Journal of Computer Applications ›› 2023, Vol. 43 ›› Issue (8): 2345-2351.DOI: 10.11772/j.issn.1001-9081.2022091355
• The 19th International Conference on Web Information Systems and Applications (WISA 2022) • Previous Articles Next Articles
Saijuan XU1, Zhenyu PEI2, Jiawei LIN2, Genggeng LIU2()
Received:
2022-09-06
Revised:
2022-09-28
Accepted:
2022-10-08
Online:
2022-11-25
Published:
2023-08-10
Contact:
Genggeng LIU
About author:
XU Saijuan, born in 1987, M. S., lecturer. Her research interests include computational intelligence.Supported by:
通讯作者:
刘耿耿
作者简介:
徐赛娟(1987—),女,福建仙游人,讲师,硕士,主要研究方向:计算智能基金资助:
CLC Number:
Saijuan XU, Zhenyu PEI, Jiawei LIN, Genggeng LIU. Constrained multi-objective evolutionary algorithm based on multi-stage search[J]. Journal of Computer Applications, 2023, 43(8): 2345-2351.
徐赛娟, 裴镇宇, 林佳炜, 刘耿耿. 基于多阶段搜索的约束多目标进化算法[J]. 《计算机应用》唯一官方网站, 2023, 43(8): 2345-2351.
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URL: https://www.joca.cn/EN/10.11772/j.issn.1001-9081.2022091355
测试函数 | M | NSGA-Ⅱ+ARSBX | PPS | ToP | I-DBEA | CMOEA-MSS | |||||
---|---|---|---|---|---|---|---|---|---|---|---|
平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | ||
MW1 | 2 | 2.000 8E-3 | 3.94E-5 | 9.55E-5 | 4.307 7E-2 | 0.00E+0 | 4.433 5E-1 | 9.50E-2 | 2.752 9E-3 | 1.27E-4 | |
MW2 | 2 | 1.60E-2 | 1.955 6E-1 | 1.50E-1 | 2.381 0E-1 | 3.20E-1 | 3.723 0E-1 | 8.89E-2 | 2.680 3E-2 | 8.93E-3 | |
MW3 | 2 | 6.917 9E-3 | 2.81E-4 | 6.114 7E-3 | 2.58E-4 | 9.331 7E-1 | 2.75E-2 | 6.152 6E-1 | 3.73E-1 | 3.06E-4 | |
MW4 | 3 | 5.324 9E-2 | 2.42E-3 | 2.10E-3 | 1.223 4E-1 | 0.00E+0 | 5.650 4E-1 | 2.33E-1 | 5.803 8E-2 | 2.42E-3 | |
MW5 | 2 | 1.490 0E-1 | 3.32E-1 | 4.01E-1 | NaN | NaN | 7.145 1E-1 | 4.61E-2 | 5.964 0E-1 | 3.27E-1 | |
MW6 | 2 | 1.81E-1 | 2.950 6E-1 | 4.70E-1 | 9.553 0E-1 | 3.08E-1 | 6.871 4E-1 | 2.50E-1 | 1.363 3E-1 | 1.99E-1 | |
MW7 | 2 | 5.152 0E-3 | 4.04E-4 | 4.04E-4 | 1.379 4E-2 | 2.17E-3 | 6.500 4E-1 | 1.30E-1 | 6.612 2E-3 | 3.36E-4 | |
MW8 | 3 | 7.83E-3 | 1.196 4E-1 | 3.06E-2 | 5.795 1E-1 | 6.42E-1 | 8.056 8E-1 | 2.07E-1 | 6.224 3E-2 | 7.27E-3 | |
MW9 | 2 | 1.86E-3 | 1.009 8E-2 | 1.40E-3 | 2.840 2E-1 | 4.01E-1 | 7.391 2E-1 | 4.77E-1 | 8.112 1E-3 | 5.88E-4 | |
