Table 8 Test result of multimodal benchmark functions with dim = 10.
F8 | |||||
|---|---|---|---|---|---|
Algorithm | Best | Mean | Median | Standard deviation | Average time per run (sec.) |
HHO | -4189.82886 | -4133.77968 | -4189.81059 | 226.0942757 | 0.00364061 |
HHO-Elite | -4189.82892 | -4189.81737 | -4189.82893 | 0.032972382 | 0.04132345 |
HHO-GA | -4189.82881 | -4189.82815 | -4189.82853 | 0.001301744 | 0.017131733 |
HHO-CHAOS | -4189.82879 | -4189.80757 | -4189.82572 | 0.046713629 | 0.014417057 |
HHO-ADAP | -4189.82887 | -4189.79541 | -4189.79402 | 0.027061586 | 0.016267637 |
HHO-PSO | -4189.82887 | -4189.82852 | -4189.8288 | 0.000671188 | 0.012230187 |
HHO-Inertia | -4189.82887 | -4189.80767 | -4189.82665 | 0.038065327 | 0.006682637 |
HHO-ULTRA | -4189.82884 | -4106.12711 | -4188.46678 | 417.1031919 | 0.074266313 |
WMA | -2515.121 | -1975.60555 | -1938.34425 | 132.0561619 | 1.232060397 |
CMA-ES | -1977.40021 | -1008.37251 | -967.373559 | 286.1526383 | 0.232086217 |
EBOwithCMAR | -4071.39054 | -3615.52701 | -3655.33931 | 291.7269223 | 0.568016213 |
L-SHADE | -4189.82887 | -4142.45354 | -4189.82887 | 59.01460999 | 0.281279693 |
LSHADE-cnEpSin | -4189.82887 | -4189.82887 | -4189.82887 | 2.77513E-12 | 0.695361533 |
SPS-L-SHADE-EIG | -4189.82887 | -4174.03709 | -4189.82887 | 51.42266611 | 0.743581307 |
OWMA | -3603.45656 | -3099.72832 | -3117.8069 | 323.9490666 | 0.79218909 |
F9 | |||||
Algorithm | Best | Mean | Median | Standard deviation | Average Time Per Run (sec.) |
HHO | 0 | 0 | 0 | 0 | 0.002861537 |
HHO-Elite | 0 | 0 | 0 | 0 | 0.0074585 |
HHO-GA | 9.43601E-12 | 1.36752E-08 | 3.60937E-09 | 2.28315E-08 | 0.004028357 |
HHO-CHAOS | 0 | 0 | 0 | 0 | 0.002387223 |
HHO-ADAP | 0 | 1.42109E-15 | 0 | 5.72098E-15 | 0.002717777 |
HHO-PSO | 0 | 0 | 0 | 0 | 0.001732553 |
HHO-Inertia | 0 | 0 | 0 | 0 | 0.001151007 |
HHO-ULTRA | 6.82121E-13 | 0.000405643 | 4.02767E-06 | 0.001152951 | 0.00979518 |
WMA | 27.24440765 | 50.95794229 | 52.02842173 | 12.70270719 | 0.249282567 |
CMA-ES | 0.994959057 | 4.97479411 | 4.974795285 | 2.023934565 | 0.103722203 |
EBOwithCMAR | 0.994959057 | 6.650867721 | 6.964710881 | 3.045161876 | 0.142750403 |
L-SHADE | 0 | 0 | 0 | 0 | 0.049067403 |
LSHADE-cnEpSin | 0 | 0 | 0 | 0 | 0.12489065 |
SPS-L-SHADE-EIG | 0 | 0 | 0 | 0 | 0.253331527 |
OWMA | 2.84217E-14 | 0.000783385 | 1.08734E-10 | 0.004288675 | 0.205795733 |
F10 | |||||
