Research Article
An Improved Adaptive Human Learning Optimization Algorithm with Reasoning Learning
Table 5
The results of five AHLORLs on the 10-dimensional CEC 15 benchmarks.
| | Fun | Metric | AHLORL | AHLORL2 | AHLORL3 | AHLORL4 | AHLORL5 |
| | F1 | Best | 7.0185E + 03 | 1.6356E + 04 | 1.6287E + 04 | 7.4843E + 03 | 5.0977E + 03 | | Mean | 1.4321E + 05 | 3.1414E + 05 | 1.7902E + 05 | 1.7662E + 05 | 1.9387E + 05 | | Std | 1.3145E + 05 | 2.7232E + 05 | 1.3685E + 05 | 1.7698E + 05 | 1.5487E + 05 | | t-Test | — | 1 | 1 | 0 | 1 | | W-test | — | 1 | 1 | 1 | 1 |
| | F2 | Best | 1.4326E + 03 | 6.8963E + 03 | 1.3610E + 03 | 2.2374E + 03 | 1.3546E + 03 | | Mean | 8.4642E + 05 | 5.9482E + 06 | 1.0999E + 06 | 1.6162E + 06 | 7.0918E + 05 | | Std | 1.9368E + 06 | 7.3543E + 06 | 2.5008E + 06 | 3.3453E + 06 | 8.7764E + 05 | | t-Test | — | 1 | 0 | 1 | 0 | | W-test | — | 1 | 0 | 0 | 0 |
| | F3 | Best | 2.5798E + 00 | 2.9440E + 00 | 2.0660E + 00 | 8.2877E + 00 | 3.4195E + 00 | | Mean | 1.8580E + 01 | 1.8803E + 01 | 1.8114E + 01 | 1.9799E + 01 | 1.8904E + 01 | | Std | 4.3836E + 00 | 4.1082E + 00 | 5.0023E + 00 | 1.4746E + 00 | 3.7793E + 00 | | t-Test | — | 0 | 0 | 1 | 0 | | W-test | — | 1 | 0 | 1 | 1 |
| | F4 | Best | 5.5808E − 01 | 3.0217E + 00 | 2.0195E + 00 | 1.1184E + 00 | 1.3070E + 00 | | Mean | 4.4647E + 00 | 5.8591E + 00 | 4.8625E + 00 | 4.7293E + 00 | 5.1812E + 00 | | Std | 1.4911E + 00 | 1.5632E + 00 | 1.6063E + 00 | 1.3735E + 00 | 1.7328E + 00 | | t-Test | — | 1 | 0 | 0 | 1 | | W-test | — | 1 | 0 | 0 | 1 |
| | F5 | Best | 2.5876E + 00 | 5.5531E + 00 | 6.7090E − 01 | 1.7313E + 00 | 8.0449E + 00 | | Mean | 5.7225E + 01 | 8.2763E + 01 | 6.4581E + 01 | 6.5224E + 01 | 7.6558E + 01 | | Std | 5.0841E + 01 | 6.9845E + 01 | 6.2850E + 01 | 6.1357E + 01 | 7.1917E + 01 | | t-Test | — | 1 | 0 | 0 | 1 | | W-test | — | 1 | 0 | 0 | 1 |
| | F6 | Best | 4.5969E + 01 | 5.9686E + 01 | 6.2284E + 01 | 3.2633E + 01 | 6.7267E + 01 | | Mean | 1.3756E + 03 | 2.5942E + 03 | 1.2486E + 03 | 1.9808E + 03 | 1.6455E + 03 | | Std | 1.3486E + 03 | 6.5814E + 03 | 1.2807E + 03 | 1.9696E + 03 | 1.4654E + 03 | | t-Test | — | 0 | 0 | 1 | 0 | | W-test | — | 1 | 0 | 1 | 0 |
| | F7 | Best | 1.5272E − 01 | 2.9158E − 01 | 1.7449E − 01 | 1.5402E − 01 | 1.0669E − 01 | | Mean | 9.1146E − 01 | 1.0890E + 00 | 9.2265E − 01 | 1.0449E + 00 | 9.2102E − 01 | | Std | 3.6188E − 01 | 4.0394E − 01 | 3.2331E − 01 | 3.7025E − 01 | 3.5455E − 01 | | t-Test | — | 1 | 0 | 1 | 0 | | W-test | — | 1 | 0 | 1 | 0 |
