Table 12 Test result of fixed dimension benchmark functions.
F14 | |||||
|---|---|---|---|---|---|
Algorithm | Best | Mean | Median | Standard deviation | Average time per run (sec.) |
HHO | 0.998003838 | 0.998003838 | 0.998003838 | 1.96947E-09 | 0.04827169 |
HHO-Elite | 0.998003838 | 0.998003838 | 0.998003838 | 1.23561E-10 | 0.074400847 |
HHO-GA | 0.998003838 | 0.998003838 | 0.998003838 | 5.00769E-16 | 0.067124033 |
HHO-CHAOS | 0.998003838 | 1.064272309 | 0.998003838 | 0.252192749 | 0.043046153 |
HHO-ADAP | 0.998003838 | 1.064272309 | 0.998003838 | 0.252192749 | 0.055536863 |
HHO-PSO | 0.998003838 | 0.998003838 | 0.998003838 | 4.0085E-11 | 0.065299963 |
HHO-Inertia | 0.998003838 | 1.031138075 | 0.998003838 | 0.181483681 | 0.0295956 |
HHO-ULTRA | 0.998003838 | 0.998003838 | 0.998003838 | 2.05404E-10 | 0.08826045 |
WMA | 1.996482785 | 9.344743677 | 8.028598272 | 5.602015528 | 0.836144667 |
CMA-ES | 1.22182174 | 7.214997138 | 6.791235363 | 3.980821516 | 0.645539847 |
EBOwithCMAR | 0.998003838 | 2.472152045 | 0.998003843 | 2.798553906 | 0.454834627 |
L-SHADE | 0.998003838 | 0.998003838 | 0.998003838 | 0 | 0.37493063 |
LSHADE-cnEpSin | 0.998003838 | 1.229417228 | 0.998003838 | 0.67283845 | 0.254512047 |
SPS-L-SHADE-EIG | 0.998003838 | 0.998003838 | 0.998003838 | 0 | 0.60191071 |
OWMA | 0.99800384 | 0.99801394 | 0.998004335 | 3.22047E-05 | 0.815238077 |
F15 | |||||
Algorithm | Best | Mean | Median | Standard deviation | Average Time Per Run (sec.) |
HHO | 0.000308032 | 0.000327385 | 0.000322066 | 1.93874E-05 | 0.003125273 |
HHO-Elite | 0.000306508 | 0.000322136 | 0.000305028 | 2.15871E-25 | 0.009930113 |
HHO-GA | 0.00030664 | 0.000343617 | 0.000316331 | 8.59007E-05 | 0.003958303 |
HHO-CHAOS | 0.000308708 | 0.000334513 | 0.000326942 | 2.31445E-05 | 0.003497037 |
HHO-ADAP | 0.000307884 | 0.000375871 | 0.000340812 | 0.000168648 | 0.00338811 |
HHO-PSO | 0.00030755 | 0.000383669 | 0.000310809 | 0.0003538 | 0.011183663 |
HHO-Inertia | 0.000308184 | 0.000326814 | 0.000320182 | 2.3202E-05 | 0.006036243 |
HHO-ULTRA | 0.000308473 | 0.000444897 | 0.000413248 | 0.000126638 | 0.01234646 |
WMA | 0.000476903 | 0.013298266 | 0.012292196 | 0.010724097 | 0.31726925 |
CMA-ES | 0.003896797 | 0.091141843 | 0.061693333 | 0.102110007 | 0.06677162 |
EBOwithCMAR | 0.000307486 | 0.001189675 | 0.000307486 | 0.003642465 | 0.15573486 |
L-SHADE | 0.000307486 | 0.00103706 | 0.000307486 | 0.003657519 | 0.057167647 |
LSHADE-cnEpSin | 0.000307486 | 0.001644543 | 0.000307486 | 0.005088333 | 0.067548723 |
SPS-L-SHADE-EIG | 0.000307486 | 0.000307486 | 0.000307486 | 1.58848E-19 | 0.25625633 |
