Table 5.
Results of PSMADE and conventional algorithms on CEC 2014 benchmark
| Function | Metric | PSMADE | PSO | WOA | ABC | GWO | SSA | CS | MFO |
|---|---|---|---|---|---|---|---|---|---|
| F1 | Avg | 1.09857E+02 | 8.44308E+06 | 2.82857E+07 | 4.49910E+06 | 5.37577E+07 | 1.75614E+06 | 1.34063E+06 | 1.19544E+08 |
| Std | 3.47205E+01 | 2.43315E+06 | 1.10056E+07 | 1.76951E+06 | 3.51812E+07 | 7.10424E+05 | 6.69876E+05 | 1.48449E+08 | |
| F2 | Avg | 2.00000E+02 | 1.45557E+08 | 3.46213E+06 | 4.06387E+02 | 1.96064E+09 | 1.17511E+04 | 1.00000E+10 | 1.29836E+10 |
| Std | 6.71055E-07 | 2.04638E+07 | 2.58424E+06 | 2.08751E+02 | 2.09879E+09 | 9.47260E+03 | 0.00000E+00 | 9.19373E+09 | |
| F3 | Avg | 3.00000E+02 | 9.66354E+02 | 3.46232E+04 | 1.32118E+03 | 3.01910E+04 | 1.51469E+03 | 3.00000E+02 | 9.82396E+04 |
| Std | 9.24956E-09 | 1.23571E+02 | 2.04008E+04 | 9.28340E+02 | 7.84123E+03 | 7.59189E+02 | 3.94370E-09 | 5.50426E+04 | |
| F4 | Avg | 4.06377E+02 | 4.69638E+02 | 5.89057E+02 | 4.29530E+02 | 6.41295E+02 | 4.73768E+02 | 4.17366E+02 | 1.47919E+03 |
| Std | 1.70664E+01 | 3.23847E+01 | 5.53157E+01 | 2.95211E+01 | 6.28318E+01 | 4.11092E+01 | 2.91772E+01 | 1.17309E+03 | |
| F5 | Avg | 5.20000E+02 | 5.20934E+02 | 5.20263E+02 | 5.20198E+02 | 5.20939E+02 | 5.20041E+02 | 5.20829E+02 | 5.20318E+02 |
| Std | 1.04272E-04 | 4.69473E-02 | 1.62726E-01 | 3.18884E-02 | 4.61491E-02 | 7.81237E-02 | 6.96997E-02 | 1.75812E-01 | |
| F6 | Avg | 6.09132E+02 | 6.23097E+02 | 6.35474E+02 | 6.14367E+02 | 6.13366E+02 | 6.18366E+02 | 6.24669E+02 | 6.24275E+02 |
| Std | 3.46776E+00 | 3.84859E+00 | 3.01073E+00 | 1.29815E+00 | 2.52994E+00 | 4.18471E+00 | 1.13242E+00 | 3.45118E+00 | |
| F7 | Avg | 7.00004E+02 | 7.02245E+02 | 7.01013E+02 | 7.00000E+02 | 7.16400E+02 | 7.00013E+02 | 7.00000E+02 | 8.07355E+02 |
| Std | 6.86921E-03 | 1.57800E-01 | 6.59499E-02 | 3.13368E-04 | 1.53507E+01 | 1.31735E-02 | 3.60296E-05 | 5.70506E+01 | |
| F8 | Avg | 8.04079E+02 | 9.81140E+02 | 9.89006E+02 | 8.00000E+02 | 8.77513E+02 | 8.99871E+02 | 8.29752E+02 | 9.51357E+02 |
| Std | 1.28935E+00 | 2.01216E+01 | 4.79795E+01 | 7.89906E-14 | 1.76294E+01 | 3.74027E+01 | 6.18174E+00 | 3.95590E+01 | |
| F9 | Avg | 9.52998E+02 | 1.10743E+03 | 1.13953E+03 | 9.84401E+02 | 9.95466E+02 | 1.02091E+03 | 1.03875E+03 | 1.12303E+03 |
| Std | 1.02268E+01 | 2.82598E+01 | 6.22604E+01 | 1.35584E+01 | 1.70199E+01 | 3.15839E+01 | 2.75233E+01 | 5.99591E+01 | |
