Table 5 Test result of unimodal benchmark functions with dim = 30.
F1 | |||||
|---|---|---|---|---|---|
Algorithm | Best | Mean | Median | Standard deviation | Average time per run (sec.) |
HHO | 3.8603E-210 | 2.174E-185 | 5.9918E-198 | 0 | 0.002860127 |
HHO-Elite | 4.1093E-216 | 1.0731E-188 | 1.842E-200 | 0 | 0.013147727 |
HHO-GA | 0.47442596 | 9.915295147 | 8.134247393 | 8.459238485 | 0.00635788 |
HHO-CHAOS | 6.9798E-205 | 9.6148E-182 | 1.5751E-192 | 0 | 0.00391798 |
HHO-ADAP | 4.10774E-81 | 2.87881E-62 | 8.59799E-73 | 1.5767E-61 | 0.00688714 |
HHO-PSO | 9.6226E-117 | 7.77456E-78 | 2.14672E-83 | 4.08798E-77 | 0.003002317 |
HHO-Inertia | 9.34615E-79 | 2.58174E-64 | 4.32073E-69 | 1.37739E-63 | 0.00267203 |
HHO-ULTRA | 1.81801E-13 | 0.000806578 | 1.64102E-05 | 0.002649908 | 0.012729617 |
WMA | 1434.973144 | 2790.587152 | 2529.925981 | 1219.241706 | 0.368655727 |
CMA-ES | 1.07751E-14 | 2.64506E-14 | 2.46336E-14 | 1.45356E-14 | 0.320064367 |
EBOwithCMAR | 4.40149E-08 | 2.21739E-06 | 7.62875E-07 | 3.27984E-06 | 0.354646187 |
L-SHADE | 2.14833E-18 | 6.59251E-13 | 2.15233E-15 | 2.37619E-12 | 0.084008257 |
LSHADE-cnEpSin | 1.4145E-27 | 7.4586E-26 | 2.31752E-26 | 1.08407E-25 | 6.73918719 |
SPS-L-SHADE-EIG | 1.08828E-16 | 2.25628E-15 | 1.37229E-15 | 2.15479E-15 | 0.654073933 |
OWMA | 3.56687E-17 | 1.33239E-15 | 4.53342E-16 | 2.41938E-15 | 0.317902973 |
F2 | |||||
Algorithm | Best | Mean | Median | Standard deviation | Average Time Per Run (sec.) |
HHO | 8.7158E-109 | 1.9446E-96 | 1.2734E-101 | 9.90204E-96 | 0.0024582 |
HHO-Elite | 5.5452E-111 | 1.22313E-98 | 8.4362E-104 | 4.32156E-98 | 0.03127214 |
HHO-GA | 0.00510922 | 0.813374194 | 0.8311032 | 0.369514329 | 0.00446196 |
HHO-CHAOS | 3.8886E-103 | 1.03169E-92 | 2.91252E-98 | 3.94729E-92 | 0.004423237 |
HHO-ADAP | 4.82551E-61 | 3.11762E-53 | 5.03556E-56 | 1.01016E-52 | 0.002790467 |
HHO-PSO | 2.25223E-46 | 1.53183E-39 | 1.07289E-41 | 5.26515E-39 | 0.003057433 |
HHO-Inertia | 8.41789E-38 | 8.85106E-35 | 2.04209E-35 | 1.47863E-34 | 0.002094177 |
HHO-ULTRA | 1.81105E-09 | 0.006594066 | 0.001221342 | 0.009365651 | 0.012260473 |
WMA | 33.1450521 | 65.59123052 | 59.57058368 | 38.26611583 | 0.42619966 |
CMA-ES | 1.85293E-07 | 3.33009E-07 | 3.15867E-07 | 9.6438E-08 | 0.331691763 |
EBOwithCMAR | 8.6409E-06 | 0.002026877 | 0.000100349 | 0.009759821 | 0.356649347 |
L-SHADE | 1.35729E-11 | 3.01249E-07 | 3.11303E-09 | 8.37341E-07 | 0.070902733 |
LSHADE-cnEpSin | 5.1707E-13 | 5.30516E-12 | 4.1336E-12 | 5.056E-12 | 6.464907357 |
SPS-L-SHADE-EIG | 5.85656E-09 | 3.74989E-08 | 3.19306E-08 | 2.29475E-08 | 0.65927056 |
OWMA | 3.5545E-09 | 1.09623E-08 | 9.28801E-09 | 8.09428E-09 | 0.32130639 |
F3 | |||||
Algorithm | Best | Mean | Median | Standard deviation | Average Time Per Run (sec.) |
HHO | 7.8185E-182 | 3.0082E-147 | 4.8525E-166 | 1.6366E-146 | 0.016862427 |
HHO-Elite | 1.4128E-195 | 3.9677E-152 | 4.2236E-174 | 2.0262E-151 | 0.049695757 |
HHO-GA | 3.623125429 | 302.0988973 | 176.0574684 | 323.6247679 | 0.034767943 |
HHO-CHAOS | 5.2738E-183 | 5.1092E-155 | 4.2855E-168 | 2.6325E-154 | 0.022131313 |