OWMA | 0.0007547 | 0.001090633 | 0.001038285 | 0.000231511 | 0.25471519 |
F16 | |||||
Algorithm | Best | Mean | Median | Standard deviation | Average Time Per Run (sec.) |
HHO | -1.03162845 | -1.031628453 | -1.031628453 | 3.94448E-11 | 0.003409713 |
HHO-Elite | -1.03162845 | -1.031628453 | -1.031628453 | 7.06076E-17 | 0.009624563 |
HHO-GA | -1.03162845 | -1.031628453 | -1.031628453 | 2.40212E-13 | 0.004878507 |
HHO-CHAOS | -1.03162845 | -1.031628453 | -1.031628453 | 2.35804E-17 | 0.003912983 |
HHO-ADAP | -1.03162845 | -1.031628453 | -1.031628453 | 3.5128E-10 | 0.003677583 |
HHO-PSO | -1.03162845 | -1.031628453 | -1.031628453 | 5.45457E-16 | 0.00351449 |
HHO-Inertia | -1.03162845 | -1.031627153 | -1.031628377 | 3.30026E-06 | 0.002161713 |
HHO-ULTRA | -1.03162845 | -1.031580816 | -1.031628271 | 0.000165924 | 0.012422913 |
WMA | -1.03149966 | -0.971013919 | -1.016294419 | 0.150504587 | 0.305675447 |
CMA-ES | -1.03142767 | -0.250372662 | -0.192976823 | 0.455533222 | 0.061607127 |
EBOwithCMAR | -1.03162845 | -1.031628453 | -1.031628453 | 6.38773E-16 | 0.143174293 |
L-SHADE | -1.03162845 | -1.031628453 | -1.031628453 | 6.77522E-16 | 0.063936063 |
LSHADE-cnEpSin | -1.03162845 | -1.031628453 | -1.031628453 | 6.64856E-16 | 0.043134753 |
SPS-L-SHADE-EIG | -1.03162845 | -1.031628453 | -1.031628453 | 6.71219E-16 | 0.241968643 |
OWMA | -1.03162567 | -1.031483335 | -1.031562647 | 0.000174644 | 0.25392594 |
F17 | |||||
Algorithm | Best | Mean | Median | Standard deviation | Average Time Per Run (sec.) |
HHO | 0.397887783 | 0.397888097 | 0.397887368 | 1.38412E-06 | 0.002256637 |
HHO-Elite | 0.397887358 | 0.397887015 | 0.397887377 | 1.26331E-06 | 0.008399497 |
HHO-GA | 0.397887358 | 0.397887358 | 0.397887358 | 5.48341E-10 | 0.003314673 |
HHO-CHAOS | 0.397887358 | 0.397889494 | 0.397887385 | 5.82553E-06 | 0.002160553 |
HHO-ADAP | 0.397887358 | 0.397887844 | 0.397887379 | 9.96375E-07 | 0.003212013 |
HHO-PSO | 0.397887358 | 0.397887358 | 0.397887358 | 0 | 0.00150747 |
HHO-Inertia | 0.397887358 | 0.398132948 | 0.397902605 | 0.001017592 | 0.00137394 |
HHO-ULTRA | 0.397887358 | 0.397924628 | 0.397888534 | 6.92592E-05 | 0.010537127 |
WMA | 0.397887358 | 0.401985595 | 0.398754572 | 0.007154492 | 0.299776163 |
CMA-ES | 0.442155858 | 2.413148969 | 1.934488484 | 1.831934539 | 0.047116583 |
EBOwithCMAR | 0.397887358 | 0.397887358 | 0.397887358 | 0 | 0.135614103 |
L-SHADE | 0.397887358 | 0.397887358 | 0.397887358 | 0 | 0.059385087 |
LSHADE-cnEpSin | 0.397887358 | 0.397887358 | 0.397887358 | 0 | 0.040704137 |