| F10 | Avg | 1.21711E+03 | 5.15048E+03 | 5.06382E+03 | 1.00036E+03 | 3.30125E+03 | 4.37991E+03 | 2.17670E+03 | 4.71821E+03 |
| Std | 1.25352E+02 | 6.30131E+02 | 6.74491E+02 | 3.41066E-01 | 4.74567E+02 | 6.41350E+02 | 2.12701E+02 | 8.32531E+02 | |
| F11 | Avg | 3.29751E+03 | 5.89169E+03 | 6.09907E+03 | 3.14870E+03 | 3.77898E+03 | 4.99703E+03 | 4.57641E+03 | 5.23141E+03 |
| Std | 5.33234E+02 | 5.08321E+02 | 8.13424E+02 | 2.16964E+02 | 6.10151E+02 | 6.46073E+02 | 2.13404E+02 | 8.24031E+02 | |
| F12 | Avg | 1.20032E+03 | 1.20246E+03 | 1.20181E+03 | 1.20024E+03 | 1.20171E+03 | 1.20044E+03 | 1.20075E+03 | 1.20048E+03 |
| Std | 1.38735E-01 | 2.92502E-01 | 4.87165E-01 | 3.93449E-02 | 1.16069E+00 | 2.18483E-01 | 1.10671E-01 | 2.64946E-01 | |
| F13 | Avg | 1.30028E+03 | 1.30035E+03 | 1.30052E+03 | 1.30023E+03 | 1.30040E+03 | 1.30050E+03 | 1.30034E+03 | 1.30204E+03 |
| Std | 5.92166E-02 | 8.07511E-02 | 9.53930E-02 | 3.48316E-02 | 1.00215E-01 | 1.38241E-01 | 5.25480E-02 | 1.19740E+00 | |
| F14 | Avg | 1.40044E+03 | 1.40029E+03 | 1.40026E+03 | 1.40019E+03 | 1.40449E+03 | 1.40033E+03 | 1.40024E+03 | 1.43555E+03 |
| Std | 2.22315E-01 | 1.06140E-01 | 4.95625E-02 | 1.75092E-02 | 6.65951E+00 | 1.96195E-01 | 4.08086E-02 | 2.26021E+01 | |
| F15 | Avg | 1.50339E+03 | 1.51673E+03 | 1.58246E+03 | 1.50763E+03 | 1.58207E+03 | 1.50796E+03 | 1.51100E+03 | 1.97857E+05 |
| Std | 7.83495E-01 | 1.32265E+00 | 3.37166E+01 | 8.27346E-01 | 2.39195E+02 | 2.98814E+00 | 1.58616E+00 | 4.08076E+05 | |
| F16 | Avg | 1.61008E+03 | 1.61210E+03 | 1.61259E+03 | 1.60981E+03 | 1.61085E+03 | 1.61155E+03 | 1.61233E+03 | 1.61273E+03 |
| Std | 9.34915E-01 | 4.36227E-01 | 5.06985E-01 | 4.17932E-01 | 6.64469E-01 | 5.93497E-01 | 2.84228E-01 | 4.06264E-01 | |
| F17 | Avg | 2.16208E+04 | 2.94362E+05 | 3.38542E+06 | 2.26666E+06 | 1.44328E+06 | 1.36419E+05 | 3.87004E+03 | 3.62723E+06 |
| Std | 1.97515E+04 | 1.43343E+05 | 2.40148E+06 | 8.33199E+05 | 2.35936E+06 | 1.05552E+05 | 3.10196E+02 | 5.88362E+06 | |
| F18 | Avg | 1.87316E+03 | 2.16264E+06 | 7.89879E+03 | 2.48588E+03 | 5.27485E+06 | 6.77711E+03 | 1.87130E+03 | 2.64746E+07 |
| Std | 1.59078E+02 | 7.28018E+05 | 1.34875E+04 | 4.02626E+02 | 1.45461E+07 | 5.98363E+03 | 1.88573E+01 | 9.97564E+07 | |
| F19 | Avg | 1.90615E+03 | 1.91747E+03 | 1.94240E+03 | 1.90710E+03 | 1.94457E+03 | 1.91396E+03 | 1.90821E+03 | 1.98008E+03 |
