Research Article
An Improved Adaptive Human Learning Optimization Algorithm with Reasoning Learning
Table 14
The results of all the algorithms on the multidimensional knapsack problems (MKPs).
| Problem | Algorithm | Best | Mean | Worst | Std | t-Test | W-test |
| 10.500.0 | AHLORL | 113770.0 | 112515.5 | 111112.0 | 520.6 | — | — | HLORL | 113392.0 | 111882.3 | 110844.0 | 508.9 | 1 | 1 | IAHLO | 103981.0 | 101229.4 | 99509.0 | 817.3 | 1 | 1 | SCHLO | 110985.0 | 109034.1 | 106690.0 | 819.4 | 1 | 1 | SFPSO | 105522.0 | 103397.3 | 99615.0 | 1083.6 | 1 | 1 | BGWO | 98719.0 | 94972.4 | 91396.0 | 1452.8 | 1 | 1 | BAAA | 109324.0 | 107065.6 | 102318.0 | 1361.2 | 1 | 1 | IBDE | 98658.0 | 95399.1 | 93779.0 | 932.2 | 1 | 1 |
| 10.500.1 | AHLORL | 115343.0 | 114185.3 | 112536.0 | 536.1 | — | — | HLORL | 114829.0 | 113352.3 | 112249.0 | 510.1 | 1 | 1 | IAHLO | 104791.0 | 102300.2 | 99872.0 | 883.3 | 1 | 1 | SCHLO | 112654.0 | 110545.4 | 108797.0 | 880.0 | 1 | 1 | SFPSO | 107092.0 | 104492.1 | 101672.0 | 1032.7 | 1 | 1 | BGWO | 98755.0 | 95498.8 | 91153.0 | 1340.1 | 1 | 1 | BAAA | 111014.0 | 108443.1 | 104757.0 | 1118.7 | 1 | 1 | IBDE | 98355.0 | 95931.3 | 93363.0 | 1019.0 | 1 | 1 |
| 10.500.2 | AHLORL | 115115.0 | 114113.1 | 113027.0 | 482.8 | — | — | HLORL | 114597.0 | 113382.7 | 112109.0 | 470.0 | 1 | 1 | IAHLO | 104090.0 | 102071.7 | 99972.0 | 799.1 | 1 | 1 | SCHLO | 112137.0 | 110417.4 | 108348.0 | 756.7 | 1 | 1 | SFPSO | 107126.0 | 104349.0 | 102060.0 | 1037.5 | 1 | 1 | BGWO | 98531.0 | 95154.7 | 91693.0 | 1459.0 | 1 | 1 | BAAA | 110563.0 | 108404.6 | 105710.0 | 1060.5 | 1 | 1 | IBDE | 98484.0 | 95936.1 | 93732.0 | 925.0 | 1 | 1 |
| 10.500.3 | AHLORL | 115177.0 | 113690.2 | 112607.0 | 501.9 | — | — | HLORL | 114500.0 | 113000.5 | 111978.0 | 490.9 | 1 | 1 | IAHLO | 103401.0 | 101526.7 | 99638.0 | 783.1 | 1 | 1 | SCHLO | 111905.0 | 109826.5 | 107634.0 | 855.7 | 1 | 1 | SFPSO | 105730.0 | 103726.9 | 101340.0 | 910.6 | 1 | 1 | BGWO | 97955.0 | 95011.9 | 91703.0 | 1370.7 | 1 | 1 | BAAA | 110349.0 | 107690.8 | 104607.0 | 1147.7 | 1 | 1 | IBDE | 98176.0 | 95512.3 | 93028.0 | 986.6 | 1 | 1 |
| 10.500.4 | AHLORL | 112734.0 | 111477.5 | 110234.0 | 438.7 | — | — | HLORL | 112142.0 | 110843.5 | 109754.0 | 488.2 | 1 | 1 | IAHLO | 102241.0 | 100001.5 | 97861.0 | 935.1 | 1 | 1 | SCHLO | 109843.0 | 108015.9 | 105552.0 | 859.6 | 1 | 1 | SFPSO | 105108.0 | 102428.1 | 99452.0 | 1134.1 | 1 | 1 | BGWO | 97090.0 | 93680.8 | 90287.0 | 1443.4 | 1 | 1 | BAAA | 108672.0 | 106086.9 | 103229.0 | 1054.5 | 1 | 1 | IBDE | 96521.0 | 93964.0 | 92109.0 | 981.0 | 1 | 1 |
