Table 11 Test result of multimodal benchmark functions with dim = 100.
F8 | |||||
|---|---|---|---|---|---|
Algorithm | Best | Mean | Median | Standard deviation | Average time per run (sec.) |
HHO | -41,898.2887 | -41,897.2396 | -41,898.0523 | 1.730723907 | 0.03702962 |
HHO-Elite | -42,901.2441 | -41,897.7655 | -41,898.2882 | 6.229692717 | 0.05652914 |
HHO-GA | -30,708.8087 | -25,306.0671 | -24,963.7433 | 2493.993361 | 0.044594697 |
HHO-CHAOS | -41,898.2883 | -41,897.8433 | -41,898.1302 | 0.662620283 | 0.01017132 |
HHO-ADAP | -41,898.2885 | -41,896.7918 | -41,898.1017 | 5.152597614 | 0.021030967 |
HHO-PSO | -41,898.2887 | -41,898.2691 | -41,898.281 | 0.025151762 | 0.01349917 |
HHO-Inertia | -41,898.2887 | -41,898.1498 | -41,898.2624 | 0.250212371 | 0.006182973 |
HHO-ULTRA | -41,897.7518 | -41,863.5392 | -41,880.9058 | 43.56192869 | 0.029619857 |
WMA | -9147.42974 | -7995.79199 | -8270.67688 | 917.0565312 | 0.480376157 |
CMA-ES | -15,169.4893 | -12,808.5659 | -12,641.2411 | 898.5607501 | 1.03298626 |
EBOwithCMAR | -28,822.041 | -26,537.7368 | -26,690.0328 | 1617.739995 | 1.11350413 |
L-SHADE | -31,269.0794 | -29,793.8525 | -29,783.8208 | 532.8454804 | 0.127621403 |
LSHADE-cnEpSin | -32,116.0388 | -31,069.9029 | -31,020.604 | 409.8936428 | 4.45993275 |
SPS-L-SHADE-EIG | -32,671.4112 | -29,619.0962 | -29,516.689 | 1330.531181 | 1.48470513 |
OWMA | -13,904.3113 | -10,374.1307 | -10,277.9615 | 1408.764505 | 0.519969493 |
F9 | |||||
Algorithm | Best | Mean | Median | Standard deviation | Average Time Per Run (sec.) |
HHO | 0 | 0 | 0 | 0 | 0.0111835 |
HHO-Elite | 0 | 0 | 0 | 0 | 0.02230698 |
HHO-GA | 104.4203264 | 195.5349526 | 202.9566438 | 38.36920023 | 0.020332933 |
HHO-CHAOS | 0 | 0 | 0 | 0 | 0.01029937 |
HHO-ADAP | 0 | 7.57912E-15 | 0 | 4.15126E-14 | 0.01302254 |
HHO-PSO | 0 | 0 | 0 | 0 | 0.00574826 |
HHO-Inertia | 0 | 0 | 0 | 0 | 0.00417425 |
HHO-ULTRA | 7.66249E-11 | 0.002019093 | 7.82147E-05 | 0.007611952 | 0.02110211 |
WMA | 866.0375995 | 989.2678922 | 983.4718027 | 70.48505308 | 0.40055306 |
CMA-ES | 484.0625369 | 823.3038104 | 855.8101054 | 94.89611388 | 1.118137393 |
EBOwithCMAR | 259.9211095 | 376.7261804 | 366.4660871 | 57.59584806 | 1.01017649 |
L-SHADE | 159.1683581 | 182.731002 | 182.9578472 | 13.88447002 | 0.107032797 |
LSHADE-cnEpSin | 140.5981118 | 159.2576537 | 159.1422252 | 7.191222403 | 3.66633708 |
SPS-L-SHADE-EIG | 286.6138129 | 336.6076489 | 335.5120678 | 36.78253826 | 1.549860063 |
OWMA | 0 | 0 | 0 | 0 | 0.41758337 |
