Table 9 Statistical results obtained from LMEDO and comparison algorithms based on engineering problems.
From: An improved enterprise development optimizer based on labor migration for numerical optimization
No | Index | LMEDO | EDO | LSHADE | LSHADE-SPACMA | APSM-jSO | EO | IRIME | MRFO | GLS-MPA | ECO | ISGTOA | QIO | EPSCA |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
E1 | Best | 5.8701E+03 | 6.3603E+03 | 6.5608E+03 | 6.4296E+03 | 6.3968E+03 | 6.4912E+03 | 7.3587E+03 | 6.2695E+03 | 6.1609E+03 | 6.5578E+03 | 7.6135E+03 | 6.8865E+03 | 7.1798E+03 |
Mean | 5.8701E+03 | 8.1575E+03 | 6.7919E+03 | 6.5701E+03 | 6.5278E+03 | 7.1135E+03 | 9.2970E+03 | 6.6031E+03 | 6.8943E+03 | 7.3632E+03 | 1.0906E+04 | 8.8967E+03 | 8.0696E+03 | |
Std | 1.1879E−03 | 3.0591E+03 | 2.5208E+02 | 1.1723E+02 | 1.5726E+02 | 7.0108E+02 | 1.8366E+03 | 3.7616E+02 | 5.4412E+02 | 6.6948E+02 | 2.8706E+03 | 1.5188E+03 | 1.4429E+03 | |
Rank | 1 | 10 | 5 | 3 | 2 | 7 | 12 | 4 | 6 | 8 | 13 | 11 | 9 | |
E2 | Best | 2.6389E+02 | 2.6390E+02 | 2.6389E+02 | 2.6389E+02 | 2.6389E+02 | 2.6390E+02 | 2.6396E+02 | 2.6390E+02 | 2.6389E+02 | 2.6389E+02 | 2.6393E+02 | 2.6393E+02 | 2.6389E+02 |
Mean | 2.6389E+02 | 2.6394E+02 | 2.6392E+02 | 2.6389E+02 | 2.6389E+02 | 2.6401E+02 | 2.6400E+02 | 2.6391E+02 | 2.6426E+02 | 2.6400E+02 | 2.6409E+02 | 2.6404E+02 | 2.6402E+02 | |
Std | 2.8422E−14 | 5.4048E−02 | 4.8007E−02 | 0.0000E+00 | 1.4829E−03 | 1.2288E−01 | 4.5337E−02 | 1.1315E−02 | 6.8564E−01 | 1.7913E−01 | 2.3338E−01 | 1.1931E−01 | 1.1146E−01 | |
Rank | 1 | 6 | 5 | 2 | 3 | 9 | 8 | 4 | 13 | 7 | 12 | 11 | 10 | |
E3 | Best | 1.6928E+00 | 1.7467E+00 | 1.7325E+00 | 1.6928E+00 | 1.0890E+15 | 1.7428E+00 | 1.7431E+00 | 1.7439E+00 | 1.7206E+00 | 2.1851E+00 | 1.7669E+00 | 1.7475E+00 | 1.7354E+00 |
Mean | 1.6928E+00 | 1.8017E+00 | 1.7767E+00 | 1.6929E+00 | 1.0890E+15 | 1.7646E+00 | 1.8627E+00 | 1.8296E+00 | 1.7961E+00 | 2.3471E+00 | 1.8882E+00 | 1.8186E+00 | 1.9130E+00 | |
Std | 3.8953E−07 | 5.4260E−02 | 3.1868E−02 | 1.2382E−04 | 3.6299E+07 | 2.1905E−02 | 9.9630E−02 | 8.3415E−02 | 8.6873E−02 | 1.4883E−01 | 1.1896E−01 | 4.8812E−02 | 3.0891E−01 | |
Rank | 1 | 6 | 4 | 2 | 13 | 3 | 9 | 8 | 5 | 12 | 10 | 7 | 11 | |
E4 | Best | 2.7009E−12 | 9.9216E−10 | 2.3576E−09 | 2.3078E−11 | 2.3078E−11 | 9.9216E−10 | 9.9216E−10 | 2.7009E−12 | 6.6021E−10 | 8.8876E−10 | 2.3078E−11 | 2.7009E−12 | 1.2634E−09 |
Mean | 7.8626E−11 | 6.2461E−09 | 1.8186E−08 | 5.7689E−10 | 7.4076E−10 | 9.6032E−09 | 5.0211E−09 | 1.0283E−09 | 1.1083E−09 | 1.3459E−08 | 1.8907E−09 | 8.6494E−09 | 2.0166E−08 | |
Std | 7.1015E−11 | 7.7689E−09 | 2.7379E−08 | 6.1043E−10 | 1.0283E−09 | 1.0490E−08 | 6.1778E−09 | 1.2184E−09 | 7.1213E−10 | 1.3019E−08 | 1.0440E−09 | 1.6894E−08 | 1.7378E−08 | |
Rank | 1 | 8 | 12 | 2 | 3 | 10 | 7 | 4 | 5 | 11 | 6 | 9 | 13 | |
E5 | Best | 1.6086E+01 | 1.6636E+01 | 1.7330E+01 | 1.6115E+01 | 1.0098E+11 | 1.7054E+01 | 1.6331E+01 | 1.6877E+01 | 1.6268E+01 | 1.7449E+01 | 1.7579E+01 | 1.7153E+01 | 1.7711E+01 |
Mean | 1.6098E+01 | 1.6814E+01 | 1.7804E+01 | 1.6185E+01 | 1.0098E+11 | 1.7600E+01 | 1.8088E + 01 | 1.7107E + 01 | 1.7022E + 01 | 1.9710E + 01 | 1.7726E + 01 | 2.2875E + 01 | 2.0964E + 01 | |
Std | 2.7093E−02 | 1.5137E−01 | 4.1424E−01 | 5.5683E−02 | 2.4805E + 04 | 4.2952E−01 | 1.2630E + 00 | 3.3611E−01 | 4.5295E−01 | 4.5228E + 00 | 2.0383E−01 | 8.8869E + 00 | 6.7025E + 00 | |
Rank | 1 | 3 | 8 | 2 | 13 | 6 | 9 | 5 | 4 | 10 | 7 | 12 | 11 | |
Friedman ranking | 1.000 | 6.600 | 6.800 | 2.200 | 6.800 | 7.000 | 9.000 | 5.000 | 6.600 | 9.600 | 9.600 | 10.000 | 10.800 | |
Wilcoxon rank sum test results |  + / = /− | 5/0/0 | 5/0/0 | 4/1/0 | 4/1/0 | 5/0/0 | 5/0/0 | 4/1/0 | 5/0/0 | 5/0/0 | 5/0/0 | 4/1/0 | 5/0/0 | |