MW10 | 2 | 2.26E-1 | 3.881 2E-1 | 0.00E+0 | NaN | NaN | 5.348 8E-1 | 1.97E-1 | 6.491 7E-2 | 6.51E-2 | |
MW11 | 2 | 6.834 1E-3 | 3.36E-4 | 7.11E-4 | 9.743 2E-2 | 1.61E-1 | 1.117 1E+0 | 2.79E-1 | 7.769 9E-3 | 5.45E-4 | |
MW12 | 2 | 5.338 0E-3 | 1.96E-4 | 1.93E-4 | 6.949 6E-1 | 2.02E-1 | 8.027 5E-1 | 3.64E-1 | 6.963 5E-3 | 6.69E-4 | |
MW13 | 2 | 6.46E-2 | 2.872 4E-1 | 1.32E-1 | 2.540 4E-1 | 8.05E-2 | 1.126 8E+0 | 6.67E-1 | 1.106 9E-1 | 4.62E-2 | |
MW14 | 3 | 1.836 4E-1 | 2.31E-2 | 2.70E-3 | 2.530 3E-1 | 1.52E-1 | 2.684 5E+0 | 3.94E-1 | 1.232 8E-1 | 5.88E-3 |
Tab. 1 IGD values obtained by CMOEA-MSS and other algorithms on MW test set
测试函数 | M | NSGA-Ⅱ+ARSBX | PPS | ToP | I-DBEA | CMOEA-MSS | |||||
---|---|---|---|---|---|---|---|---|---|---|---|
平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | ||
MW1 | 2 | 2.000 8E-3 | 3.94E-5 | 9.55E-5 | 4.307 7E-2 | 0.00E+0 | 4.433 5E-1 | 9.50E-2 | 2.752 9E-3 | 1.27E-4 | |
MW2 | 2 | 1.60E-2 | 1.955 6E-1 | 1.50E-1 | 2.381 0E-1 | 3.20E-1 | 3.723 0E-1 | 8.89E-2 | 2.680 3E-2 | 8.93E-3 | |
MW3 | 2 | 6.917 9E-3 | 2.81E-4 | 6.114 7E-3 | 2.58E-4 | 9.331 7E-1 | 2.75E-2 | 6.152 6E-1 | 3.73E-1 | 3.06E-4 | |
MW4 | 3 | 5.324 9E-2 | 2.42E-3 | 2.10E-3 | 1.223 4E-1 | 0.00E+0 | 5.650 4E-1 | 2.33E-1 | 5.803 8E-2 | 2.42E-3 | |
MW5 | 2 | 1.490 0E-1 | 3.32E-1 | 4.01E-1 | NaN | NaN | 7.145 1E-1 | 4.61E-2 | 5.964 0E-1 | 3.27E-1 | |
MW6 | 2 | 1.81E-1 | 2.950 6E-1 | 4.70E-1 | 9.553 0E-1 | 3.08E-1 | 6.871 4E-1 | 2.50E-1 | 1.363 3E-1 | 1.99E-1 | |
MW7 | 2 | 5.152 0E-3 | 4.04E-4 | 4.04E-4 | 1.379 4E-2 | 2.17E-3 | 6.500 4E-1 | 1.30E-1 | 6.612 2E-3 | 3.36E-4 | |
MW8 | 3 | 7.83E-3 | 1.196 4E-1 | 3.06E-2 | 5.795 1E-1 | 6.42E-1 | 8.056 8E-1 | 2.07E-1 | 6.224 3E-2 | 7.27E-3 | |
MW9 | 2 | 1.86E-3 | 1.009 8E-2 | 1.40E-3 | 2.840 2E-1 | 4.01E-1 | 7.391 2E-1 | 4.77E-1 | 8.112 1E-3 | 5.88E-4 | |
MW10 | 2 | 2.26E-1 | 3.881 2E-1 | 0.00E+0 | NaN | NaN | 5.348 8E-1 | 1.97E-1 | 6.491 7E-2 | 6.51E-2 | |
MW11 | 2 | 6.834 1E-3 | 3.36E-4 | 7.11E-4 | 9.743 2E-2 | 1.61E-1 | 1.117 1E+0 | 2.79E-1 | 7.769 9E-3 | 5.45E-4 | |
MW12 | 2 | 5.338 0E-3 | 1.96E-4 | 1.93E-4 | 6.949 6E-1 | 2.02E-1 | 8.027 5E-1 | 3.64E-1 | 6.963 5E-3 | 6.69E-4 | |