| Std | 1.20175E+00 | 2.80257E+00 | 3.90750E+01 | 7.98721E-01 | 2.66201E+01 | 2.17681E+00 | 8.75813E-01 | 8.12316E+01 | |
| F20 | Avg | 2.14343E+03 | 2.30736E+03 | 2.91137E+04 | 8.96765E+03 | 1.85622E+04 | 2.35219E+03 | 2.05944E+03 | 6.56586E+04 |
| Std | 1.39649E+02 | 6.23234E+01 | 1.93601E+04 | 2.82234E+03 | 1.19928E+04 | 7.73988E+01 | 1.72969E+01 | 4.41141E+04 | |
| F21 | Avg | 1.93793E+04 | 1.26178E+05 | 1.54397E+06 | 2.12349E+05 | 1.16711E+06 | 6.14462E+04 | 3.12552E+03 | 9.23990E+05 |
| Std | 2.36982E+04 | 7.64836E+04 | 1.97010E+06 | 1.02565E+05 | 2.21866E+06 | 4.40992E+04 | 2.15830E+02 | 2.36268E+06 | |
| F22 | Avg | 2.47684E+03 | 2.88678E+03 | 3.01178E+03 | 2.46069E+03 | 2.53766E+03 | 2.59391E+03 | 2.45174E+03 | 2.97672E+03 |
| Std | 1.57688E+02 | 2.33664E+02 | 2.39437E+02 | 8.45668E+01 | 1.37195E+02 | 1.45922E+02 | 9.73843E+01 | 3.44090E+02 | |
| F23 | Avg | 2.50000E+03 | 2.61599E+03 | 2.63588E+03 | 2.61539E+03 | 2.63188E+03 | 2.61531E+03 | 2.61524E+03 | 2.66442E+03 |
| Std | 0.00000E+00 | 4.74172E-01 | 1.33984E+01 | 1.86175E-01 | 6.98184E+00 | 1.13070E-01 | 1.38756E-12 | 2.67511E+01 | |
| F24 | Avg | 2.60000E+03 | 2.62755E+03 | 2.60563E+03 | 2.62739E+03 | 2.60000E+03 | 2.64230E+03 | 2.62596E+03 | 2.69070E+03 |
| Std | 0.00000E+00 | 8.21927E+00 | 4.32802E+00 | 1.37930E+00 | 8.12379E-04 | 8.34590E+00 | 1.38743E+00 | 3.27067E+01 | |
| F25 | Avg | 2.70000E+03 | 2.71143E+03 | 2.71113E+03 | 2.70763E+03 | 2.71120E+03 | 2.71185E+03 | 2.70537E+03 | 2.71719E+03 |
| Std | 0.00000E+00 | 5.52814E+00 | 1.56843E+01 | 1.40835E+00 | 4.56335E+00 | 3.58027E+00 | 1.23189E+00 | 9.81901E+00 | |
| F26 | Avg | 2.70027E+03 | 2.77377E+03 | 2.70380E+03 | 2.70045E+03 | 2.76350E+03 | 2.70050E+03 | 2.70034E+03 | 2.71116E+03 |
| Std | 7.15660E-02 | 4.50143E+01 | 1.81704E+01 | 7.12784E-02 | 4.88044E+01 | 1.15199E-01 | 5.43145E-02 | 4.82765E+01 | |
| F27 | Avg | 2.90000E+03 | 3.41130E+03 | 3.69539E+03 | 3.10793E+03 | 3.34468E+03 | 3.37434E+03 | 3.10591E+03 | 3.61906E+03 |
| Std | 0.00000E+00 | 2.99680E+02 | 4.03620E+02 | 2.43403E+00 | 1.11739E+02 | 1.47395E+02 | 2.10089E+00 | 1.98870E+02 | |
| F28 | Avg | 3.00000E+03 | 6.96685E+03 | 5.21016E+03 | 3.80003E+03 | 4.00390E+03 | 3.83997E+03 | 3.78391E+03 | 3.94223E+03 |
| Std | 0.00000E+00 | 9.22570E+02 | 5.81678E+02 | 7.06540E+01 | 2.86352E+02 | 1.43014E+02 | 5.04540E+01 | 1.89334E+02 | |