F10 | |||||
Algorithm | Best | Mean | Median | Standard deviation | Average Time Per Run (sec.) |
HHO | 4.44089E-16 | 4.44089E-16 | 4.44089E-16 | 0 | 0.02816376 |
HHO-Elite | 4.44089E-16 | 4.44089E-16 | 4.44089E-16 | 0 | 0.0543802 |
HHO-GA | 7.191766172 | 8.965747216 | 8.913324883 | 0.91388834 | 0.033400943 |
HHO-CHAOS | 4.44089E-16 | 4.44089E-16 | 4.44089E-16 | 0 | 0.018410483 |
HHO-ADAP | 4.44089E-16 | 4.4705E-15 | 3.9968E-15 | 2.59454E-15 | 0.023143317 |
HHO-PSO | 4.44089E-16 | 4.44089E-16 | 4.44089E-16 | 0 | 0.012681973 |
HHO-Inertia | 4.44089E-16 | 1.86517E-15 | 4.44089E-16 | 1.77022E-15 | 0.008226443 |
HHO-ULTRA | 6.54596E-06 | 0.005989373 | 0.002058827 | 0.007484221 | 0.062091303 |
WMA | 19.70430843 | 19.9278976 | 19.94250495 | 0.05152543 | 1.359304407 |
CMA-ES | 0.013592517 | 17.31125436 | 19.96676885 | 6.89582978 | 3.215705393 |
EBOwithCMAR | 6.750588344 | 10.45187919 | 9.578634841 | 3.415394827 | 2.96539246 |
L-SHADE | 0.368691968 | 3.437737693 | 3.414529953 | 1.794938327 | 0.346836 |
LSHADE-cnEpSin | 1.17578E-06 | 2.58312E-06 | 2.5565E-06 | 9.13127E-07 | 5.024007917 |
SPS-L-SHADE-EIG | 1.093905908 | 1.645293024 | 1.582416666 | 0.404222188 | 1.813339007 |
OWMA | 1.45805E-09 | 7.07648E-09 | 6.65668E-09 | 3.62562E-09 | 0.46688764 |
F11 | |||||
Algorithm | Best | Mean | Median | Standard deviation | Average Time Per Run (sec.) |
HHO | 0 | 0 | 0 | 0 | 0.033466087 |
HHO-Elite | 0 | 0 | 0 | 0 | 0.024038047 |
HHO-GA | 23.25526401 | 50.89145528 | 53.4555738 | 16.83376111 | 0.051980127 |
HHO-CHAOS | 0 | 0 | 0 | 0 | 0.03398129 |
HHO-ADAP | 0 | 0 | 0 | 0 | 0.019642183 |
HHO-PSO | 0 | 0 | 0 | 0 | 0.008492157 |
HHO-Inertia | 0 | 0 | 0 | 0 | 0.005937033 |
HHO-ULTRA | 7.22888E-12 | 0.002635777 | 0.000232291 | 0.006515856 | 0.09416929 |
WMA | 562.4908261 | 1232.81486 | 1301.640149 | 284.8144486 | 1.805890167 |
CMA-ES | 0.043812483 | 0.062957971 | 0.060936315 | 0.01111953 | 2.858338147 |
EBOwithCMAR | 3.832880633 | 14.26036222 | 14.0951958 | 6.652722609 | 2.818984943 |
L-SHADE | 0.231808419 | 1.161026614 | 1.050450606 | 0.778900063 | 0.59129863 |
LSHADE-cnEpSin | 5.03064E-11 | 2.27638E-10 | 1.69856E-10 | 1.61073E-10 | 14.92371173 |
SPS-L-SHADE-EIG | 0.004995285 | 0.039086324 | 0.031541096 | 0.02800569 | 4.26429109 |
OWMA | 0 | 1.84667E-15 | 6.66134E-16 | 3.11743E-15 | 2.063003547 |
F12 | |||||
Algorithm | Best | Mean | Median | Standard deviation | Average Time Per Run (sec.) |
HHO | 3.34498E-11 | 8.8228E-07 | 3.16296E-07 | 1.26118E-06 | 0.23523212 |