SPS-L-SHADE-EIG | 0.397887358 | 0.397887358 | 0.397887358 | 0 | 0.265956943 |
OWMA | 0.397918687 | 0.398596655 | 0.398440069 | 0.000650756 | 0.216628813 |
F18 | |||||
Algorithm | Best | Mean | Median | Standard deviation | Average Time Per Run (sec.) |
HHO | 3 | 3.00000002 | 3 | 4.80772E-08 | 0.00238835 |
HHO-Elite | 3 | 3.00000003 | 3 | 1.48763E-17 | 0.017833583 |
HHO-GA | 3 | 3 | 3 | 1.82959E-13 | 0.003343033 |
HHO-CHAOS | 3 | 3 | 3 | 8.94213E-16 | 0.002311687 |
HHO-ADAP | 3 | 3.00000005 | 3 | 1.47028E-07 | 0.003813927 |
HHO-PSO | 3 | 3 | 3 | 3.56418E-15 | 0.00126131 |
HHO-Inertia | 3 | 3.00067064 | 3.00013497 | 0.001271416 | 0.00110255 |
HHO-ULTRA | 3 | 3.0001441 | 3.00000005 | 0.000341116 | 0.00983239 |
WMA | 3.00551212 | 14.2564979 | 7.16011492 | 16.11593805 | 0.294649133 |
CMA-ES | 3.38762341 | 225.179775 | 224.277819 | 207.1239703 | 0.045728337 |
EBOwithCMAR | 3 | 3 | 3 | 8.68826E-16 | 0.135203693 |
L-SHADE | 3 | 3 | 3 | 1.35504E-15 | 0.05033043 |
LSHADE-cnEpSin | 3 | 3 | 3 | 1.29866E-15 | 0.03690493 |
SPS-L-SHADE-EIG | 3 | 3 | 3 | 1.67792E-15 | 0.213829943 |
OWMA | 3.00032099 | 3.00698901 | 3.00405576 | 0.00790445 | 0.22902672 |
F19 | |||||
Algorithm | Best | Mean | Median | Standard deviation | Average Time Per Run (sec.) |
HHO | -3.86278214 | -3.86189326 | -3.86247384 | 0.001362302 | 0.00372948 |
HHO-Elite | -3.86278217 | -3.86107621 | -3.86243381 | 0.00355353 | 0.011154487 |
HHO-GA | -3.86278215 | -3.86278215 | -3.86278215 | 7.29515E-16 | 0.0056591 |
HHO-CHAOS | -3.86277102 | -3.85945547 | -3.86240002 | 0.009383326 | 0.004089947 |
HHO-ADAP | -3.86278214 | -3.861485 | -3.86219991 | 0.001644941 | 0.00482076 |
HHO-PSO | -3.86278215 | -3.86261576 | -3.86278215 | 0.000911105 | 0.003038093 |
HHO-Inertia | -3.86278037 | -3.84783673 | -3.85834436 | 0.02914667 | 0.00220979 |
HHO-ULTRA | -3.86265742 | -3.8463083 | -3.85028799 | 0.016357786 | 0.013706387 |
WMA | -3.85986319 | -3.74805452 | -3.79542916 | 0.119083014 | 0.32386254 |
CMA-ES | -3.84897281 | -3.34937451 | -3.44409254 | 0.370355054 | 0.065566127 |
EBOwithCMAR | -3.86278215 | -3.86278215 | -3.86278215 | 2.71009E-15 | 0.158471193 |
L-SHADE | -3.86278215 | -3.86278215 | -3.86278215 | 2.71009E-15 | 0.059082603 |
LSHADE-cnEpSin | -3.86278215 | -3.86278215 | -3.86278215 | 2.71009E-15 | 0.057602817 |
SPS-L-SHADE-EIG | -3.86278215 | -3.86278215 | -3.86278215 | 2.71009E-15 | 0.243450183 |
OWMA | -3.86276501 | -3.86258423 | -3.86260478 | 0.000125088 | 0.238549057 |
F20 | |||||
Algorithm | Best | Mean | Median | Standard deviation | Average Time Per Run (sec.) |