| F29 | Avg | 3.40123E+03 | 4.54328E+04 | 5.73724E+06 | 3.93394E+03 | 7.37675E+05 | 2.57523E+06 | 3.90524E+03 | 3.20339E+06 |
| Std | 5.00388E+02 | 9.87549E+04 | 4.68243E+06 | 9.58902E+01 | 1.51968E+06 | 4.79743E+06 | 7.66480E+01 | 3.65849E+06 | |
| F30 | Avg | 3.86139E+03 | 1.54413E+04 | 9.82272E+04 | 5.45281E+03 | 5.49253E+04 | 1.04715E+04 | 4.83092E+03 | 5.12597E+04 |
| Std | 2.38714E+02 | 6.77786E+03 | 5.98133E+04 | 6.16567E+02 | 3.60247E+04 | 2.92969E+03 | 3.06931E+02 | 4.42759E+04 |
| Function | Metric | HHO | BA | SCA | JAYA | TLBO | DE | SMA |
|---|---|---|---|---|---|---|---|---|
| F1 | Avg | 9.97423E+06 | 8.08199E+05 | 2.20166E+08 | 2.87552E+08 | 6.58450E+05 | 2.03311E+07 | 2.10690E+06 |
| Std | 5.26966E+06 | 3.57865E+05 | 6.28888E+07 | 1.21955E+08 | 1.28854E+06 | 7.28222E+06 | 9.11719E+05 | |
| F2 | Avg | 1.20825E+07 | 6.36291E+05 | 1.62737E+10 | 4.85303E+10 | 2.04659E+02 | 6.38053E+02 | 6.43731E+03 |
| Std | 2.82208E+06 | 3.38417E+05 | 2.39023E+09 | 1.15383E+10 | 7.91452E+00 | 1.91571E+03 | 1.02552E+04 | |
| F3 | Avg | 5.80049E+03 | 5.13058E+02 | 3.66024E+04 | 2.12622E+05 | 5.14536E+02 | 3.81618E+02 | 4.08070E+02 |
| Std | 2.01773E+03 | 4.13993E+02 | 6.02024E+03 | 4.53268E+04 | 2.69510E+02 | 7.62520E+01 | 1.29899E+02 | |
| F4 | Avg | 5.42797E+02 | 4.33153E+02 | 1.47988E+03 | 1.13467E+04 | 4.77911E+02 | 4.98794E+02 | 4.96932E+02 |
| Std | 4.14227E+01 | 3.95152E+01 | 2.85274E+02 | 4.65888E+03 | 3.81417E+01 | 2.22886E+01 | 4.15977E+01 | |
| F5 | Avg | 5.20248E+02 | 5.20950E+02 | 5.20934E+02 | 5.20908E+02 | 5.20950E+02 | 5.20570E+02 | 5.20806E+02 |
| Std | 2.00569E-01 | 5.69218E-02 | 6.45071E-02 | 4.90918E-02 | 8.14438E-02 | 6.12389E-02 | 2.48426E-01 | |
| F6 | Avg | 6.30632E+02 | 6.32453E+02 | 6.33506E+02 | 6.38336E+02 | 6.18934E+02 | 6.19994E+02 | 6.14733E+02 |
| Std | 3.00551E+00 | 3.94561E+00 | 2.28094E+00 | 3.36595E+00 | 2.88850E+00 | 1.62513E+00 | 3.27269E+00 | |
| F7 | Avg | 7.01115E+02 | 7.00584E+02 | 8.39379E+02 | 8.79197E+02 | 7.00096E+02 | 7.00000E+02 | 7.00287E+02 |
| Std | 2.25070E-02 | 1.84311E-01 | 2.94778E+01 | 3.66214E+01 | 1.69074E-01 | 5.98792E-11 | 9.69376E-02 | |
| F8 | Avg | 8.95895E+02 | 1.02469E+03 | 1.04111E+03 | 1.10042E+03 | 8.90044E+02 | 8.00865E+02 | 8.12505E+02 |
| Std | 1.76129E+01 | 5.43078E+01 | 2.17550E+01 | 4.21593E+01 | 1.38475E+01 | 9.83253E-01 | 3.49276E+00 | |
| F9 | Avg | 1.08627E+03 | 1.15936E+03 | 1.17420E+03 | 1.28023E+03 | 9.91781E+02 | 1.00810E+03 | 9.91688E+02 |