MW13 | 2 | 6.46E-2 | 2.872 4E-1 | 1.32E-1 | 2.540 4E-1 | 8.05E-2 | 1.126 8E+0 | 6.67E-1 | 1.106 9E-1 | 4.62E-2 | |
MW14 | 3 | 1.836 4E-1 | 2.31E-2 | 2.70E-3 | 2.530 3E-1 | 1.52E-1 | 2.684 5E+0 | 3.94E-1 | 1.232 8E-1 | 5.88E-3 |
测试函数 | M | NSGA⁃Ⅱ+ARSBX | PPS | ToP | I⁃DBEA | CMOEA-MSS | |||||
---|---|---|---|---|---|---|---|---|---|---|---|
平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | ||
MW1 | 2 | 4.899 2E-1 | 1.52E-5 | 1.38E-4 | 4.146 4E-1 | 0.00E+0 | 1.241 3E-1 | 8.30E-2 | 4.882 7E-1 | 6.04E-4 | |
MW2 | 2 | 2.22E-2 | 3.510 5E-1 | 1.62E-1 | 3.538 6E-1 | 2.40E-1 | 2.378 0E-1 | 6.38E-2 | 5.434 2E-1 | 1.31E-2 | |
MW3 | 2 | 5.413 1E-1 | 4.81E-4 | 5.436 6E-1 | 4.59E-4 | 0.000 0E+0 | 0.00E+0 | 1.557 7E-1 | 1.55E-1 | 9.08E-4 | |
MW4 | 3 | 8.259 9E-1 | 2.25E-3 | 3.68E-3 | 7.087 8E-1 | 0.00E+0 | 2.317 6E-1 | 1.44E-1 | 8.129 6E-1 | 6.81E-3 | |
MW5 | 2 | 2.776 6E-1 | 1.04E-1 | 1.24E-1 | NaN | NaN | 4.237 2E-2 | 3.97E-2 | 1.361 8E-1 | 1.01E-1 | |
MW6 | 2 | 4.98E-2 | 1.905 0E-1 | 1.09E-1 | 2.014 4E-2 | 4.03E-2 | 7.607 4E-2 | 4.67E-2 | 2.463 9E-1 | 7.38E-2 | |
MW7 | 2 | 4.114 7E-1 | 4.56E-4 | 4.120 2E-1 | 2.00E-4 | 3.987 6E-1 | 2.17E-3 | 1.249 5E-1 | 3.54E-2 | 3.33E-4 | |
MW8 | 3 | 1.45E-2 | 3.666 1E-1 | 5.44E-2 | 1.794 2E-1 | 2.54E-1 | 8.526 6E-2 | 3.19E-2 | 4.988 0E-1 | 1.98E-2 | |
MW9 | 2 | 3.896 7E-1 | 2.35E-3 | 3.845 5E-1 | 1.76E-3 | 2.232 2E-1 | 1.95E-1 | 9.135 8E-2 | 1.33E-1 | 6.76E-4 | |
MW10 | 2 | 2.656 2E-1 | 1.05E-1 | 0.00E+0 | NaN | NaN | 1.405 3E-1 | 5.93E-2 | 3.994 6E-1 | 4.15E-2 | |
MW11 | 2 | 8.18E-5 | 4.477 1E-1 | 4.79E-5 | 4.155 1E-1 | 5.33E-2 | 1.334 3E-1 | 7.83E-2 | 4.475 6E-1 | 1.79E-4 | |
MW12 | 2 | 6.041 4E-1 | 1.92E-4 | 6.024 9E-1 | 5.65E-4 | 4.667 4E-2 | 8.08E-2 | 5.458 5E-2 | 8.19E-2 | 9.66E-4 | |
MW13 | 2 | 3.570 0E-1 | 3.79E-2 | 3.124 1E-1 | 7.82E-2 | 3.296 2E-1 | 4.71E-2 | 1.987 2E-1 | 1.11E-1 | 4.222 5E-1 | 3.18E-2 |
MW14 | 3 | 4.291 9E-1 | 4.64E-3 | 4.530 6E-1 | 3.00E-3 | 3.951 1E-1 | 7.37E-2 | 1.071 4E-2 | 9.68E-4 | 2.67E-3 |
Tab. 2 HV values obtained by CMOEA-MSS and other algorithms on MW test set
测试函数 | M | NSGA⁃Ⅱ+ARSBX | PPS | ToP | I⁃DBEA | CMOEA-MSS | |||||
