Research Article
An Improved Adaptive Human Learning Optimization Algorithm with Reasoning Learning
Table 6
The results of five AHLORLs on the 10-dimensional CEC 15 benchmarks.
| | Fun | Metric | AHLORL | AHLORL2 | AHLORL3 | AHLORL4 | AHLORL5 |
| | F1 | Best | 3.5098E + 05 | 1.4133E + 06 | 1.0411E + 06 | 8.4655E + 05 | 7.4393E + 05 | | Mean | 2.9313E + 06 | 6.1536E + 06 | 3.4012E + 06 | 3.4200E + 06 | 3.0466E + 06 | | Std | 1.5240E + 06 | 4.0321E + 06 | 1.7932E + 06 | 2.5401E + 06 | 1.2297E + 06 | | t-Test | — | 1 | 0 | 0 | 0 | | W-test | — | 1 | 0 | 0 | 0 |
| | F2 | Best | 1.0894E + 06 | 1.2545E + 07 | 7.6671E + 05 | 3.3620E + 05 | 2.1615E + 06 | | Mean | 2.5609E + 07 | 2.7935E + 08 | 2.0945E + 07 | 3.7516E + 07 | 3.0009E + 07 | | Std | 2.0518E + 07 | 3.2278E + 08 | 1.6985E + 07 | 2.8472E + 07 | 2.1323E + 07 | | t-Test | — | 1 | 0 | 1 | 0 | | W-test | — | 1 | 0 | 1 | 0 |
| | F3 | Best | 2.0015E + 01 | 2.0480E + 01 | 2.0051E + 01 | 2.0032E + 01 | 2.0095E + 01 | | Mean | 2.0088E + 01 | 2.0736E + 01 | 2.0194E + 01 | 2.0099E + 01 | 2.0248E + 01 | | Std | 4.4153E − 02 | 8.1513E − 02 | 8.3327E − 02 | 4.1915E − 02 | 9.7447E − 02 | | t-Test | — | 1 | 1 | 0 | 1 | | W-test | — | 1 | 1 | 1 | 1 |
| | F4 | Best | 1.6636E + 01 | 2.5367E + 01 | 1.7398E + 01 | 2.0935E + 01 | 1.9020E + 01 | | Mean | 3.5857E + 01 | 4.6908E + 01 | 3.7162E + 01 | 3.8234E + 01 | 3.7059E + 01 | | Std | 7.3883E + 00 | 1.0394E + 01 | 7.4725E + 00 | 7.8884E + 00 | 8.2516E + 00 | | t-Test | — | 1 | 0 | 1 | 0 | | W-test | — | 1 | 0 | 0 | 0 |
| | F5 | Best | 3.1978E + 02 | 7.7955E + 02 | 5.7000E + 02 | 4.4575E + 02 | 6.0766E + 02 | | Mean | 1.3751E + 03 | 1.8290E + 03 | 1.6460E + 03 | 1.5358E + 03 | 1.6217E + 03 | | Std | 4.0458E + 02 | 4.7633E + 02 | 3.7057E + 02 | 4.0991E + 02 | 3.7949E + 02 | | t-Test | — | 1 | 1 | 1 | 1 | | W-test | — | 1 | 1 | 1 | 1 |
| | F6 | Best | 5.9882E + 04 | 7.2691E + 04 | 6.3261E + 04 | 1.1807E + 05 | 3.9817E + 04 | | Mean | 4.0067E + 05 | 5.3018E + 05 | 4.5017E + 05 | 5.2750E + 05 | 4.9655E + 05 | | Std | 2.2508E + 05 | 4.4915E + 05 | 2.5779E + 05 | 3.9484E + 05 | 3.0791E + 05 | | t-Test | — | 1 | 0 | 1 | 1 | | W-test | — | 1 | 0 | 1 | 1 |
| | F7 | Best | 6.4758E + 00 | 6.9204E + 00 | 7.4183E + 00 | 7.5758E + 00 | 7.8512E + 00 | | Mean | 1.0124E + 01 | 1.2739E + 01 | 1.0199E + 01 | 1.0704E + 01 | 1.0105E + 01 | | Std | 1.3229E + 00 | 2.0361E + 00 | 1.1682E + 00 | 1.2033E + 00 | 1.1061E + 00 | | t-Test | — | 1 | 0 | 1 | 0 | | W-test | — | 1 | 0 | 1 | 0 |