HHO-ADAP | 6.41532E-07 | 0.156102205 | 0.017561022 | 0.369358805 | 0.027454257 |
HHO-PSO | 3.46936E-64 | 1.62819E-49 | 6.82369E-56 | 8.31017E-49 | 0.03140927 |
HHO-Inertia | 6.6898E-43 | 1.32476E-20 | 4.09181E-29 | 6.9856E-20 | 0.01395405 |
HHO-ULTRA | 4.15182E-06 | 0.77045138 | 0.079146465 | 3.047083656 | 0.036788283 |
WMA | 3800.202486 | 26,601.90709 | 12,847.20418 | 33,922.28688 | 0.606221443 |
CMA-ES | 3.13696E-10 | 2544.992217 | 2.64691E-09 | 13,939.49646 | 0.49445358 |
EBOwithCMAR | 399.5590082 | 1926.958078 | 1695.301074 | 1091.942208 | 0.438811503 |
L-SHADE | 8.04192075 | 60.39089059 | 32.19536968 | 86.03630022 | 0.160974047 |
LSHADE-cnEpSin | 2.64565E-13 | 3.52275E-09 | 6.9287E-10 | 7.04582E-09 | 12.81822983 |
SPS-L-SHADE-EIG | 0.219319426 | 1.005724779 | 0.730091636 | 0.893512066 | 2.73532745 |
OWMA | 1.75828E-16 | 7.47006E-15 | 4.1985E-15 | 1.00013E-14 | 0.983789153 |
F4 | |||||
Algorithm | Best | Mean | Median | Standard deviation | Average Time Per Run (sec.) |
HHO | 1.3956E-105 | 5.20177E-94 | 8.15543E-98 | 2.43503E-93 | 0.00464322 |
HHO-Elite | 1.1948E-108 | 1.38724E-96 | 7.669E-102 | 7.542E-96 | 0.018876677 |
HHO-GA | 0.451722915 | 2.178974735 | 2.441025243 | 1.10235307 | 0.010357773 |
HHO-CHAOS | 7.904E-103 | 6.02005E-94 | 1.44573E-98 | 2.96372E-93 | 0.005136157 |
HHO-ADAP | 2.97604E-07 | 0.000324156 | 4.03526E-05 | 0.000642595 | 0.009995527 |
HHO-PSO | 6.80543E-48 | 6.87835E-40 | 1.55625E-41 | 2.28622E-39 | 0.00366497 |
HHO-Inertia | 1.73612E-38 | 9.23392E-33 | 1.42507E-34 | 3.37913E-32 | 0.002532673 |
HHO-ULTRA | 4.15665E-05 | 0.010252396 | 0.007929816 | 0.010638579 | 0.036816863 |
WMA | 23.17408764 | 31.43618208 | 30.19081223 | 6.184152946 | 0.666244167 |
CMA-ES | 4.38975E-05 | 14.8233594 | 0.045826718 | 33.30886034 | 1.03795274 |
EBOwithCMAR | 3.670404183 | 13.6835965 | 13.48530342 | 5.045493063 | 1.51920719 |
L-SHADE | 0.725516143 | 1.638551092 | 1.572309618 | 0.650688448 | 0.40756486 |
LSHADE-cnEpSin | 1.61131E-06 | 1.08896E-05 | 7.68422E-06 | 1.27027E-05 | 13.25433134 |
SPS-L-SHADE-EIG | 0.206790102 | 1.352149162 | 1.157391333 | 0.812734313 | 2.321575137 |
OWMA | 1.4786E-09 | 1.0011E-08 | 9.50842E-09 | 5.72635E-09 | 0.56498434 |
F5 | |||||
Algorithm | Best | Mean | Median | Standard deviation | Average Time Per Run (sec.) |
HHO | 1.63034E-06 | 0.002057442 | 0.000851559 | 0.00324396 | 0.00851023 |
HHO-Elite | 0 | 0.001958587 | 8.37148E-05 | 0.005171208 | 0.02044906 |
HHO-GA | 36.43654937 | 146.6069547 | 138.9088265 | 83.12238901 | 0.008090083 |
HHO-CHAOS | 1.17666E-06 | 0.001288937 | 0.000399683 | 0.002013763 | 0.00757936 |
HHO-ADAP | 1.30947E-07 | 0.007376341 | 0.003987795 | 0.007466474 | 0.011975767 |
HHO-PSO | 2.22146E-05 | 0.005220851 | 0.001492289 | 0.006870348 | 0.005002337 |
HHO-Inertia | 2.89012E-06 | 0.002723044 | 0.000789542 | 0.005684358 | 0.003715767 |
HHO-ULTRA | 2.39594E-06 | 0.027691892 | 0.003744206 | 0.080615062 | 0.019312923 |
WMA | 577,491.515 | 1,875,514.839 | 1,542,729.247 | 1,086,259.462 | 0.381426717 |