---|---|---|---|---|---|---|---|---|---|---|---|
平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | ||
MW1 | 2 | 4.899 2E-1 | 1.52E-5 | 1.38E-4 | 4.146 4E-1 | 0.00E+0 | 1.241 3E-1 | 8.30E-2 | 4.882 7E-1 | 6.04E-4 | |
MW2 | 2 | 2.22E-2 | 3.510 5E-1 | 1.62E-1 | 3.538 6E-1 | 2.40E-1 | 2.378 0E-1 | 6.38E-2 | 5.434 2E-1 | 1.31E-2 | |
MW3 | 2 | 5.413 1E-1 | 4.81E-4 | 5.436 6E-1 | 4.59E-4 | 0.000 0E+0 | 0.00E+0 | 1.557 7E-1 | 1.55E-1 | 9.08E-4 | |
MW4 | 3 | 8.259 9E-1 | 2.25E-3 | 3.68E-3 | 7.087 8E-1 | 0.00E+0 | 2.317 6E-1 | 1.44E-1 | 8.129 6E-1 | 6.81E-3 | |
MW5 | 2 | 2.776 6E-1 | 1.04E-1 | 1.24E-1 | NaN | NaN | 4.237 2E-2 | 3.97E-2 | 1.361 8E-1 | 1.01E-1 | |
MW6 | 2 | 4.98E-2 | 1.905 0E-1 | 1.09E-1 | 2.014 4E-2 | 4.03E-2 | 7.607 4E-2 | 4.67E-2 | 2.463 9E-1 | 7.38E-2 | |
MW7 | 2 | 4.114 7E-1 | 4.56E-4 | 4.120 2E-1 | 2.00E-4 | 3.987 6E-1 | 2.17E-3 | 1.249 5E-1 | 3.54E-2 | 3.33E-4 | |
MW8 | 3 | 1.45E-2 | 3.666 1E-1 | 5.44E-2 | 1.794 2E-1 | 2.54E-1 | 8.526 6E-2 | 3.19E-2 | 4.988 0E-1 | 1.98E-2 | |
MW9 | 2 | 3.896 7E-1 | 2.35E-3 | 3.845 5E-1 | 1.76E-3 | 2.232 2E-1 | 1.95E-1 | 9.135 8E-2 | 1.33E-1 | 6.76E-4 | |
MW10 | 2 | 2.656 2E-1 | 1.05E-1 | 0.00E+0 | NaN | NaN | 1.405 3E-1 | 5.93E-2 | 3.994 6E-1 | 4.15E-2 | |
MW11 | 2 | 8.18E-5 | 4.477 1E-1 | 4.79E-5 | 4.155 1E-1 | 5.33E-2 | 1.334 3E-1 | 7.83E-2 | 4.475 6E-1 | 1.79E-4 | |
MW12 | 2 | 6.041 4E-1 | 1.92E-4 | 6.024 9E-1 | 5.65E-4 | 4.667 4E-2 | 8.08E-2 | 5.458 5E-2 | 8.19E-2 | 9.66E-4 | |
MW13 | 2 | 3.570 0E-1 | 3.79E-2 | 3.124 1E-1 | 7.82E-2 | 3.296 2E-1 | 4.71E-2 | 1.987 2E-1 | 1.11E-1 | 4.222 5E-1 | 3.18E-2 |
MW14 | 3 | 4.291 9E-1 | 4.64E-3 | 4.530 6E-1 | 3.00E-3 | 3.951 1E-1 | 7.37E-2 | 1.071 4E-2 | 9.68E-4 | 2.67E-3 |
测试函数 | M | NSGA⁃Ⅱ+ARSBX | PPS | ToP | I⁃DBEA | CMOEA⁃MSS | |||||
---|---|---|---|---|---|---|---|---|---|---|---|
平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | ||
DASCMOP1 | 2 | 1.328 2E-1 | 2.69E-1 | 3.13E-1 | 8.075 7E-1 | 2.74E-2 | 8.228 8E-1 | 4.09E-2 | 6.869 2E-1 | 2.90E-2 | |
DASCMOP2 | 2 | 1.64E-2 | 1.526 0E-1 | 8.40E-2 | 7.037 7E-1 | 1.72E-1 | 3.472 0E-1 | 3.43E-2 | 2.457 9E-1 | 1.91E-2 | |