Algorithm | Best | Mean | Median | Standard deviation | Average Time Per Run (sec.) |
HHO | 4.44089E-16 | 4.44089E-16 | 4.44089E-16 | 0 | 0.002762007 |
HHO-Elite | 4.45096E-16 | 4.44089E-16 | 4.44089E-16 | 0 | 0.008299573 |
HHO-GA | 4.49037E-06 | 9.93885E-05 | 6.82426E-05 | 0.000110455 | 0.004376407 |
HHO-CHAOS | 4.45089E-16 | 4.44089E-16 | 4.44089E-16 | 0 | 0.0026084 |
HHO-ADAP | 4.45082E-16 | 4.11523E-15 | 3.9968E-15 | 2.55225E-15 | 0.002747323 |
HHO-PSO | 4.44089E-16 | 4.44089E-16 | 4.44089E-16 | 0 | 0.001823367 |
HHO-Inertia | 4.44089E-16 | 1.39148E-15 | 4.44089E-16 | 1.59793E-15 | 0.00129818 |
HHO-ULTRA | 2.19289E-08 | 0.004443613 | 0.001561068 | 0.006029731 | 0.011041383 |
WMA | 5.082985712 | 15.07189293 | 19.16768584 | 6.087759337 | 0.254681597 |
CMA-ES | 4.44089E-16 | 3.04356721 | 3.9968E-15 | 6.934140822 | 0.10549348 |
EBOwithCMAR | 3.9968E-15 | 4.70735E-15 | 3.9968E-15 | 2.16807E-15 | 0.14067998 |
L-SHADE | 3.9968E-15 | 3.9968E-15 | 3.9968E-15 | 0 | 0.051852117 |
LSHADE-cnEpSin | 3.9968E-15 | 3.9968E-15 | 3.9968E-15 | 0 | 0.124450327 |
SPS-L-SHADE-EIG | 3.9968E-15 | 3.9968E-15 | 3.9968E-15 | 0 | 0.256980937 |
OWMA | 6.88964E-10 | 5.73344E-09 | 4.33266E-09 | 3.91879E-09 | 0.202536277 |
F11 | |||||
Algorithm | Best | Mean | Median | Standard deviation | Average Time Per Run (sec.) |
HHO | 0 | 0 | 0 | 0 | 0.004253443 |
HHO-Elite | 0 | 0 | 0 | 0 | 0.00914242 |
HHO-GA | 3.4638E-09 | 0.01007576 | 7.24786E-07 | 0.027262474 | 0.00517243 |
HHO-CHAOS | 0 | 0 | 0 | 0 | 0.003659533 |
HHO-ADAP | 0 | 0 | 0 | 0 | 0.003975413 |
HHO-PSO | 0 | 0 | 0 | 0 | 0.003312213 |
HHO-Inertia | 0 | 0 | 0 | 0 | 0.002050707 |
HHO-ULTRA | 0 | 0.000718064 | 4.28315E-05 | 0.001540731 | 0.012541387 |
WMA | 0.810112447 | 2.992251968 | 1.658409036 | 3.089188453 | 0.274742227 |
CMA-ES | 0 | 0.003201755 | 0 | 0.005824639 | 0.122199983 |
EBOwithCMAR | 0.012328293 | 0.097031085 | 0.090702743 | 0.069682299 | 0.159766563 |
L-SHADE | 0 | 0.00172157 | 1.33227E-15 | 0.005744104 | 0.060076073 |
LSHADE-cnEpSin | 0 | 0 | 0 | 0 | 0.15642868 |
SPS-L-SHADE-EIG | 0 | 0.000410538 | 1.02474E-13 | 0.002248597 | 0.254256157 |
OWMA | 0 | 1.9725E-15 | 1.11022E-15 | 2.33605E-15 | 0.22843718 |
F12 | |||||
Algorithm | Best | Mean | Median | Standard deviation | Average Time Per Run (sec.) |
HHO | 3.19513E-10 | 9.23094E-06 | 1.34423E-06 | 2.35747E-05 | 0.014930393 |
HHO-Elite | 4.47008E-15 | 2.19414E-06 | 6.77362E-08 | 5.39905E-06 | 0.027050367 |