| Std | 1.90858E+01 | 6.66046E+01 | 1.87304E+01 | 5.04828E+01 | 1.65109E+01 | 9.52898E+00 | 2.36080E+01 | |
| F10 | Avg | 2.86333E+03 | 5.31956E+03 | 6.80693E+03 | 4.54426E+03 | 3.08353E+03 | 1.02742E+03 | 1.63569E+03 |
| Std | 6.07639E+02 | 6.98285E+02 | 5.08693E+02 | 1.83569E+03 | 5.92027E+02 | 3.00284E+01 | 1.98920E+02 | |
| F11 | Avg | 5.40578E+03 | 5.73029E+03 | 8.03029E+03 | 8.24579E+03 | 5.28450E+03 | 5.81604E+03 | 3.90039E+03 |
| Std | 6.92539E+02 | 5.47433E+02 | 2.49962E+02 | 3.31757E+02 | 1.44160E+03 | 3.68120E+02 | 6.65242E+02 | |
| F12 | Avg | 1.20153E+03 | 1.20127E+03 | 1.20251E+03 | 1.20249E+03 | 1.20253E+03 | 1.20093E+03 | 1.20030E+03 |
| Std | 5.30924E-01 | 4.57755E-01 | 2.90242E-01 | 2.51086E-01 | 2.49766E-01 | 1.34007E-01 | 1.45704E-01 | |
| F13 | Avg | 1.30048E+03 | 1.30048E+03 | 1.30298E+03 | 1.30612E+03 | 1.30047E+03 | 1.30034E+03 | 1.30052E+03 |
| Std | 1.38590E-01 | 9.92765E-02 | 2.77158E-01 | 6.69230E-01 | 1.00015E-01 | 4.06942E-02 | 1.12004E-01 | |
| F14 | Avg | 1.40029E+03 | 1.40031E+03 | 1.44301E+03 | 1.47033E+03 | 1.40028E+03 | 1.40036E+03 | 1.40068E+03 |
| Std | 1.51415E-01 | 1.06563E-01 | 8.00617E+00 | 1.72958E+01 | 6.03402E-02 | 8.83546E-02 | 2.94768E-01 | |
| F15 | Avg | 1.53793E+03 | 1.52819E+03 | 4.66572E+03 | 2.66362E+03 | 1.52844E+03 | 1.51168E+03 | 1.50620E+03 |
| Std | 7.99928E+00 | 5.02099E+00 | 2.32154E+03 | 1.24713E+03 | 1.56136E+01 | 1.12207E+00 | 1.73461E+00 | |
| F16 | Avg | 1.61237E+03 | 1.61323E+03 | 1.61284E+03 | 1.61328E+03 | 1.61135E+03 | 1.61150E+03 | 1.61093E+03 |
| Std | 3.28374E-01 | 4.17660E-01 | 2.41189E-01 | 1.72052E-01 | 4.82681E-01 | 2.73215E-01 | 6.44286E-01 | |
| F17 | Avg | 1.63637E+06 | 8.97661E+04 | 6.33771E+06 | 3.38028E+07 | 1.17429E+05 | 1.67523E+06 | 3.16965E+05 |
| Std | 1.10939E+06 | 5.57390E+04 | 3.27333E+06 | 1.09951E+07 | 1.21736E+05 | 8.72545E+05 | 1.73061E+05 | |
| F18 | Avg | 9.35309E+04 | 9.45386E+04 | 1.55479E+08 | 8.35892E+08 | 5.45487E+03 | 7.55210E+03 | 2.08712E+04 |
| Std | 4.04609E+04 | 3.71339E+04 | 7.51910E+07 | 5.72885E+08 | 5.29574E+03 | 4.49383E+03 | 7.46159E+03 | |
| F19 | Avg | 1.93473E+03 | 1.93673E+03 | 1.99079E+03 | 2.05412E+03 | 1.92194E+03 | 1.90834E+03 | 1.93177E+03 |
| Std | 3.30943E+01 | 3.98173E+01 | 2.22810E+01 | 6.72141E+01 | 2.30056E+01 | 6.93852E-01 | 3.82442E+01 | |