DASCMOP3 | 2 | 3.438 6E-1 | 1.79E-4 | 5.03E-4 | 8.023 9E-1 | 3.89E-2 | 4.682 3E-1 | 1.92E-1 | 3.849 0E-1 | 5.50E-2 | |
DASCMOP4 | 3 | 3.632 1E-1 | 2.74E-2 | 6.753 5E-1 | 1.65E-2 | NaN | NaN | 1.031 0E+0 | 1.13E-1 | 2.01E-1 | |
DASCMOP5 | 2 | 5.080 1E-1 | 2.05E-2 | 4.93E-1 | NaN | NaN | 1.058 7E+0 | 1.48E-1 | 1.721 1E-2 | 1.47E-2 | |
DASCMOP6 | 2 | 6.709 3E-1 | 8.21E-2 | 4.27E-1 | NaN | NaN | 9.470 8E-1 | 1.44E-1 | 2.235 7E-2 | 4.90E-3 | |
DASCMOP7 | 2 | 3.94E-2 | 2.309 6E-1 | 2.21E-1 | NaN | NaN | 8.471 7E-1 | 4.43E-1 | 5.460 4E-2 | 6.64E-3 | |
DASCMOP8 | 3 | 7.318 8E-2 | 2.43E-2 | 2.973 2E-1 | 2.06E-1 | NaN | NaN | 1.089 5E+0 | 3.88E-1 | 3.04E-2 | |
DASCMOP9 | 2 | 3.644 6E-1 | 5.70E-2 | 1.58E-1 | 6.785 9E-1 | 2.90E-1 | 8.220 4E-1 | 1.26E-1 | 7.195 8E-1 | 4.20E-2 |
Tab. 3 IGD values obtained by CMOEA-MSS and other algorithms on DASCMOP test set
测试函数 | M | NSGA⁃Ⅱ+ARSBX | PPS | ToP | I⁃DBEA | CMOEA⁃MSS | |||||
---|---|---|---|---|---|---|---|---|---|---|---|
平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | ||
DASCMOP1 | 2 | 1.328 2E-1 | 2.69E-1 | 3.13E-1 | 8.075 7E-1 | 2.74E-2 | 8.228 8E-1 | 4.09E-2 | 6.869 2E-1 | 2.90E-2 | |
DASCMOP2 | 2 | 1.64E-2 | 1.526 0E-1 | 8.40E-2 | 7.037 7E-1 | 1.72E-1 | 3.472 0E-1 | 3.43E-2 | 2.457 9E-1 | 1.91E-2 | |
DASCMOP3 | 2 | 3.438 6E-1 | 1.79E-4 | 5.03E-4 | 8.023 9E-1 | 3.89E-2 | 4.682 3E-1 | 1.92E-1 | 3.849 0E-1 | 5.50E-2 | |
DASCMOP4 | 3 | 3.632 1E-1 | 2.74E-2 | 6.753 5E-1 | 1.65E-2 | NaN | NaN | 1.031 0E+0 | 1.13E-1 | 2.01E-1 | |
DASCMOP5 | 2 | 5.080 1E-1 | 2.05E-2 | 4.93E-1 | NaN | NaN | 1.058 7E+0 | 1.48E-1 | 1.721 1E-2 | 1.47E-2 | |
DASCMOP6 | 2 | 6.709 3E-1 | 8.21E-2 | 4.27E-1 | NaN | NaN | 9.470 8E-1 | 1.44E-1 | 2.235 7E-2 | 4.90E-3 | |
DASCMOP7 | 2 | 3.94E-2 | 2.309 6E-1 | 2.21E-1 | NaN | NaN | 8.471 7E-1 | 4.43E-1 | 5.460 4E-2 | 6.64E-3 | |
DASCMOP8 | 3 | 7.318 8E-2 | 2.43E-2 | 2.973 2E-1 | 2.06E-1 | NaN | NaN | 1.089 5E+0 | 3.88E-1 | 3.04E-2 | |
DASCMOP9 | 2 | 3.644 6E-1 | 5.70E-2 | 1.58E-1 | 6.785 9E-1 | 2.90E-1 | 8.220 4E-1 | 1.26E-1 | 7.195 8E-1 | 4.20E-2 |
测试函数 | M | NSGA⁃Ⅱ+ARSBX | PPS | ToP | I⁃DBEA | CMOEA⁃MSS | |||||
---|---|---|---|---|---|---|---|---|---|---|---|