| 10.500.5 | AHLORL | 115816.0 | 114534.9 | 113008.0 | 545.9 | — | — | HLORL | 115172.0 | 113916.6 | 112556.0 | 466.1 | 1 | 1 | IAHLO | 103176.0 | 101530.9 | 100124.0 | 721.4 | 1 | 1 | SCHLO | 112958.0 | 110823.1 | 108643.0 | 943.8 | 1 | 1 | SFPSO | 107709.0 | 104292.7 | 102048.0 | 1154.5 | 1 | 1 | BGWO | 98901.0 | 94952.6 | 90938.0 | 1504.2 | 1 | 1 | BAAA | 110665.0 | 108352.3 | 105058.0 | 1003.0 | 1 | 1 | IBDE | 97354.0 | 94899.5 | 92461.0 | 1007.2 | 1 | 1 |
| 10.500.6 | AHLORL | 115971.0 | 114783.5 | 113426.0 | 486.1 | — | — | HLORL | 115261.0 | 114186.3 | 112740.0 | 497.9 | 1 | 1 | IAHLO | 104943.0 | 102615.8 | 100549.0 | 828.7 | 1 | 1 | SCHLO | 113446.0 | 111451.9 | 109636.0 | 802.9 | 1 | 1 | SFPSO | 106527.0 | 105021.0 | 101896.0 | 994.4 | 1 | 1 | BGWO | 99483.0 | 95590.0 | 91570.0 | 1533.4 | 1 | 1 | BAAA | 111964.0 | 109092.6 | 106503.0 | 1107.5 | 1 | 1 | IBDE | 98693.0 | 95908.3 | 93870.0 | 1067.9 | 1 | 1 |
| 10.500.7 | AHLORL | 114142.0 | 113243.2 | 112113.0 | 459.7 | — | — | HLORL | 113305.0 | 112510.0 | 111271.0 | 420.6 | 1 | 1 | IAHLO | 103489.0 | 101443.4 | 99754.0 | 864.6 | 1 | 1 | SCHLO | 111576.0 | 109702.2 | 107436.0 | 883.5 | 1 | 1 | SFPSO | 105719.0 | 103562.6 | 100190.0 | 1078.6 | 1 | 1 | BGWO | 98657.0 | 94523.5 | 91059.0 | 1421.6 | 1 | 1 | BAAA | 109896.0 | 107575.2 | 104160.0 | 1096.9 | 1 | 1 | IBDE | 98332.0 | 95295.1 | 92864.0 | 959.8 | 1 | 1 |
| 10.500.8 | AHLORL | 113833.0 | 112635.4 | 111321.0 | 504.6 | — | — | HLORL | 112964.0 | 112040.4 | 110359.0 | 508.3 | 1 | 1 | IAHLO | 103400.0 | 101125.5 | 99572.0 | 823.2 | 1 | 1 | SCHLO | 111031.0 | 109272.2 | 105571.0 | 924.4 | 1 | 1 | SFPSO | 105540.0 | 103384.4 | 100600.0 | 1019.1 | 1 | 1 | BGWO | 97854.0 | 94697.9 | 91237.0 | 1402.8 | 1 | 1 | BAAA | 109954.0 | 107151.7 | 103881.0 | 1249.5 | 1 | 1 | IBDE | 98882.0 | 95393.9 | 93069.0 | 1043.7 | 1 | 1 |
| 10.500.9 | AHLORL | 114983.0 | 114184.6 | 113012.0 | 434.7 | — | — | HLORL | 114788.0 | 113580.5 | 112484.0 | 474.3 | 1 | 1 | IAHLO | 104168.0 | 102295.6 | 100085.0 | 786.6 | 1 | 1 | SCHLO | 112202.0 | 110479.1 | 108249.0 | 839.4 | 1 | 1 | SFPSO | 107208.0 | 104519.9 | 101627.0 | 1204.7 | 1 | 1 | BGWO | 98752.0 | 95404.3 | 91729.0 | 1425.1 | 1 | 1 | BAAA | 110823.0 | 108415.5 | 102170.0 | 1339.6 | 1 | 1 | IBDE | 98965.0 | 96162.1 | 94342.0 | 952.5 | 1 | 1 |
