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. 2023 Aug 28;26(10):107736. doi: 10.1016/j.isci.2023.107736

Table 8.

Results of PSMADE and improved algorithms on CEC 2014 benchmark

Function Metric PSMADE EBOwithCMAR LSHADE_cnEpSi JADE HHODE ALCPSO CLPSO LSHADE
F1 Avg 1.12097E+02 4.33078E+03 5.75943E+03 1.19864E+03 1.08565E+07 3.76568E+06 6.03749E+06 8.68517E+03
Std 4.26006E+01 6.00577E+03 3.39937E+03 2.25657E+03 5.28222E+06 4.24727E+06 1.98906E+06 1.24464E+04
F2 Avg 2.00000E+02 2.00000E+02 2.00000E+02 2.00000E+02 1.45634E+07 2.15253E+03 5.79577E+02 2.00000E+02
Std 7.24483E-07 1.97476E-14 2.23904E-09 1.31839E-13 4.23080E+06 3.71287E+03 1.39691E+03 1.51133E-13
F3 Avg 3.00000E+02 3.00576E+02 3.00000E+02 3.00000E+02 4.12854E+03 4.66167E+02 4.58340E+02 3.00000E+02
Std 1.02126E-08 2.18782E+00 2.08212E-12 1.13687E-13 2.37382E+03 4.79983E+02 1.84987E+02 1.03265E-11
F4 Avg 4.02617E+02 4.00476E+02 4.10685E+02 4.00000E+02 5.45616E+02 5.14593E+02 4.63431E+02 4.08628E+02
Std 4.80146E+00 1.23621E+00 2.78315E+01 4.67893E-06 3.73282E+01 4.39541E+01 2.25229E+01 2.18630E+01
F5 Avg 5.20000E+02 5.20001E+02 5.20011E+02 5.20043E+02 5.20390E+02 5.20803E+02 5.20313E+02 5.20005E+02
Std 5.07697E-05 1.77395E-03 5.53928E-03 1.38327E-02 1.06022E-01 5.38705E-02 4.12383E-02 1.45559E-02
F6 Avg 6.09568E+02 6.08532E+02 6.11868E+02 6.06161E+02 6.19459E+02 6.16165E+02 6.12244E+02 6.10837E+02
Std 3.00410E+00 3.09392E+00 2.51668E+00 3.28856E+00 3.30748E+00 3.37199E+00 1.32702E+00 2.31851E+00
F7 Avg 7.00004E+02 7.00000E+02 7.00022E+02 7.00006E+02 7.01166E+02 7.00020E+02 7.00000E+02 7.00014E+02
Std 6.70911E-03 5.17115E-14 2.41975E-02 8.41605E-03 4.86053E-02 2.53402E-02 4.70840E-06 1.78230E-02
F8 Avg 8.03648E+02 8.01492E+02 8.03018E+02 8.00000E+02 8.77772E+02 8.24039E+02 8.00000E+02 8.00033E+02
Std 1.94363E+00 1.86140E+00 3.16238E+00 0.00000E+00 2.24057E+01 9.89337E+00 1.13687E-13 1.81654E-01
F9 Avg 9.49914E+02 9.23968E+02 9.41872E+02 9.32723E+02 1.02523E+03 1.01747E+03 9.52791E+02 9.34028E+02
Std 1.22446E+01 6.09422E+00 9.03265E+00 7.29902E+00 3.17609E+01 3.15784E+01 7.13686E+00 9.33500E+00
F10 Avg 1.18280E+03 1.04798E+03 1.08889E+03 1.01226E+03 2.42065E+03 1.59886E+03 1.00021E+03 1.00797E+03
Std 1.28828E+02 7.36256E+01 8.79818E+01 3.61050E+01 4.85462E+02 2.63635E+02 3.33284E-01 3.00573E+01
F11 Avg 3.13864E+03 2.79186E+03 2.76001E+03 2.84372E+03 4.56307E+03 4.45060E+03 3.14068E+03 2.86645E+03
Std 4.66519E+02 2.66470E+02 3.07111E+02 3.06787E+02 9.46492E+02 6.86588E+02 3.17661E+02 3.58692E+02
F12 Avg 1.20032E+03 1.20018E+03 1.20011E+03 1.20012E+03 1.20119E+03 1.20139E+03 1.20033E+03 1.20013E+03
Std 1.34756E-01 3.89110E-02 1.87919E-02 2.16837E-02 6.80804E-01 5.10038E-01 5.55728E-02 1.25390E-01
