical results[C]// Proceedings of the 11th International Conference on Bio-inspired Computing-Theories and Applications, Xi’an, Oct 28-30, 2016. Cham: Springer, 2016: 466-472. |
[5] | GE F Z, HONG L R, SHI L, et al. An autonomous teaching-learning-based optimization algorithm for single objective global optimization[J]. International Journal of Computatio-nal Intelligence Systems, 2016, 9(3): 506-524. |
[6] |
ZHANG Z, HUANG H, HUANG C, et al. An improved TLBO with logarithmic spiral and triangular mutation for global optimization[J]. Neural Computing and Applications, 2018, 31(8): 4435-4450.
DOI URL |
[7] | 何杰光, 彭志平, 崔得龙, 等. 一种多反向学习的教与学优化算法[J]. 工程科学与技术, 2019, 51(6): 159-167. |
HE J G, PENG Z P, CUI D L, et al. Multi-opposition teaching-learning-based optimization[J]. Advanced Engineering Sciences, 2019, 51(6): 159-167. | |
[8] | LI X, LI K, YANG Z L. Teaching-learning-feedback-based optimization[C]// LNCS 10385: Proceedings of the Interna-tional Conference on Swarm Intelligence: Advances in Swarm Intelligence, Fukuoka, Jul 27-Aug 1, 2017. Cham: Springer, 2017: 71-79. |
[9] | 李丽荣, 李木子, 李崔灿, 等. 具有动态自适应学习机制的教与学优化算法[J]. 计算机工程与应用, 2020, 56(19): 62-67. |
LI L R, LI M Z, LI C C, et al. Teaching and learning based optimization with dynamic self-adaptive learning[J]. Com-puter Engineering and Applications, 2020, 56(19): 62-67. | |
[10] | VERMA A, AGRAWAL S, AGRAWAL J, et al. Advance teaching-learning based optimization for global function opti-mization[C]// Proceedings of the 3rd International Conference on Advanced Computing, Networking and Informatics, Bhu-baneswar, Jun 23-25, 2015. Cham: Springer, 2016: 573-580. |
[11] |
WU Z S, FU W P, XUE R. Nonlinear inertia weighted teaching-learning-based optimization for solving global optimization problem[J]. Computational Intelligence and Neuroscience, 2015: 292576. DOI: 10.1155/2015/292576.
DOI |
[12] | 吴聪聪, 贺毅朝, 赵建立. 改进的教与学优化算法求解集合联盟背包问题[J]. 计算机科学与探索, 2018, 12(12): 2007-2020. |
WU C C, HE Y Z, ZHAO J L. Solving set-union knapsack problem by modified teaching-learning-based optimization algorithm[J]. Journal of Frontiers of Computer Science and Technology, 2018, 12(12): 2007-2020. | |
[13] | ZHAI Z B, JIA G P, WANG K. A novel teaching-learning-based optimization with error correction and Cauchy distri-bution for path planning of unmanned air vehicle[J]. Com-putational Intelligence and Neuroscience, 2018, 3: 1-12. |
[14] | 黎延海, 拓守恒, 雍龙泉. 动态选择策略的和声教与学混合算法[J]. 计算机应用研究, 2019, 36(12): 3679-3684. |
LI Y H, TUO S H, YONG L Q. Hybrid algorithm based on harmony search and teaching-learning-based optimization using dynamic selection strategies[J]. Application Research of Computers, 2019, 36(12): 3679-3684. | |
[15] | 李丽荣, 杨坤, 王培崇. 融合头脑风暴思想的教与学优化算法[J]. 计算机应用, 2020, 40(9): 2677-2682. |
LI L R, YANG K, WANG P C. Improved teaching & learning based optimization with brain storming[J]. Journal of Com-puter Applications, 2020, 40(9): 2677-2682. | |
[16] |
TUO S, YONG L, DENG F, et al. HSTLBO: a hybrid algori-thm based on Harmony search and teaching-learning-based optimization for complex high-dimensional optimization pro-blems[J]. PLoS One, 2017, 12(4): e0175114.
DOI URL |
[17] | 陈宁, 张庆林. 教师期待效应的启示[J]. 教育探索, 2006(6): 84-85. |
CHEN N, ZHANG Q L. Enlightenment of teachers’ expecta-tion effect[J]. Education Exploration, 2006(6): 84-85. | |
[18] | 曾晓青, 刘建平, 陈关荣. 场独立-场依存型认知风格与内隐、外显记忆关系的实验研究[J]. 心理科学, 2010, 33(1): 138-140. |
ZENG X Q, LIU J P, CHEN G R. The relationship between cognitive style and implicit/explicit memory[J]. Psychologi-cal Science, 2010, 33(1): 138-140. | |
[19] | 吴亚婕. 影响学习者在线深度学习的因素及其测量研究[J]. 电化教育研究, 2017, 38(9): 57-63. |
WU Y J. Research on influential factors and its measure-ment of learners’ online deep learning[J]. E-education Re-search, 2017, 38(9): 57-63. | |
[20] | 刘静, 王志江. 企业人力资源管理中期望效应实证研究[J]. 商业经济, 2004(2): 72-73. |
LIU J, WANG Z J. An empirical study on expectation effect in enterprise human resource management[J]. Commercial Economy, 2004(2): 72-73. | |
[21] | 迈尔斯. 社会心理学[M]. 北京: 人民邮电出版社, 2006. |
MYERS G. Social psychology[M]. Beijing: Posts & Telecom Press, 2006. | |
[22] | JAMIL M, YANG X S. A literature survey of benchmark functions for global optimization problems[J]. International Journal of Mathematical Modelling & Numerical Optimi-sation, 2013, 4(2): 150-194. |
[23] | 包子阳, 余继周. 智能优化算法及其MATLAB实例[M]. 北京: 电子工业出版社, 2016. |
BAO Z Y, YU J Z. Intelligent optimization algorithm and its MATLAB example[M]. Beijing: Publishing House of Electronics Industry, 2016. |
[1] | 吴聪聪,贺毅朝,赵建立. 改进的教与学优化算法求解集合联盟背包问题[J]. 计算机科学与探索, 2018, 12(12): 2007-2020. |
阅读次数 | ||||||
全文 |
|
|||||
摘要 |
|
|||||