HHO-Elite | 6.46714E-26 | 3.45231E-07 | 3.38103E-09 | 7.92767E-07 | 0.134775117 |
HHO-GA | 12.58443442 | 131,825.1029 | 31,066.41825 | 274,985.8547 | 0.339371567 |
HHO-CHAOS | 1.12384E-09 | 3.62672E-07 | 4.69961E-08 | 8.1456E-07 | 0.122110447 |
HHO-ADAP | 3.61099E-08 | 8.33554E-06 | 3.54182E-06 | 2.14898E-05 | 0.255344277 |
HHO-PSO | 1.09649E-08 | 8.18476E-07 | 4.31415E-07 | 1.10332E-06 | 0.280721243 |
HHO-Inertia | 3.64761E-09 | 1.36999E-06 | 4.03929E-07 | 2.107E-06 | 0.11402601 |
HHO-ULTRA | 3.30231E-09 | 1.09545E-05 | 2.42443E-06 | 2.61564E-05 | 0.389207817 |
WMA | 7633.784873 | 1,283,608.22 | 654,499.1201 | 1,575,324.051 | 4.51850908 |
CMA-ES | 0.00019303 | 0.000298664 | 0.000300468 | 5.54771E-05 | 3.945854287 |
EBOwithCMAR | 1320.327424 | 2,649,904.142 | 97,175.54259 | 11,889,917.97 | 3.6374309 |
L-SHADE | 7.378978022 | 11.56266993 | 11.20810562 | 3.222971777 | 1.31483587 |
LSHADE-cnEpSin | 6.26546E-13 | 3.03033E-12 | 2.38803E-12 | 1.94928E-12 | 33.9199064 |
SPS-L-SHADE-EIG | 0.681751447 | 2.753373867 | 2.698033108 | 1.161942458 | 2.921386067 |
OWMA | 0.91867546 | 1.186057141 | 1.200741003 | 0.075915439 | 1.957272987 |
F13 | |||||
Algorithm | Best | Mean | Median | Standard deviation | Average Time Per Run (sec.) |
HHO | 1.61325E-08 | 3.36441E-05 | 8.54062E-06 | 4.20502E-05 | 0.17510364 |
HHO-Elite | 6.31019E-17 | 2.28761E-05 | 1.55861E-07 | 6.90039E-05 | 0.287987497 |
HHO-GA | 540.7106446 | 1,983,651.881 | 1,199,027.147 | 1,821,937.542 | 0.31179043 |
HHO-CHAOS | 9.47997E-08 | 1.90271E-05 | 5.64146E-06 | 3.1249E-05 | 0.160183733 |
HHO-ADAP | 1.37035E-06 | 0.000192182 | 9.96964E-05 | 0.000212386 | 0.248497287 |
HHO-PSO | 4.28778E-08 | 4.19959E-05 | 2.67678E-05 | 5.42855E-05 | 0.285568167 |
HHO-Inertia | 1.04901E-09 | 3.57506E-05 | 2.65279E-06 | 0.00010875 | 0.121985517 |
HHO-ULTRA | 4.95476E-06 | 0.000475388 | 0.00017654 | 0.001043788 | 0.36522966 |
WMA | 1,562,568.788 | 8,160,289.681 | 5,393,145.095 | 7,113,940.735 | 3.63435894 |
CMA-ES | 0.00366297 | 0.005074148 | 0.004695352 | 0.001141175 | 4.683495007 |
EBOwithCMAR | 90,659.98366 | 3,135,943.066 | 987,449.3013 | 6,902,632.697 | 3.794170923 |
L-SHADE | 33.03101345 | 252.7139819 | 118.0088758 | 470.6282879 | 1.5272275 |
LSHADE-cnEpSin | 4.56517E-11 | 0.000732491 | 1.20819E-10 | 0.002787584 | 42.05781318 |
SPS-L-SHADE-EIG | 0.15007731 | 19.24383479 | 15.3186708 | 17.67218345 | 5.487273777 |
OWMA | 9.986194348 | 9.995004804 | 9.995411841 | 0.002856727 | 3.030370663 |