| | F8 | Best | 2.8786E + 00 | 5.5281E + 00 | 2.1503E + 00 | 8.0870E + 00 | 1.4100E + 01 | | Mean | 3.3990E + 02 | 5.2568E + 02 | 3.1279E + 02 | 4.6150E + 02 | 3.2763E + 02 | | Std | 3.3356E + 02 | 7.6387E + 02 | 3.4204E + 02 | 5.1608E + 02 | 2.5034E + 02 | | t-Test | — | 1 | 0 | 0 | 0 | | W-test | — | 0 | 0 | 0 | 0 |
| | F9 | Best | 1.0009E + 02 | 1.0014E + 02 | 1.0007E + 02 | 1.0006E + 02 | 1.0008E + 02 | | Mean | 1.0017E + 02 | 1.0025E + 02 | 1.0019E + 02 | 1.0017E + 02 | 1.0019E + 02 | | Std | 3.2463E − 02 | 5.7059E − 02 | 3.4712E − 02 | 3.7246E − 02 | 3.7393E − 02 | | t-Test | — | 1 | 1 | 0 | 1 | | W-test | — | 1 | 1 | 0 | 1 |
| | F10 | Best | 2.2384E + 02 | 2.5789E + 02 | 2.2198E + 02 | 2.2334E + 02 | 2.3119E + 02 | | Mean | 3.5107E + 02 | 4.2840E + 02 | 3.5086E + 02 | 3.6722E + 02 | 3.6328E + 02 | | Std | 6.6269E + 01 | 1.3156E + 02 | 7.1596E + 01 | 6.4233E + 01 | 6.1590E + 01 | | t-Test | — | 1 | 0 | 0 | 0 | | W-test | — | 1 | 0 | 1 | 0 |
| | F11 | Best | 2.7164E + 00 | 3.2384E + 00 | 2.0988E + 00 | 2.1370E + 00 | 3.0977E + 00 | | Mean | 2.1417E + 01 | 1.2580E + 02 | 2.2096E + 01 | 2.7560E + 01 | 9.9780E + 00 | | Std | 6.4015E + 01 | 1.4263E + 02 | 6.3877E + 01 | 7.4865E + 01 | 2.9252E + 01 | | t-Test | — | 1 | 0 | 0 | 0 | | W-test | — | 1 | 0 | 0 | 0 |
| | F12 | Best | 1.0052E + 02 | 1.0140E + 02 | 1.0102E + 02 | 1.0076E + 02 | 1.0091E + 02 | | Mean | 1.0155E + 02 | 1.0249E + 02 | 1.0166E + 02 | 1.0155E + 02 | 1.0168E + 02 | | Std | 4.3034E − 01 | 5.9355E − 01 | 3.6841E − 01 | 4.3902E − 01 | 3.5919E − 01 | | t-Test | — | 1 | 0 | 0 | 1 | | W-test | — | 1 | 0 | 0 | 1 |
| | F13 | Best | 2.1308E + 01 | 2.2542E + 01 | 2.2485E + 01 | 2.1947E + 01 | 2.2726E + 01 | | Mean | 2.5728E + 01 | 2.7713E + 01 | 2.6419E + 01 | 2.6109E + 01 | 2.6735E + 01 | | Std | 1.8822E + 00 | 2.0439E + 00 | 1.7183E + 00 | 1.9366E + 00 | 1.7349E + 00 | | t-Test | — | 1 | 1 | 0 | 1 | | W-test | — | 1 | 1 | 0 | 1 |
| | F14 | Best | 3.3572E + 02 | 5.1767E + 02 | 1.7705E + 02 | 3.4012E + 02 | 3.3437E + 02 | | Mean | 2.7176E + 03 | 4.1555E + 03 | 2.6734E + 03 | 2.9169E + 03 | 2.5102E + 03 | | Std | 9.2981E + 02 | 1.9663 E + 03 | 7.3991E + 02 | 8.8523E + 02 | 8.2462E + 02 | | t-Test | — | 1 | 0 | 0 | 0 | | W-test | — | 1 | 0 | 0 | 0 |
| | F15 | Best | 1.0002E + 02 | 1.0002E + 02 | 1.0010E + 02 | 1.0015E + 02 | 1.0002E + 02 | | Mean | 1.0234E + 02 | 1.0622E + 02 | 1.0268E + 02 | 1.0293E + 02 | 1.0253E + 02 | | Std | 1.9637E + 00 | 4.3625E + 00 | 2.1304E + 00 | 2.6496E + 00 | 1.3014E + 00 | | t-Test | — | 1 | 0 | 0 | 0 | | W-test | — | 1 | 0 | 0 | 0 |
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