F13 Avg 1.30030E+03 1.30027E+03 1.30034E+03 1.30028E+03 1.30043E+03 1.30054E+03 1.30029E+03 1.30031E+03
Std 5.87244E-02 7.74232E-02 9.15365E-02 8.63082E-02 1.17191E-01 7.67734E-02 4.97937E-02 5.39541E-02
F14 Avg 1.40044E+03 1.40028E+03 1.40032E+03 1.40027E+03 1.40026E+03 1.40051E+03 1.40027E+03 1.40034E+03
Std 2.39928E-01 5.75133E-02 1.16234E-01 5.23318E-02 5.96465E-02 2.82040E-01 2.79913E-02 1.55609E-01
F15 Avg 1.50333E+03 1.50386E+03 1.50735E+03 1.50318E+03 1.52181E+03 1.51192E+03 1.50731E+03 1.50481E+03
Std 1.01505E+00 1.03680E+00 5.17952E+00 8.00554E-01 1.18091E+01 5.01739E+00 1.37616E+00 1.31297E+00
F16 Avg 1.61029E+03 1.60922E+03 1.60915E+03 1.60959E+03 1.61168E+03 1.61181E+03 1.60990E+03 1.60947E+03
Std 7.43831E-01 5.89364E-01 4.21038E-01 3.71230E-01 4.41231E-01 3.66188E-01 4.73564E-01 7.35598E-01
F17 Avg 2.48210E+04 5.65308E+03 3.62563E+03 4.13897E+04 1.52761E+06 5.99996E+05 8.38006E+05 3.15714E+03
Std 2.18452E+04 5.81566E+03 5.05437E+02 1.21951E+05 9.85682E+05 6.59849E+05 4.27565E+05 4.06979E+02
F18 Avg 1.88863E+03 1.90055E+03 1.93277E+03 2.23038E+03 5.82880E+03 7.69809E+03 1.89697E+03 1.95141E+03
Std 1.48810E+02 3.23131E+01 4.51105E+01 1.46164E+03 4.86297E+03 7.05835E+03 7.22539E+01 4.83280E+01
F19 Avg 1.90603E+03 1.90869E+03 1.91222E+03 1.90851E+03 1.92047E+03 1.91390E+03 1.90735E+03 1.91404E+03
Std 1.97176E+00 1.81512E+00 1.03843E+01 1.24956E+01 1.93242E+01 1.59612E+01 6.05300E-01 1.98452E+01
F20 Avg 2.13010E+03 2.97137E+03 2.29764E+03 6.06817E+03 5.57827E+03 2.96242E+03 4.94993E+03 2.18058E+03
Std 6.85768E+01 2.95692E+03 1.17746E+02 4.99891E+03 2.40852E+03 5.36128E+02 1.83541E+03 7.57621E+01
F21 Avg 1.56693E+04 3.25710E+03 3.03260E+03 3.01504E+04 3.78068E+05 8.48987E+04 8.93065E+04 2.74953E+03
Std 1.39007E+04 3.34315E+02 2.76526E+02 8.32709E+04 2.64961E+05 9.01191E+04 5.08263E+04 2.46526E+02
F22 Avg 2.47532E+03 2.45242E+03 2.44424E+03 2.42289E+03 2.66481E+03 2.57369E+03 2.40542E+03 2.44091E+03
Std 1.88719E+02 1.09572E+02 8.93908E+01 9.19923E+01 1.78217E+02 1.51607E+02 9.64851E+01 1.15204E+02
F23 Avg 2.50000E+03 2.61524E+03 2.61494E+03 2.61524E+03 2.50000E+03 2.61530E+03 2.61524E+03 2.61524E+03
Std 0.00000E+00 3.59280E-06 1.45854E-01 1.70987E-12 0.00000E+00 2.39898E-01 2.77191E-06 2.04418E-12
F24 Avg 2.60000E+03 2.62285E+03 2.64082E+03 2.63463E+03 2.60000E+03 2.63595E+03 2.62512E+03 2.64280E+03
Std 0.00000E+00 8.11387E+00 6.93872E+00 6.58750E+00 3.13644E-04 6.36424E+00 6.58975E-01 6.16819E+00
F25 Avg 2.70000E+03 2.70645E+03 2.70881E+03 2.70781E+03 2.70000E+03 2.71081E+03 2.70743E+03 2.70540E+03
Std 0.00000E+00 3.05998E+00 4.16706E+00 2.29859E+00 0.00000E+00 3.55543E+00 8.16427E-01 3.16362E+00