| 10.500.10 | AHLORL | 212879.0 | 211667.0 | 210108.0 | 515.8 | — | — | HLORL | 212239.0 | 210406.5 | 208933.0 | 557.1 | 1 | 1 | IAHLO | 203992.0 | 201407.8 | 199591.0 | 784.8 | 1 | 1 | SCHLO | 209760.0 | 208011.5 | 205448.0 | 976.9 | 1 | 1 | SFPSO | 207024.0 | 203787.1 | 200739.0 | 923.2 | 1 | 1 | BGWO | 195031.0 | 189837.5 | 186272.0 | 1707.4 | 1 | 1 | BAAA | 209238.0 | 207181.9 | 204201.0 | 1040.1 | 1 | 1 | IBDE | 193836.0 | 190033.6 | 187542.0 | 1138.6 | 1 | 1 |
| 10.500.11 | AHLORL | 214822.0 | 213715.3 | 211772.0 | 516.5 | — | — | HLORL | 214022.0 | 212461.0 | 211032.0 | 578.3 | 1 | 1 | IAHLO | 204449.0 | 202539.6 | 200745.0 | 720.4 | 1 | 1 | SCHLO | 212097.0 | 209782.1 | 208038.0 | 762.9 | 1 | 1 | SFPSO | 207488.0 | 205121.6 | 202628.0 | 933.2 | 1 | 1 | BGWO | 193401.0 | 190283.1 | 186498.0 | 1569.5 | 1 | 1 | BAAA | 211544.0 | 208978.8 | 206337.0 | 994.1 | 1 | 1 | IBDE | 192953.0 | 190320.0 | 188121.0 | 1074.3 | 1 | 1 |
| 10.500.12 | AHLORL | 213703.0 | 212376.1 | 211168.0 | 514.3 | — | — | HLORL | 212398.0 | 211141.2 | 209222.0 | 580.3 | 1 | 1 | IAHLO | 204266.0 | 201329.4 | 199793.0 | 794.9 | 1 | 1 | SCHLO | 210798.0 | 208467.0 | 206135.0 | 978.1 | 1 | 1 | SFPSO | 206413.0 | 203802.0 | 201967.0 | 927.5 | 1 | 1 | BGWO | 192662.0 | 189101.0 | 186318.0 | 1504.8 | 1 | 1 | BAAA | 209650.0 | 207360.8 | 203869.0 | 1273.6 | 1 | 1 | IBDE | 191857.0 | 189242.2 | 187582.0 | 912.2 | 1 | 1 |
| 10.500.13 | AHLORL | 212625.0 | 211482.2 | 209900.0 | 489.5 | — | — | HLORL | 211326.0 | 210310.1 | 209271.0 | 498.5 | 1 | 1 | IAHLO | 202212.0 | 200167.8 | 197838.0 | 820.2 | 1 | 1 | SCHLO | 209298.0 | 207633.1 | 205217.0 | 908.6 | 1 | 1 | SFPSO | 205407.0 | 202710.3 | 199971.0 | 1025.4 | 1 | 1 | BGWO | 191428.0 | 187601.5 | 183122.0 | 1731.4 | 1 | 1 | BAAA | 209058.0 | 206739.7 | 203571.0 | 1217.1 | 1 | 1 | IBDE | 191141.0 | 187978.1 | 185301.0 | 1135.0 | 1 | 1 |
| 10.500.14 | AHLORL | 209743.0 | 208596.5 | 207667.0 | 460.2 | — | — | HLORL | 208863.0 | 207382.8 | 206203.0 | 562.9 | 1 | 1 | IAHLO | 200131.0 | 198124.2 | 196529.0 | 849.1 | 1 | 1 | SCHLO | 206980.0 | 204761.5 | 202417.0 | 854.0 | 1 | 1 | SFPSO | 202602.0 | 200608.0 | 198290.0 | 996.2 | 1 | 1 | BGWO | 189680.0 | 186146.3 | 182509.0 | 1479.1 | 1 | 1 | BAAA | 206637.0 | 204316.4 | 200682.0 | 1035.2 | 1 | 1 | IBDE | 189184.0 | 186891.2 | 184202.0 | 1053.8 | 1 | 1 |