| | F8 | Best | 9.5273E + 03 | 1.5489E + 04 | 1.7583E + 04 | 1.7795E + 04 | 6.1712E + 03 | | Mean | 1.0991E + 05 | 1.6202E + 05 | 1.1810E + 05 | 1.5987E + 05 | 1.1532E + 05 | | Std | 6.0527E + 04 | 9.5848E + 04 | 6.8404E + 04 | 8.8975E + 04 | 6.4274E + 04 | | t-Test | — | 1 | 0 | 1 | 0 | | W-test | — | 1 | 0 | 1 | 0 |
| | F9 | Best | 1.0244E + 02 | 1.0297E + 02 | 1.0250E + 02 | 1.0249E + 02 | 1.0237E + 02 | | Mean | 1.0288E + 02 | 1.0432E + 02 | 1.0295E + 02 | 1.0293E + 02 | 1.0294E + 02 | | Std | 2.1536E − 01 | 1.4430E + 00 | 1.9787E − 01 | 2.4404E − 01 | 2.0690E − 01 | | t-Test | — | 1 | 1 | 0 | 1 | | W-test | — | 1 | 1 | 0 | 1 |
| | F10 | Best | 8.0989E + 03 | 3.1026E + 04 | 2.3093E + 04 | 1.4837E + 04 | 1.6642E + 04 | | Mean | 1.5791E + 05 | 2.2310E + 05 | 1.8441E + 05 | 2.3865E + 05 | 1.6185E + 05 | | Std | 9.7338E + 04 | 1.5798E + 05 | 9.7905E + 04 | 1.4587E + 05 | 9.0725E + 04 | | t-Test | — | 1 | 0 | 1 | 0 | | W-test | — | 1 | 0 | 1 | 0 |
| | F11 | Best | 3.0624E + 02 | 3.0737E + 02 | 3.1190E + 02 | 3.0621E + 02 | 3.0970E + 02 | | Mean | 3.2617E + 02 | 6.0056E + 02 | 3.3005E + 02 | 3.5009E + 02 | 3.3688E + 02 | | Std | 3.8006E + 01 | 1.6202E + 02 | 2.5714E + 01 | 8.5204E + 01 | 3.6888E + 01 | | t-Test | — | 1 | 0 | 1 | 0 | | W-test | — | 1 | 1 | 0 | 1 |
| | F12 | Best | 1.0417E + 02 | 1.0500E + 02 | 1.0407E + 02 | 1.0426E + 02 | 1.0442E + 02 | | Mean | 1.0555E + 02 | 1.0679E + 02 | 1.0578E + 02 | 1.0556E + 02 | 1.0578E + 02 | | Std | 5.3918E − 01 | 7.4995E − 01 | 5.4516E − 01 | 5.2658E − 01 | 5.5395E − 01 | | t-Test | — | 1 | 1 | 0 | 1 | | W-test | — | 1 | 1 | 0 | 1 |
| | F13 | Best | 7.5673E + 01 | 8.4114E + 01 | 7.8988E + 01 | 7.9979E + 01 | 8.0951E + 01 | | Mean | 9.1145E + 01 | 9.9983E + 01 | 9.3561E + 01 | 9.1643E + 01 | 9.5014E + 01 | | Std | 6.8232E + 00 | 5.5460E + 00 | 5.6323E + 00 | 5.3644E + 00 | 4.8753E + 00 | | t-Test | — | 1 | 1 | 0 | 1 | | W-test | — | 1 | 1 | 0 | 1 |
| | F14 | Best | 3.1272E + 04 | 3.1326E + 04 | 3.1176E + 04 | 3.1297E + 04 | 3.1460E + 04 | | Mean | 3.2927E + 04 | 3.3531E + 04 | 3.2934E + 04 | 3.2993E + 04 | 3.2947E + 04 | | Std | 8.3761E + 02 | 1.1279E + 03 | 8.0199E + 02 | 7.9269E + 02 | 7.1843E + 02 | | t-Test | — | 1 | 0 | 0 | 0 | | W-test | — | 1 | 0 | 0 | 0 |
| | F15 | Best | 1.0182E + 02 | 1.0434E + 02 | 1.0234E + 02 | 1.0121E + 02 | 1.0222E + 02 | | Mean | 1.0562E + 02 | 1.1068E + 02 | 1.0591E + 02 | 1.0579E + 02 | 1.0615E + 02 | | Std | 1.3104E + 00 | 4.2595E + 00 | 1.3376E + 00 | 1.6978E + 00 | 1.4430E + 00 | | t-Test | — | 1 | 0 | 0 | 1 | | W-test | — | 1 | 0 | 0 | 1 |
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