F26 Avg 2.70028E+03 2.71028E+03 2.72365E+03 2.70703E+03 2.70045E+03 2.76529E+03 2.70037E+03 2.71362E+03
Std 6.45662E-02 3.04211E+01 4.28517E+01 2.52738E+01 1.50494E-01 7.87213E+01 6.92246E-02 3.44699E+01
F27 Avg 2.90000E+03 3.17381E+03 3.29712E+03 3.13882E+03 2.90000E+03 3.42285E+03 3.11354E+03 3.28204E+03
Std 0.00000E+00 7.85417E+01 1.41031E+02 6.57608E+01 0.00000E+00 2.31279E+02 8.02802E+00 1.00678E+02
F28 Avg 3.00000E+03 3.85992E+03 3.97132E+03 3.67211E+03 3.00000E+03 4.37844E+03 3.71968E+03 3.77099E+03
Std 0.00000E+00 1.40829E+02 1.98944E+02 1.16669E+02 0.00000E+00 4.52193E+02 7.11100E+01 1.36562E+02
F29 Avg 3.40497E+03 3.01595E+05 3.67608E+03 3.92713E+05 3.10434E+05 2.42229E+06 3.82254E+03 3.15116E+05
Std 4.36641E+02 1.62738E+06 6.41565E+01 2.13055E+06 1.67260E+06 6.35965E+06 1.24801E+02 1.70585E+06
F30 Avg 3.89017E+03 6.33677E+03 5.70787E+03 5.57781E+03 1.65134E+04 1.35396E+04 6.25220E+03 5.58622E+03
Std 2.51064E+02 4.24407E+03 1.27114E+03 1.17774E+03 1.45589E+04 9.10207E+03 7.52121E+02 9.55020E+02
Function Metric SADE SHADE RCBA CBA LWOA IWOA IGWO LGWO
F1 Avg 4.41625E+05 2.18812E+03 1.20045E+06 4.13849E+06 4.05268E+06 2.08040E+07 1.65192E+07 3.74720E+08
Std 2.80151E+05 3.19251E+03 4.46889E+05 1.69333E+06 1.39712E+06 1.31502E+07 6.12272E+06 5.66707E+07
F2 Avg 2.00000E+02 2.00000E+02 2.85920E+04 1.15884E+04 5.27082E+05 6.85370E+06 3.06703E+06 2.34790E+10
Std 1.78835E-08 2.84217E-14 1.10279E+04 8.58185E+03 1.53157E+05 1.92822E+07 1.59796E+06 2.18125E+09
F3 Avg 4.69344E+02 3.00000E+02 3.24875E+02 5.99103E+03 9.02101E+02 2.04229E+04 6.63488E+03 4.66694E+04
Std 5.71185E+02 2.10847E-13 8.77306E+00 6.84519E+03 2.98744E+02 1.32829E+04 2.18574E+03 5.69716E+03
F4 Avg 4.40074E+02 4.06794E+02 4.79874E+02 5.07446E+02 5.08565E+02 5.60133E+02 5.24922E+02 2.47205E+03
Std 4.35548E+01 1.94080E+01 4.10133E+01 3.53639E+01 3.64575E+01 3.56889E+01 2.68376E+01 4.62698E+02
F5 Avg 5.20516E+02 5.20011E+02 5.20059E+02 5.20158E+02 5.20451E+02 5.20255E+02 5.20475E+02 5.20947E+02
Std 4.27023E-02 2.56782E-03 6.44028E-02 1.87180E-01 1.25638E-01 1.61274E-01 1.00081E-01 5.07290E-02
F6 Avg 6.09040E+02 6.07815E+02 6.38066E+02 6.40464E+02 6.29465E+02 6.30586E+02 6.18978E+02 6.36283E+02
Std 1.89627E+00 3.25098E+00 2.95702E+00 2.79612E+00 3.48614E+00 4.09053E+00 2.99172E+00 1.60386E+00
F7 Avg 7.00020E+02 7.00007E+02 7.00067E+02 7.00023E+02 7.00672E+02 7.00905E+02 7.00989E+02 9.28124E+02
Std 3.73518E-02 1.16692E-02 2.12456E-02 5.69988E-02 1.05290E-01 1.37294E-01 4.81903E-02 2.31714E+01
F8 Avg 8.01658E+02 8.00133E+02 1.01183E+03 1.02331E+03 8.68788E+02 9.18685E+02 8.84295E+02 1.06116E+03
Std 1.17822E+00 7.26614E-01 5.61642E+01 4.35938E+01 1.65707E+01 1.87836E+01 1.72735E+01 1.60039E+01
