Table 10 Test result of multimodal benchmark functions with dim = 50.
F8 | |||||
|---|---|---|---|---|---|
Algorithm | Best | Mean | Median | Standard deviation | Average time per run (sec.) |
HHO | -20,949.1444 | -20,948.83 | -20,949.0513 | 0.611607917 | 0.0119623 |
HHO-Elite | -20,949.1444 | -20,948.8293 | -20,949.1434 | 0.796444958 | 0.015599717 |
HHO-GA | -17,312.1877 | -15,861.7388 | -15,888.8664 | 719.0504277 | 0.011283497 |
HHO-CHAOS | -20,949.1444 | -20,949.0249 | -20,949.1215 | 0.265687452 | 0.007649363 |
HHO-ADAP | -20,949.1444 | -20,948.8165 | -20,949.0642 | 0.541616024 | 0.01291926 |
HHO-PSO | -20,949.1444 | -20,949.1356 | -20,949.1425 | 0.018368951 | 0.012665823 |
HHO-Inertia | -20,949.1444 | -20,948.9638 | -20,949.1221 | 0.404058307 | 0.00326626 |
HHO-ULTRA | -20,948.55 | -20,925.4576 | -20,942.9276 | 34.79726324 | 0.030546193 |
WMA | -7339.0847 | -5673.25173 | -5774.16156 | 711.758287 | 0.501557253 |
CMA-ES | -9029.45793 | -9005.37937 | -9029.45793 | 91.63387603 | 0.520836247 |
EBOwithCMAR | -17,350.1961 | -14,805.4745 | -14,705.9849 | 898.9528325 | 0.546996547 |
L-SHADE | -20,236.0096 | -19,665.3395 | -19,763.0489 | 407.2859516 | 0.11784429 |
LSHADE-cnEpSin | -20,840.3281 | -20,710.6423 | -20,718.1381 | 83.67725035 | 1.629825503 |
SPS-L-SHADE-EIG | -20,938.8211 | -20,218.4515 | -20,268.136 | 333.7361673 | 0.875021563 |
OWMA | -9085.44948 | -7027.79965 | -6980.70044 | 907.2279521 | 0.460219733 |
F9 | |||||
Algorithm | Best | Mean | Median | Standard deviation | Average Time Per Run (sec.) |
HHO | 0 | 0 | 0 | 0 | 0.015448697 |
HHO-Elite | 0 | 0 | 0 | 0 | 0.017934753 |
HHO-GA | 27.45399743 | 46.79460234 | 45.0438627 | 13.26126026 | 0.026958463 |
HHO-CHAOS | 0 | 0 | 0 | 0 | 0.019680983 |
HHO-ADAP | 0 | 0 | 0 | 0 | 0.021737613 |
HHO-PSO | 0 | 0 | 0 | 0 | 0.00940665 |
HHO-Inertia | 0 | 0 | 0 | 0 | 0.007468357 |
HHO-ULTRA | 9.17453E-11 | 0.000427508 | 3.54421E-05 | 0.001049949 | 0.049091507 |
WMA | 356.209501 | 452.9438648 | 444.2527611 | 47.88371167 | 1.752214283 |
CMA-ES | 35.05936228 | 59.2047401 | 47.262366 | 56.62934324 | 0.931819393 |
EBOwithCMAR | 82.88567911 | 125.1779006 | 125.3738557 | 28.41833364 | 0.991556103 |
L-SHADE | 10.16471512 | 16.88162698 | 16.17681658 | 3.464328708 | 0.324235173 |
LSHADE-cnEpSin | 3.25214621 | 6.036491374 | 5.975375809 | 1.102956454 | 3.632012157 |
SPS-L-SHADE-EIG | 32.03009755 | 45.3491983 | 44.40958472 | 8.166122277 | 1.457422903 |
OWMA | 0 | 3.78956E-14 | 0 | 1.15951E-13 | 1.493260473 |