| 10.500.15 | AHLORL | 210871.0 | 209569.9 | 207919.0 | 564.3 | — | — | HLORL | 209850.0 | 208598.7 | 206823.0 | 553.6 | 1 | 1 | IAHLO | 200124.0 | 198504.7 | 196616.0 | 782.2 | 1 | 1 | SCHLO | 208065.0 | 205853.3 | 203907.0 | 949.9 | 1 | 1 | SFPSO | 203250.0 | 200889.3 | 198190.0 | 920.7 | 1 | 1 | BGWO | 190424.0 | 186044.0 | 180941.0 | 1762.4 | 1 | 1 | BAAA | 207532.0 | 204522.0 | 201071.0 | 1296.2 | 1 | 1 | IBDE | 189469.0 | 186533.5 | 184525.0 | 1009.2 | 1 | 1 |
| 10.500.16 | AHLORL | 213979.0 | 212733.5 | 211607.0 | 447.9 | — | — | HLORL | 212788.0 | 211584.1 | 210003.0 | 551.2 | 1 | 1 | IAHLO | 204257.0 | 201416.1 | 199614.0 | 884.6 | 1 | 1 | SCHLO | 210549.0 | 208953.1 | 206989.0 | 824.8 | 1 | 1 | SFPSO | 206749.0 | 204229.6 | 201470.0 | 989.1 | 1 | 1 | BGWO | 193898.0 | 188963.6 | 183804.0 | 1906.9 | 1 | 1 | BAAA | 210623.0 | 207895.1 | 204029.0 | 1334.9 | 1 | 1 | IBDE | 192404.0 | 189239.5 | 187040.0 | 1112.4 | 1 | 1 |
| 10.500.17 | AHLORL | 216086.0 | 214444.2 | 213022.0 | 584.7 | — | — | HLORL | 214649.0 | 213125.9 | 212126.0 | 532.0 | 1 | 1 | IAHLO | 205296.0 | 203324.2 | 201504.0 | 818.6 | 1 | 1 | SCHLO | 212509.0 | 210242.7 | 208412.0 | 877.8 | 1 | 1 | SFPSO | 207927.0 | 205715.2 | 203416.0 | 837.5 | 1 | 1 | BGWO | 196171.0 | 191007.8 | 187060.0 | 1875.3 | 1 | 1 | BAAA | 212163.0 | 209648.1 | 206546.0 | 1139.5 | 1 | 1 | IBDE | 196214.0 | 191684.0 | 189545.0 | 975.8 | 1 | 1 |
| 10.500.18 | AHLORL | 210263.0 | 208878.4 | 207740.0 | 508.1 | — | — | HLORL | 209673.0 | 207895.3 | 206792.0 | 488.9 | 1 | 1 | IAHLO | 200589.0 | 198119.2 | 195967.0 | 812.7 | 1 | 1 | SCHLO | 207557.0 | 205288.4 | 202595.0 | 866.1 | 1 | 1 | SFPSO | 203146.0 | 200614.0 | 198019.0 | 976.6 | 1 | 1 | BGWO | 190317.0 | 185829.2 | 181380.0 | 1766.6 | 1 | 1 | BAAA | 206481.0 | 204376.6 | 199841.0 | 1147.8 | 1 | 1 | IBDE | 189435.0 | 186275.1 | 184217.0 | 1009.3 | 1 | 1 |
| 10.500.19 | AHLORL | 216256.0 | 214914.9 | 213692.0 | 506.7 | — | — | HLORL | 215023.0 | 213617.5 | 212300.0 | 590.9 | 1 | 1 | IAHLO | 206333.0 | 204386.1 | 201917.0 | 833.5 | 1 | 1 | SCHLO | 212876.0 | 210941.3 | 208463.0 | 978.6 | 1 | 1 | SFPSO | 209270.0 | 206606.9 | 203959.0 | 949.3 | 1 | 1 | BGWO | 195908.0 | 192282.2 | 188736.0 | 1445.6 | 1 | 1 | BAAA | 213062.0 | 210214.8 | 207258.0 | 1105.2 | 1 | 1 | IBDE | 195994.0 | 192959.8 | 191050.0 | 1064.3 | 1 | 1 |