CMA-ES | 12.99595083 | 25.05183131 | 14.78090309 | 22.97205538 | 0.423005917 |
EBOwithCMAR | 10.00497812 | 63.92494848 | 74.56073924 | 37.23656431 | 0.461732663 |
L-SHADE | 16.31942705 | 45.6261254 | 26.66851847 | 28.33864927 | 0.095336997 |
LSHADE-cnEpSin | 10.82650237 | 12.7856922 | 12.77622503 | 1.234431617 | 10.11588716 |
SPS-L-SHADE-EIG | 8.908024621 | 26.7156869 | 21.89234566 | 16.18899303 | 2.144814177 |
OWMA | 28.92746344 | 28.97037947 | 28.97476717 | 0.015713856 | 0.575534923 |
F6 | |||||
Algorithm | Best | Mean | Median | Standard deviation | Average Time Per Run (sec.) |
HHO | 1.46203E-08 | 4.09491E-05 | 7.54463E-06 | 7.08037E-05 | 0.002494243 |
HHO-Elite | 7.148E-18 | 3.6107E-05 | 1.32761E-05 | 5.51301E-05 | 0.00608673 |
HHO-GA | 2.172850502 | 8.71033618 | 8.521587479 | 5.827534426 | 0.002461783 |
HHO-CHAOS | 2.83294E-08 | 3.44531E-05 | 1.10098E-05 | 7.24494E-05 | 0.00489194 |
HHO-ADAP | 8.3807E-06 | 0.000385386 | 0.00025394 | 0.00048558 | 0.00671844 |
HHO-PSO | 1.35984E-08 | 7.44926E-05 | 9.17074E-06 | 0.000254007 | 0.002468443 |
HHO-Inertia | 2.97883E-09 | 7.40789E-05 | 2.67824E-05 | 0.000120417 | 0.00231405 |
HHO-ULTRA | 5.79992E-06 | 0.003769342 | 0.000525643 | 0.010518363 | 0.039133923 |
WMA | 1255.300941 | 2667.100564 | 2503.692903 | 937.9529017 | 1.205085937 |
CMA-ES | 8.91287E-15 | 3.25426E-14 | 2.48832E-14 | 2.15613E-14 | 0.60777986 |
EBOwithCMAR | 6.37085E-08 | 4.8949E-06 | 6.58164E-07 | 1.12674E-05 | 0.676060753 |
L-SHADE | 3.13861E-19 | 1.5218E-12 | 6.59238E-16 | 5.47435E-12 | 0.203090233 |
LSHADE-cnEpSin | 1.89831E-27 | 5.4076E-26 | 2.69101E-26 | 8.47324E-26 | 14.39458474 |
SPS-L-SHADE-EIG | 2.0868E-16 | 4.91281E-15 | 1.73009E-15 | 9.0797E-15 | 1.22460217 |
OWMA | 5.430434257 | 6.699192101 | 6.868212448 | 0.496081933 | 0.894392277 |
F7 | |||||
Algorithm | Best | Mean | Median | Standard deviation | Average Time Per Run (sec.) |
HHO | 1.63336E-06 | 6.07545E-05 | 3.88836E-05 | 5.2648E-05 | 0.029244093 |
HHO-Elite | 2.09899E-06 | 6.90486E-05 | 4.52588E-05 | 6.94382E-05 | 0.066357043 |
HHO-GA | 0.003848265 | 0.02324244 | 0.025146086 | 0.014074665 | 0.043710607 |
HHO-CHAOS | 1.30954E-06 | 7.22344E-05 | 6.47644E-05 | 5.80232E-05 | 0.02888135 |
HHO-ADAP | 1.86727E-06 | 0.000177807 | 0.000129345 | 0.000198175 | 0.03041889 |
HHO-PSO | 8.74256E-06 | 0.00015645 | 8.53565E-05 | 0.000152854 | 0.03310505 |
HHO-Inertia | 2.40762E-07 | 8.73656E-05 | 6.61718E-05 | 8.35771E-05 | 0.01570154 |
HHO-ULTRA | 9.95481E-06 | 0.000146012 | 0.000117642 | 0.000140954 | 0.07485959 |
WMA | 0.97698168 | 3.081928954 | 2.579477788 | 2.190396 | 1.649057383 |
CMA-ES | 0.009487075 | 0.024944524 | 0.023670328 | 0.006869535 | 0.747184173 |
EBOwithCMAR | 0.007892328 | 0.045317688 | 0.041929225 | 0.029348073 | 0.854810067 |
L-SHADE | 0.007720137 | 0.025022459 | 0.020608182 | 0.012775351 | 0.33363646 |
LSHADE-cnEpSin | 0.001038058 | 0.002590636 | 0.002290114 | 0.001014726 | 16.92858768 |
SPS-L-SHADE-EIG | 0.006363577 | 0.015572658 | 0.015098109 | 0.005106684 | 1.154934017 |
OWMA | 0.000191068 | 0.002066261 | 0.001627086 | 0.001522515 | 1.29593858 |