| F20 | Avg | 1.46150E+04 | 2.46044E+03 | 1.77041E+04 | 9.50340E+04 | 2.54945E+03 | 4.80283E+03 | 2.21502E+03 |
| Std | 6.85632E+03 | 1.68728E+02 | 4.99066E+03 | 7.69268E+04 | 1.97653E+02 | 1.65852E+03 | 2.12630E+02 | |
| F21 | Avg | 6.25701E+05 | 5.29042E+04 | 1.29594E+06 | 5.12880E+06 | 6.58189E+04 | 2.70672E+05 | 1.60505E+05 |
| Std | 4.11998E+05 | 2.46847E+04 | 6.28852E+05 | 2.72402E+06 | 7.01267E+04 | 1.64876E+05 | 7.10942E+04 | |
| F22 | Avg | 3.04417E+03 | 3.36635E+03 | 2.97193E+03 | 3.55534E+03 | 2.54981E+03 | 2.32993E+03 | 2.69803E+03 |
| Std | 2.92168E+02 | 3.23304E+02 | 1.81908E+02 | 1.86676E+02 | 1.35237E+02 | 8.18740E+01 | 2.23161E+02 | |
| F23 | Avg | 2.50000E+03 | 2.61525E+03 | 2.67168E+03 | 2.93275E+03 | 2.61524E+03 | 2.61524E+03 | 2.50000E+03 |
| Std | 0.00000E+00 | 2.15818E-03 | 1.69671E+01 | 1.16873E+02 | 1.85747E-07 | 1.38756E-12 | 0.00000E+00 | |
| F24 | Avg | 2.60000E+03 | 2.66582E+03 | 2.60006E+03 | 2.64418E+03 | 2.60001E+03 | 2.62596E+03 | 2.60000E+03 |
| Std | 5.63683E-05 | 2.06931E+01 | 4.34490E-02 | 6.92545E+01 | 7.30336E-04 | 2.91189E+00 | 0.00000E+00 | |
| F25 | Avg | 2.70000E+03 | 2.73390E+03 | 2.72551E+03 | 2.75887E+03 | 2.70000E+03 | 2.70734E+03 | 2.70000E+03 |
| Std | 0.00000E+00 | 1.62934E+01 | 7.86095E+00 | 1.54773E+01 | 0.00000E+00 | 1.15088E+00 | 0.00000E+00 | |
| F26 | Avg | 2.76681E+03 | 2.70050E+03 | 2.70211E+03 | 2.71568E+03 | 2.72373E+03 | 2.70034E+03 | 2.70055E+03 |
| Std | 4.77450E+01 | 1.35760E-01 | 6.81525E-01 | 5.53680E+01 | 4.27993E+01 | 2.89185E-02 | 1.63941E-01 | |
| F27 | Avg | 2.90000E+03 | 3.85363E+03 | 3.38213E+03 | 4.11693E+03 | 3.38111E+03 | 3.22890E+03 | 2.90000E+03 |
| Std | 0.00000E+00 | 3.94149E+02 | 2.79554E+02 | 1.69233E+02 | 2.29824E+02 | 9.77594E+01 | 0.00000E+00 | |
| F28 | Avg | 3.00000E+03 | 5.49137E+03 | 4.81360E+03 | 4.94709E+03 | 4.13481E+03 | 3.64137E+03 | 3.00000E+03 |
| Std | 0.00000E+00 | 8.74843E+02 | 3.57929E+02 | 3.06208E+02 | 3.72009E+02 | 1.96779E+01 | 0.00000E+00 | |
| F29 | Avg | 3.10000E+03 | 3.96585E+07 | 9.53550E+06 | 3.85900E+07 | 3.49051E+06 | 6.95627E+03 | 4.11959E+03 |
| Std | 0.00000E+00 | 2.87107E+07 | 4.31435E+06 | 1.10169E+07 | 4.87224E+06 | 1.08154E+04 | 1.00655E+03 | |
| F30 | Avg | 5.55692E+03 | 1.91137E+04 | 2.09228E+05 | 5.69307E+05 | 7.37947E+03 | 6.36847E+03 | 5.48065E+03 |
| Std | 5.74435E+03 | 3.96356E+04 | 7.94079E+04 | 3.12161E+05 | 4.18871E+03 | 1.19214E+03 | 2.13537E+03 |