平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | ||
DASCMOP1 | 2 | 1.727 2E-1 | 8.19E-2 | 8.79E-2 | 0.000 0E+0 | 0.00E+0 | 0.000 0E+0 | 0.00E+0 | 2.483 8E-2 | 2.24E-2 | |
DASCMOP2 | 2 | 5.39E-3 | 3.055 0E-1 | 2.82E-2 | 4.380 6E-2 | 4.02E-2 | 2.036 9E-1 | 7.96E-3 | 2.572 2E-1 | 8.19E-3 | |
DASCMOP3 | 2 | 2.086 6E-1 | 2.10E-5 | 1.54E-4 | 7.665 1E-3 | 1.26E-2 | 1.480 1E-1 | 8.30E-2 | 2.084 6E-1 | 1.24E-4 | |
DASCMOP4 | 3 | 7.97E-3 | 1.127 7E-2 | 5.58E-3 | NaN | NaN | 0.000 0E+0 | 0.00E+0 | 1.089 2E-1 | 5.06E-2 | |
DASCMOP5 | 2 | 7.167 1E-2 | 4.86E-3 | 1.65E-1 | NaN | NaN | 0.000 0E+0 | 0.00E+0 | 3.437 8E-1 | 7.56E-3 | |
DASCMOP6 | 2 | 2.566 9E-2 | 1.51E-2 | 1.42E-1 | NaN | NaN | 2.691 3E-3 | 4.15E-3 | 3.074 3E-1 | 7.51E-3 | |
DASCMOP7 | 2 | 2.23E-2 | 2.103 2E-1 | 7.56E-2 | NaN | NaN | 6.209 6E-2 | 5.79E-2 | 2.786 0E-1 | 2.96E-3 | |
DASCMOP8 | 3 | 1.31E-2 | 1.171 9E-1 | 7.27E-2 | NaN | NaN | 1.821 6E-2 | 2.51E-2 | 1.945 7E-1 | 6.81E-3 | |
DASCMOP9 | 2 | 1.311 0E-1 | 1.01E-2 | 3.93E-2 | 6.768 0E-2 | 4.46E-2 | 4.286 6E-2 | 6.03E-3 | 4.928 8E-2 | 4.22E-3 |
Tab. 4 HV values obtained by CMOEA-MSS and other algorithms on DASCMOP test set
测试函数 | M | NSGA⁃Ⅱ+ARSBX | PPS | ToP | I⁃DBEA | CMOEA⁃MSS | |||||
---|---|---|---|---|---|---|---|---|---|---|---|
平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | ||
DASCMOP1 | 2 | 1.727 2E-1 | 8.19E-2 | 8.79E-2 | 0.000 0E+0 | 0.00E+0 | 0.000 0E+0 | 0.00E+0 | 2.483 8E-2 | 2.24E-2 | |
DASCMOP2 | 2 | 5.39E-3 | 3.055 0E-1 | 2.82E-2 | 4.380 6E-2 | 4.02E-2 | 2.036 9E-1 | 7.96E-3 | 2.572 2E-1 | 8.19E-3 | |
DASCMOP3 | 2 | 2.086 6E-1 | 2.10E-5 | 1.54E-4 | 7.665 1E-3 | 1.26E-2 | 1.480 1E-1 | 8.30E-2 | 2.084 6E-1 | 1.24E-4 | |
DASCMOP4 | 3 | 7.97E-3 | 1.127 7E-2 | 5.58E-3 | NaN | NaN | 0.000 0E+0 | 0.00E+0 | 1.089 2E-1 | 5.06E-2 | |
DASCMOP5 | 2 | 7.167 1E-2 | 4.86E-3 | 1.65E-1 | NaN | NaN | 0.000 0E+0 | 0.00E+0 | 3.437 8E-1 | 7.56E-3 | |
DASCMOP6 | 2 | 2.566 9E-2 | 1.51E-2 | 1.42E-1 | NaN | NaN | 2.691 3E-3 | 4.15E-3 | 3.074 3E-1 | 7.51E-3 | |
DASCMOP7 | 2 | 2.23E-2 | 2.103 2E-1 | 7.56E-2 | NaN | NaN | 6.209 6E-2 | 5.79E-2 | 2.786 0E-1 | 2.96E-3 | |
DASCMOP8 | 3 | 1.31E-2 | 1.171 9E-1 | 7.27E-2 | NaN | NaN | 1.821 6E-2 | 2.51E-2 | 1.945 7E-1 | 6.81E-3 | |