| 10.500.20 | AHLORL | 302215.0 | 301298.5 | 300236.0 | 425.6 | — | — | HLORL | 301585.0 | 300838.4 | 300115.0 | 366.4 | 1 | 1 | IAHLO | 292406.0 | 290153.6 | 288741.0 | 719.5 | 1 | 1 | SCHLO | 300292.0 | 298668.5 | 296817.0 | 656.6 | 1 | 1 | SFPSO | 294739.0 | 292406.7 | 290576.0 | 951.7 | 1 | 1 | BGWO | 287155.0 | 284406.9 | 281145.0 | 1408.7 | 1 | 1 | BAAA | 298427.0 | 296235.6 | 293445.0 | 882.2 | 1 | 1 | IBDE | 285664.0 | 283137.3 | 280969.0 | 1048.1 | 1 | 1 |
| 10.500.21 | AHLORL | 300047.0 | 299211.0 | 298122.0 | 405.6 | — | — | HLORL | 299638.0 | 298799.1 | 297873.0 | 327.1 | 1 | 1 | IAHLO | 289863.0 | 288335.8 | 286770.0 | 677.9 | 1 | 1 | SCHLO | 298287.0 | 296598.2 | 294000.0 | 740.7 | 1 | 1 | SFPSO | 292800.0 | 290481.4 | 287934.0 | 863.6 | 1 | 1 | BGWO | 286431.0 | 282791.7 | 279058.0 | 1648.1 | 1 | 1 | BAAA | 296665.0 | 294396.9 | 292360.0 | 880.0 | 1 | 1 | IBDE | 284002.0 | 281474.2 | 279179.0 | 928.3 | 1 | 1 |
| 10.500.22 | AHLORL | 300385.0 | 299216.8 | 298454.0 | 349.2 | — | — | HLORL | 299515.0 | 298766.9 | 297999.0 | 330.4 | 1 | 1 | IAHLO | 291114.0 | 288994.8 | 286745.0 | 710.2 | 1 | 1 | SCHLO | 298391.0 | 296598.6 | 295026.0 | 688.5 | 1 | 1 | SFPSO | 292972.0 | 290987.8 | 288860.0 | 807.3 | 1 | 1 | BGWO | 287567.0 | 283495.6 | 280420.0 | 1557.7 | 1 | 1 | BAAA | 296630.0 | 294581.2 | 291335.0 | 951.9 | 1 | 1 | IBDE | 284770.0 | 282112.8 | 280297.0 | 954.0 | 1 | 1 |
| 10.500.23 | AHLORL | 298371.0 | 297631.9 | 296972.0 | 351.0 | — | — | HLORL | 298305.0 | 297154.6 | 296254.0 | 402.6 | 1 | 1 | IAHLO | 288461.0 | 286591.8 | 284931.0 | 735.8 | 1 | 1 | SCHLO | 296509.0 | 295004.6 | 292914.0 | 646.8 | 1 | 1 | SFPSO | 291285.0 | 288761.1 | 285978.0 | 893.4 | 1 | 1 | BGWO | 284344.0 | 280812.0 | 277107.0 | 1410.5 | 1 | 1 | BAAA | 294646.0 | 292441.2 | 289923.0 | 930.5 | 1 | 1 | IBDE | 282517.0 | 279893.4 | 277913.0 | 991.9 | 1 | 1 |
| 10.500.24 | AHLORL | 301958.0 | 301178.2 | 300267.0 | 364.3 | — | — | HLORL | 301937.0 | 300726.7 | 299962.0 | 397.6 | 1 | 1 | IAHLO | 291715.0 | 289829.9 | 287890.0 | 755.7 | 1 | 1 | SCHLO | 300078.0 | 298565.6 | 296701.0 | 757.8 | 1 | 1 | SFPSO | 293581.0 | 292161.5 | 289638.0 | 809.6 | 1 | 1 | BGWO | 287947.0 | 283995.3 | 280454.0 | 1566.0 | 1 | 1 | BAAA | 298585.0 | 295992.7 | 294506.0 | 837.1 | 1 | 1 | IBDE | 285550.0 | 283100.8 | 280529.0 | 1065.3 | 1 | 1 |