HHO | -3.3083422 | -3.1615468 | -3.17229892 | 0.074357393 | 0.003694817 |
HHO-Elite | -3.28721805 | -3.14374656 | -3.14485227 | 0.03359069 | 0.012136333 |
HHO-GA | -3.32199517 | -3.29029034 | -3.32199517 | 0.053475325 | 0.005531807 |
HHO-CHAOS | -3.30586953 | -3.1240583 | -3.15003606 | 0.112515664 | 0.00363403 |
HHO-ADAP | -3.29166609 | -3.14587478 | -3.16836878 | 0.041575869 | 0.006052157 |
HHO-PSO | -3.32134838 | -3.23458532 | -3.23368449 | 0.0745122 | 0.00338699 |
HHO-Inertia | -3.29106857 | -3.06433421 | -3.09384075 | 0.160273052 | 0.00209097 |
HHO-ULTRA | -3.26671413 | -2.85414631 | -2.93941228 | 0.26651756 | 0.014596703 |
WMA | -3.20951502 | -2.4961924 | -2.48658355 | 0.465977316 | 0.32531604 |
CMA-ES | -2.57324465 | -1.66706127 | -1.7395174 | 0.444799557 | 0.084081727 |
EBOwithCMAR | -3.32199517 | -3.30217965 | -3.32199517 | 0.045066321 | 0.17179679 |
L-SHADE | -3.32199517 | -3.27047482 | -3.32199517 | 0.059922957 | 0.062159413 |
LSHADE-cnEpSin | -3.32199517 | -3.30217965 | -3.32199517 | 0.045066321 | 0.100928037 |
SPS-L-SHADE-EIG | -3.32199517 | -3.29821655 | -3.32199517 | 0.048370252 | 0.276485153 |
OWMA | -3.31486514 | -3.26682698 | -3.30250475 | 0.054878736 | 0.240544203 |
F21 | |||||
Algorithm | Best | Mean | Median | Standard deviation | Average Time Per Run (sec.) |
HHO | -5.05515 | -5.05422376 | -5.05458879 | 0.001019956 | 0.00414003 |
HHO-Elite | -9.66440895 | -5.20364843 | -5.05064469 | 0.842509681 | 0.010403803 |
HHO-GA | -10.1531997 | -5.22513113 | -5.05519773 | 0.930763555 | 0.00530354 |
HHO-CHAOS | -5.05510917 | -5.05469775 | -5.05493433 | 0.000463236 | 0.003507077 |
HHO-ADAP | -9.95110286 | -5.21644815 | -5.05417187 | 0.894241222 | 0.005604923 |
HHO-PSO | -10.1531996 | -10.1520252 | -10.1531996 | 0.002405177 | 0.004179017 |
HHO-Inertia | -10.1218188 | -5.86179001 | -5.05427562 | 1.840059589 | 0.002293293 |
HHO-ULTRA | -9.61063806 | -5.26087173 | -5.05453179 | 1.206978174 | 0.01405645 |
WMA | -8.93378025 | -3.24412236 | -2.37343159 | 2.220144788 | 0.305263353 |
CMA-ES | -1.92254876 | -0.80673687 | -0.6827435 | 0.322433431 | 0.07722604 |
EBOwithCMAR | -10.1531996 | -8.81857965 | -10.1531483 | 2.764473342 | 0.160905597 |
L-SHADE | -10.1531996 | -8.6501654 | -10.1531483 | 2.833403304 | 0.06394785 |
LSHADE-cnEpSin | -10.1531996 | -8.90814313 | -10.1531483 | 2.831624798 | 0.07831791 |
SPS-L-SHADE-EIG | -10.1531986 | -9.81637118 | -10.1531483 | 1.281841951 | 0.253426403 |
OWMA | -10.1001794 | -9.69917402 | -9.69481147 | 0.241080159 | 0.24555247 |
F22 | |||||
Algorithm | Best | Mean | Median | Standard deviation | Average Time Per Run (sec.) |