DASCMOP9 | 2 | 1.311 0E-1 | 1.01E-2 | 3.93E-2 | 6.768 0E-2 | 4.46E-2 | 4.286 6E-2 | 6.03E-3 | 4.928 8E-2 | 4.22E-3 |
1 | CUI Y F, GENG Z Q, ZHU Q X, et al. Review: multi-objective optimization methods and application in energy saving[J]. Energy, 2017, 125: 681-704. 10.1016/j.energy.2017.02.174 |
2 | BASU M. Economic environmental dispatch using multi-objective differential evolution[J]. Applied Soft Computing, 2011, 11(2): 2845-2853. 10.1016/j.asoc.2010.11.014 |
3 | DEB K, PRATAP A, AGARWAL S, et al. A fast and elitist multiobjective genetic algorithm: NSGA-Ⅱ[J]. IEEE Transactions on Evolutionary Computation, 2002, 6(2): 182-197. 10.1109/4235.996017 |
4 | TAKAHAMA T, SAKAI S. Constrained optimization by ε constrained particle swarm optimizer with ε-level control[C]// ABRAHAM A, DOTE, Y, FURUHASHI T, et al. Soft Computing as Transdisciplinary Science and Technology: Proceedings of the 4th IEEE International Workshop WSTST’ 05, AINSC 29. Berlin: Springer, 2005: 1019-1029. 10.1007/3-540-32391-0_105 |
5 | RUNARSSON T P, YAO X. Stochastic ranking for constrained evolutionary optimization[J]. IEEE Transactions on Evolutionary Computation, 2000, 4(3): 284-294. 10.1109/4235.873238 |
6 | ZITZLER E, LAUMANNS M, THIELE L. SPEA2: improving the strength Pareto evolutionary algorithm for multiobjective optimization: TIK-Report 103[R/OL]. (2001-05) [2022-05-21].. |
7 | ZHANG Q F, LI H. MOEA/D: a multiobjective evolutionary algorithm based on decomposition[J]. IEEE Transactions on Evolutionary Computation, 2007, 11(6): 712-731. 10.1109/tevc.2007.892759 |
8 | LI K, DEB K, ZHANG Q F, et al. An evolutionary many-objective optimization algorithm based on dominance and decomposition[J]. IEEE Transactions on Evolutionary Computation, 2015, 19(5): 694-716. 10.1109/tevc.2014.2373386 |
9 | EMMERICH M, BEUME N, NAUJOKS B. An EMO algorithm using the hypervolume measure as selection criterion[C]// Proceedings of the 2005 International Conference on Evolutionary Multi-Criterion Optimization, LNCS 3410. Berlin: Springer, 2005: 62-76. |