F10 | |||||
Algorithm | Best | Mean | Median | Standard deviation | Average Time Per Run (sec.) |
HHO | 4.43064E-16 | 4.43064E-16 | 4.43064E-16 | 0 | 0.022300257 |
HHO-Elite | 4.44089E-16 | 4.44089E-16 | 4.44089E-16 | 0 | 0.04562844 |
HHO-GA | 2.120802974 | 4.673460599 | 4.840429624 | 0.951553221 | 0.00779708 |
HHO-CHAOS | 4.44089E-16 | 4.44089E-16 | 4.44089E-16 | 0 | 0.01469064 |
HHO-ADAP | 4.44089E-16 | 4.11523E-15 | 3.9968E-15 | 2.87314E-15 | 0.016191153 |
HHO-PSO | 4.44089E-16 | 4.44089E-16 | 4.44089E-16 | 0 | 0.008925343 |
HHO-Inertia | 4.44089E-16 | 1.27306E-15 | 4.44089E-16 | 1.52832E-15 | 0.00569107 |
HHO-ULTRA | 1.12328E-05 | 0.007697771 | 0.003289889 | 0.013311474 | 0.015093847 |
WMA | 19.74179583 | 19.91232337 | 19.92741432 | 0.053855335 | 0.39343301 |
CMA-ES | 2.73707E-05 | 11.31206338 | 19.96145303 | 10.06118135 | 0.67793551 |
EBOwithCMAR | 1.031899224 | 3.961454209 | 2.822236498 | 3.605687967 | 0.39848781 |
L-SHADE | 8.55379E-05 | 1.229958523 | 1.422655899 | 1.003370489 | 0.076500283 |
LSHADE-cnEpSin | 6.12876E-10 | 2.40825E-09 | 2.16807E-09 | 1.27273E-09 | 1.084805127 |
SPS-L-SHADE-EIG | 9.32861E-06 | 0.107030111 | 4.87584E-05 | 0.326976732 | 0.662781763 |
OWMA | 1.36117E-09 | 5.52372E-09 | 4.87412E-09 | 3.5162E-09 | 0.31844681 |
F11 | |||||
Algorithm | Best | Mean | Median | Standard deviation | Average Time Per Run (sec.) |
HHO | 0 | 0 | 0 | 0 | 0.00720831 |
HHO-Elite | 0 | 0 | 0 | 0 | 0.01507128 |
HHO-GA | 1.565299124 | 4.431817297 | 4.358805273 | 1.369426301 | 0.01123917 |
HHO-CHAOS | 0 | 0 | 0 | 0 | 0.02543847 |
HHO-ADAP | 0 | 0 | 0 | 0 | 0.030015003 |
HHO-PSO | 0 | 0 | 0 | 0 | 0.005256997 |
HHO-Inertia | 0 | 0 | 0 | 0 | 0.002970633 |
HHO-ULTRA | 1.54785E-08 | 0.003403329 | 0.000428277 | 0.007435512 | 0.020146857 |
WMA | 172.6294252 | 429.8408231 | 417.2174287 | 161.8666369 | 1.539695677 |
CMA-ES | 6.11207E-07 | 1.56325E-06 | 1.55136E-06 | 5.27957E-07 | 1.05116052 |
EBOwithCMAR | 0.046072511 | 0.510004675 | 0.239590215 | 1.300342644 | 1.092221493 |
L-SHADE | 6.8187E-09 | 0.013539622 | 4.27002E-05 | 0.032097306 | 0.383588483 |
LSHADE-cnEpSin | 0 | 6.88153E-14 | 4.94049E-15 | 2.72314E-13 | 1.91602929 |
SPS-L-SHADE-EIG | 2.11643E-09 | 0.001066914 | 2.9062E-08 | 0.004072793 | 0.662290147 |
OWMA | 0 | 2.06872E-15 | 6.66134E-16 | 3.15901E-15 | 0.340214343 |
F12 | |||||
Algorithm | Best | Mean | Median | Standard deviation | Average Time Per Run (sec.) |
HHO | 1.29637E-08 | 1.24862E-06 | 4.48645E-07 | 2.00946E-06 | 0.051735603 |