HHO | -9.92122656 | -5.247907419 | -5.087039824 | 0.882649898 | 0.00483784 |
HHO-Elite | -10.3845806 | -5.395261306 | -5.081204693 | 1.766192964 | 0.014405747 |
HHO-GA | -10.4028406 | -5.442023075 | -5.087671825 | 1.348526902 | 0.006276313 |
HHO-CHAOS | -10.4028445 | -5.610099723 | -5.087237633 | 1.597980979 | 0.00552762 |
HHO-ADAP | -10.4028661 | -5.598691902 | -5.086321066 | 1.566291636 | 0.005945557 |
HHO-PSO | -10.4029391 | -10.40281722 | -10.40282174 | 0.001479141 | 0.00880273 |
HHO-Inertia | -10.3870602 | -6.295266336 | -5.087045005 | 2.230797978 | 0.005707497 |
HHO-ULTRA | -10.3576276 | -5.392743956 | -5.087414787 | 1.205877328 | 0.030384537 |
WMA | -10.3665908 | -3.238198689 | -2.519511343 | 1.950937586 | 0.588185267 |
CMA-ES | -2.25323814 | -0.876920915 | -0.806249694 | 0.334747239 | 0.152063847 |
EBOwithCMAR | -10.4029406 | -9.525954153 | -10.40254057 | 2.294760347 | 0.336010467 |
L-SHADE | -10.4029406 | -9.972568533 | -10.40264057 | 1.666962394 | 0.07802725 |
LSHADE-cnEpSin | -10.4029406 | -10.40294057 | -10.40254057 | 1.23423E-15 | 0.09684741 |
SPS-L-SHADE-EIG | -10.4029406 | -10.22713664 | -10.40254057 | 0.962917758 | 0.249611157 |
OWMA | -10.2296744 | -9.684767751 | -9.691241013 | 0.390911202 | 0.252425307 |
F23 | |||||
Algorithm | Best | Mean | Median | Standard deviation | Average Time Per Run (sec.) |
HHO | -10.4807217 | -5.30474067 | -5.12800634 | 0.977615559 | 0.00556013 |
HHO-Elite | -10.5364083 | -5.1931409 | -5.12265957 | 1.06418908 | 0.013329367 |
HHO-GA | -5.12848079 | -5.03825589 | -5.12848079 | 0.494182086 | 0.00758492 |
HHO-CHAOS | -10.4975962 | -5.47987765 | -5.12807435 | 1.339313879 | 0.00487326 |
HHO-ADAP | -10.1859098 | -5.45482586 | -5.12691104 | 1.252598609 | 0.006819557 |
HHO-PSO | -10.5364083 | -10.5352553 | -10.5362354 | 0.00274604 | 0.005812363 |
HHO-Inertia | -10.5281021 | -7.6818243 | -7.12784704 | 2.612922737 | 0.002850637 |
HHO-ULTRA | -9.71586711 | -5.0311019 | -5.12809356 | 1.639725279 | 0.017091543 |
WMA | -10.4415073 | -3.86351086 | -3.07977733 | 2.298816734 | 0.34099211 |
CMA-ES | -1.75845494 | -1.07784618 | -1.01287932 | 0.240617963 | 0.10738978 |
EBOwithCMAR | -10.5363098 | -9.41574473 | -10.5363098 | 2.573308619 | 0.17867149 |
L-SHADE | -10.5363098 | -10.2809009 | -10.5363098 | 1.399479902 | 0.077058963 |
LSHADE-cnEpSin | -10.5363098 | -10.2809009 | -10.5363098 | 1.399479902 | 0.089971623 |
SPS-L-SHADE-EIG | -10.5363098 | -10.5314098 | -10.5363098 | 1.89491E-15 | 0.260749317 |
OWMA | -10.2495462 | -9.67789441 | -9.67270231 | 0.386301701 | 0.27116224 |