10 | BADER J, ZITZLER E. HypE: an algorithm for fast hypervolume-based many-objective optimization[J]. Evolutionary Computation, 2011, 19(1): 45-76. 10.1162/evco_a_00009 |
11 | WANG Y, XU B, SUN G Y, et al. A two-phase differential evolution for uniform designs in constrained experimental domains[J]. IEEE Transactions on Evolutionary Computation, 2017, 21(5): 665-680. 10.1109/tevc.2017.2669098 |
12 | MA H P, WEI H Y, TIAN Y, et al. A multi-stage evolutionary algorithm for multi-objective optimization with complex constraints[J]. Information Sciences, 2021, 560: 68-91. 10.1016/j.ins.2021.01.029 |
13 | FAN Z, LI W J, CAI X Y, et al. Push and pull search for solving constrained multi-objective optimization problems[J]. Swarm and Evolutionary Computation, 2019, 44: 665-679. 10.1016/j.swevo.2018.08.017 |
14 | LIU Z Z, WANG Y. Handling constrained multiobjective optimization problems with constraints in both the decision and objective spaces[J]. IEEE Transactions on Evolutionary Computation, 2019, 23(5): 870-884. 10.1109/tevc.2019.2894743 |
15 | PAN L Q, XU W T, LI L H, et al. Adaptive simulated binary crossover for rotated multi-objective optimization[J]. Swarm and Evolutionary Computation, 2021, 60: No.100759. 10.1016/j.swevo.2020.100759 |
16 | ASAFUDDOULA M, RAY T, SARKER R. A decomposition-based evolutionary algorithm for many objective optimization[J]. IEEE Transactions on Evolutionary Computation, 2015, 19(3): 445-460. 10.1109/tevc.2014.2339823 |
17 | TIAN Y, CHENG R, ZHANG X Y, et al. PlatEMO: a Matlab platform for evolutionary multi-objective optimization [Educational Forum][J]. IEEE Computational Intelligence Magazine, 2017, 12(4): 73-87. 10.1109/mci.2017.2742868 |
18 | MA Z W, WANG Y. Evolutionary constrained multiobjective optimization: test suite construction and performance comparisons[J]. IEEE Transactions on Evolutionary Computation, 2019, 23(6): 972-986. 10.1109/tevc.2019.2896967 |
19 | YUAN J W, LIU H L, ONG Y S, et al. Indicator-based evolutionary algorithm for solving constrained multiobjective optimization problems[J]. IEEE Transactions on Evolutionary Computation, 2022, 26(2): 379-391. 10.1109/tevc.2021.3089155 |
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