| 10.500.25 | AHLORL | 299260.0 | 298446.4 | 297617.0 | 335.9 | — | — | HLORL | 298901.0 | 297980.0 | 297156.0 | 372.2 | 1 | 1 | IAHLO | 290256.0 | 288533.4 | 286662.0 | 759.2 | 1 | 1 | SCHLO | 297688.0 | 295979.4 | 294106.0 | 644.7 | 1 | 1 | SFPSO | 292616.0 | 290445.8 | 288062.0 | 867.3 | 1 | 1 | BGWO | 286462.0 | 283057.1 | 279369.0 | 1295.0 | 1 | 1 | BAAA | 295892.0 | 293902.7 | 290951.0 | 961.4 | 1 | 1 | IBDE | 285118.0 | 282043.4 | 279656.0 | 1006.0 | 1 | 1 |
| 10.500.26 | AHLORL | 303031.0 | 301745.0 | 301001.0 | 371.9 | — | — | HLORL | 302049.0 | 301300.9 | 300374.0 | 361.9 | 1 | 1 | IAHLO | 293550.0 | 290964.8 | 289203.0 | 748.5 | 1 | 1 | SCHLO | 300923.0 | 299336.0 | 297649.0 | 609.4 | 1 | 1 | SFPSO | 295285.0 | 293236.9 | 290848.0 | 846.7 | 1 | 1 | BGWO | 288028.0 | 285192.2 | 280841.0 | 1441.5 | 1 | 1 | BAAA | 298930.0 | 296835.7 | 294529.0 | 877.2 | 1 | 1 | IBDE | 287349.0 | 283893.9 | 281788.0 | 1073.6 | 1 | 1 |
| 10.500.27 | AHLORL | 294409.0 | 293232.0 | 292501.0 | 378.3 | — | — | HLORL | 293538.0 | 292822.7 | 291939.0 | 334.3 | 1 | 1 | IAHLO | 285759.0 | 283169.4 | 281179.0 | 759.5 | 1 | 1 | SCHLO | 292222.0 | 290747.6 | 289393.0 | 644.2 | 1 | 1 | SFPSO | 286925.0 | 285025.9 | 282668.0 | 858.5 | 1 | 1 | BGWO | 280920.0 | 277702.1 | 273044.0 | 1518.9 | 1 | 1 | BAAA | 290489.0 | 288805.8 | 287020.0 | 818.9 | 1 | 1 | IBDE | 279027.0 | 276672.2 | 273862.0 | 959.2 | 1 | 1 |
| 10.500.28 | AHLORL | 299442.0 | 298382.7 | 297751.0 | 347.8 | — | — | HLORL | 298678.0 | 297848.4 | 296912.0 | 364.1 | 1 | 1 | IAHLO | 290118.0 | 287148.3 | 285486.0 | 739.9 | 1 | 1 | SCHLO | 297333.0 | 295810.7 | 293097.0 | 730.5 | 1 | 1 | SFPSO | 291563.0 | 289273.7 | 286573.0 | 932.5 | 1 | 1 | BGWO | 285815.0 | 281373.3 | 277453.0 | 1529.9 | 1 | 1 | BAAA | 295388.0 | 293188.0 | 290847.0 | 1029.9 | 1 | 1 | IBDE | 283464.0 | 280183.5 | 277694.0 | 1048.9 | 1 | 1 |
| 10.500.29 | AHLORL | 304836.0 | 303754.2 | 303009.0 | 351.8 | — | — | HLORL | 304383.0 | 303361.8 | 302190.0 | 387.9 | 1 | 1 | IAHLO | 295204.0 | 292865.5 | 290276.0 | 872.5 | 1 | 1 | SCHLO | 303018.0 | 301395.3 | 299597.0 | 712.2 | 1 | 1 | SFPSO | 297197.0 | 294974.5 | 292606.0 | 958.2 | 1 | 1 | BGWO | 290420.0 | 286599.3 | 283284.0 | 1725.2 | 1 | 1 | BAAA | 300634.0 | 298845.4 | 296797.0 | 929.4 | 1 | 1 | IBDE | 289072.0 | 285729.0 | 283654.0 | 968.1 | 1 | 1 |
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