HHO-Elite | 1.61257E-17 | 1.25581E-06 | 9.04656E-08 | 3.16409E-06 | 0.10160841 |
HHO-GA | 0.984690563 | 2.288711261 | 2.264326939 | 0.824082797 | 0.135240033 |
HHO-CHAOS | 5.67743E-10 | 8.40222E-07 | 4.8858E-07 | 9.51931E-07 | 0.056057927 |
HHO-ADAP | 3.49051E-08 | 7.38634E-06 | 1.43844E-06 | 1.37107E-05 | 0.062984767 |
HHO-PSO | 2.94487E-08 | 1.13687E-06 | 4.96227E-07 | 1.46116E-06 | 0.077582053 |
HHO-Inertia | 3.98173E-12 | 1.57536E-06 | 1.37628E-07 | 3.65807E-06 | 0.026619713 |
HHO-ULTRA | 9.92031E-09 | 2.47557E-05 | 3.4473E-06 | 6.75045E-05 | 0.09770979 |
WMA | 35.6167339 | 349,706.0468 | 115,745.3989 | 541,550.2588 | 1.1324925 |
CMA-ES | 2.80297E-09 | 7.0348E-09 | 6.73692E-09 | 2.74304E-09 | 0.86872829 |
EBOwithCMAR | 2.414115544 | 227.943048 | 5.78762673 | 1197.473084 | 0.66662932 |
L-SHADE | 5.56225E-07 | 0.483123927 | 0.033039554 | 0.793359291 | 0.465818197 |
LSHADE-cnEpSin | 4.27691E-18 | 1.63131E-16 | 7.98132E-17 | 2.37464E-16 | 6.83512641 |
SPS-L-SHADE-EIG | 6.22879E-10 | 0.018723742 | 1.28049E-07 | 0.091509265 | 1.123242853 |
OWMA | 0.833156694 | 1.17097168 | 1.179996652 | 0.110284561 | 1.15955264 |
F13 | |||||
Algorithm | Best | Mean | Median | Standard deviation | Average Time Per Run (sec.) |
HHO | 3.20826E-09 | 5.08169E-05 | 1.67206E-05 | 8.48611E-05 | 0.064199763 |
HHO-Elite | 2.13826E-18 | 9.57183E-06 | 1.07775E-06 | 1.59596E-05 | 0.084547523 |
HHO-GA | 5.69868874 | 24.87532043 | 23.4511216 | 16.72986206 | 0.0830589 |
HHO-CHAOS | 1.30457E-08 | 1.25673E-05 | 6.76899E-06 | 1.36963E-05 | 0.044227607 |
HHO-ADAP | 1.43831E-08 | 0.000146268 | 6.35553E-05 | 0.00017107 | 0.07295663 |
HHO-PSO | 5.58185E-07 | 2.21986E-05 | 1.01769E-05 | 3.18509E-05 | 0.08398709 |
HHO-Inertia | 3.87891E-09 | 3.09009E-05 | 7.74866E-06 | 5.09799E-05 | 0.034322363 |
HHO-ULTRA | 1.61637E-06 | 0.000473513 | 9.21108E-05 | 0.000656171 | 0.096528283 |
WMA | 583,294.0632 | 3,814,283.829 | 2,462,148.068 | 4,134,420.805 | 1.166944173 |
CMA-ES | 4.89627E-08 | 1.22339E-07 | 1.22746E-07 | 5.06931E-08 | 0.977693403 |
EBOwithCMAR | 8.992467645 | 34.20218883 | 29.95909586 | 16.91795072 | 0.726171193 |
L-SHADE | 1.24532E-05 | 0.835137737 | 0.002890243 | 1.385458502 | 0.435818243 |
LSHADE-cnEpSin | 1.26013E-16 | 1.13874E-15 | 9.55235E-16 | 9.3952E-16 | 7.231873427 |
SPS-L-SHADE-EIG | 7.64734E-10 | 0.00361212 | 3.56109E-08 | 0.017821377 | 1.094100743 |
OWMA | 4.989493369 | 5.03854196 | 4.99533265 | 0.145427356 | 1.117346993 |