HHO-GA | 6.129E-08 | 5.83807E-07 | 3.50882E-07 | 5.19738E-07 | 0.022586607 |
HHO-CHAOS | 1.68616E-08 | 2.32633E-06 | 1.53609E-06 | 2.27799E-06 | 0.01556233 |
HHO-ADAP | 3.64917E-09 | 3.95289E-05 | 9.95312E-06 | 6.13902E-05 | 0.017199217 |
HHO-PSO | 2.6644E-09 | 3.95187E-06 | 2.42456E-06 | 4.27821E-06 | 0.019092757 |
HHO-Inertia | 4.86713E-09 | 5.79344E-06 | 1.26237E-06 | 8.09169E-06 | 0.00811897 |
HHO-ULTRA | 1.83778E-07 | 4.09927E-05 | 5.07081E-06 | 0.000129068 | 0.03327838 |
WMA | 0.933530806 | 884.3839995 | 9.612988037 | 3820.225362 | 0.42141754 |
CMA-ES | 4.71163E-32 | 4.71163E-32 | 4.71163E-32 | 1.67022E-47 | 0.271461327 |
EBOwithCMAR | 5.02626E-32 | 9.30608E-30 | 4.11581E-30 | 1.38151E-29 | 0.234678727 |
L-SHADE | 4.71163E-32 | 4.71325E-32 | 4.71163E-32 | 6.14023E-35 | 0.144625747 |
LSHADE-cnEpSin | 4.71163E-32 | 4.71163E-32 | 4.71163E-32 | 1.67022E-47 | 0.414360283 |
SPS-L-SHADE-EIG | 4.71163E-32 | 6.08308E-32 | 4.98996E-32 | 2.83899E-32 | 0.37435322 |
OWMA | 0.308793206 | 0.793434468 | 0.751224026 | 0.322211545 | 0.374392757 |
F13 | |||||
Algorithm | Best | Mean | Median | Standard deviation | Average Time Per Run (sec.) |
HHO | 5.96276E-08 | 3.03959E-05 | 8.58869E-06 | 5.18957E-05 | 0.01573391 |
HHO-Elite | 2.40687E-21 | 1.73146E-05 | 4.50009E-06 | 2.83274E-05 | 0.0284145 |
HHO-GA | 5.62796E-08 | 0.000737962 | 1.88634E-06 | 0.00278944 | 0.019981527 |
HHO-CHAOS | 1.04211E-09 | 9.31602E-06 | 3.65345E-06 | 1.14394E-05 | 0.013971537 |
HHO-ADAP | 1.7918E-07 | 0.000100085 | 4.71885E-05 | 0.000161869 | 0.018455307 |
HHO-PSO | 5.87491E-08 | 2.94779E-05 | 1.54122E-05 | 4.46149E-05 | 0.02446012 |
HHO-Inertia | 9.07903E-09 | 3.1574E-05 | 8.72548E-06 | 6.77174E-05 | 0.008633847 |
HHO-ULTRA | 8.20628E-07 | 0.000337542 | 3.37076E-05 | 0.000892457 | 0.03648495 |
WMA | 2.104856087 | 3485.726142 | 80.31928834 | 9334.063484 | 0.44737284 |
CMA-ES | 1.34978E-32 | 1.35389E-32 | 1.34978E-32 | 2.2504E-34 | 0.27785443 |
EBOwithCMAR | 1.3306E-31 | 4.72101E-27 | 1.61285E-29 | 2.41373E-26 | 0.244410593 |
L-SHADE | 1.34978E-32 | 1.34978E-32 | 1.34978E-32 | 5.5674E-48 | 0.14777942 |
LSHADE-cnEpSin | 1.34978E-32 | 1.37444E-32 | 1.34978E-32 | 1.35024E-33 | 0.42149801 |
SPS-L-SHADE-EIG | 1.34978E-32 | 3.59311E-32 | 1.96608E-32 | 4.30641E-32 | 0.383743163 |
OWMA | 0.513564345 | 0.973635797 | 1.002854048 | 0.128219331 | 0.378984457 |