F9 Avg 9.42054E+02 9.30316E+02 1.15540E+03 1.14185E+03 1.12484E+03 1.10997E+03 1.01066E+03 1.17817E+03
Std 1.09988E+01 5.88835E+00 6.32420E+01 4.77074E+01 6.27572E+01 3.78939E+01 2.07817E+01 1.25746E+01
F10 Avg 1.00573E+03 1.00842E+03 5.74856E+03 5.82463E+03 2.04641E+03 2.77162E+03 3.39457E+03 7.90023E+03
Std 2.16329E+01 2.99517E+01 8.10965E+02 7.50261E+02 3.46940E+02 4.65773E+02 5.62751E+02 3.40055E+02
F11 Avg 2.98855E+03 2.85327E+03 5.66966E+03 5.83827E+03 5.27719E+03 5.30451E+03 4.49091E+03 8.15377E+03
Std 4.24962E+02 3.39268E+02 7.15629E+02 5.36995E+02 6.03178E+02 8.48363E+02 7.68050E+02 3.74930E+02
F12 Avg 1.20070E+03 1.20011E+03 1.20053E+03 1.20114E+03 1.20085E+03 1.20100E+03 1.20070E+03 1.20245E+03
Std 7.66967E-02 2.46500E-02 2.34233E-01 3.49681E-01 3.09211E-01 3.69568E-01 3.11974E-01 2.92009E-01
F13 Avg 1.30028E+03 1.30031E+03 1.30049E+03 1.30051E+03 1.30055E+03 1.30053E+03 1.30058E+03 1.30398E+03
Std 5.07710E-02 8.28648E-02 1.13998E-01 1.26768E-01 1.13424E-01 1.12825E-01 1.15690E-01 2.47031E-01
F14 Avg 1.40024E+03 1.40033E+03 1.40029E+03 1.40037E+03 1.40028E+03 1.40027E+03 1.40038E+03 1.47759E+03
Std 3.66347E-02 1.36751E-01 7.01820E-02 1.69745E-01 4.33932E-02 4.92272E-02 2.98360E-01 8.53620E+00
F15 Avg 1.50647E+03 1.50313E+03 1.53702E+03 1.56057E+03 1.52106E+03 1.56018E+03 1.51551E+03 1.27012E+04
Std 2.30052E+00 6.79152E-01 9.55210E+00 1.69508E+01 4.89660E+00 1.99481E+01 3.59558E+00 4.93603E+03
F16 Avg 1.61055E+03 1.60935E+03 1.61344E+03 1.61339E+03 1.61265E+03 1.61253E+03 1.61172E+03 1.61285E+03
Std 4.84808E-01 7.03814E-01 4.02703E-01 3.10418E-01 3.72153E-01 5.61621E-01 6.84455E-01 2.52363E-01
F17 Avg 5.39208E+04 3.16883E+03 1.29011E+05 2.82893E+05 6.40334E+05 3.09158E+06 9.26169E+05 8.03248E+06
Std 4.22166E+04 3.81606E+02 9.77292E+04 1.57262E+05 2.83522E+05 1.79642E+06 5.72456E+05 3.41898E+06
F18 Avg 2.71655E+03 1.94507E+03 1.11717E+04 9.87050E+03 1.05503E+04 1.09021E+04 2.41245E+04 2.05557E+08
Std 1.40819E+03 5.69635E+01 1.09042E+04 8.40388E+03 1.23579E+04 2.21157E+04 3.51308E+04 9.27845E+07
F19 Avg 1.90674E+03 1.90579E+03 1.92464E+03 1.92999E+03 1.92727E+03 1.94347E+03 1.92085E+03 2.01667E+03
Std 1.08752E+01 1.06905E+00 2.58107E+01 2.53723E+01 3.23692E+01 4.48066E+01 1.84465E+01 1.90301E+01
F20 Avg 3.12645E+03 2.17751E+03 2.40982E+03 2.93412E+03 3.03369E+03 1.57407E+04 3.17035E+03 2.36329E+04
Std 1.20063E+03 7.47546E+01 1.39629E+02 7.56893E+02 6.41313E+02 9.38441E+03 9.27083E+02 8.02891E+03
F21 Avg 2.07046E+04 2.75547E+03 7.87072E+04 9.47816E+04 2.16591E+05 8.18429E+05 3.21466E+05 2.37071E+06
Std 1.89649E+04 2.32155E+02 4.88862E+04 4.67006E+04 2.06629E+05 6.81499E+05 2.92593E+05 8.96005E+05
F22 Avg 2.40439E+03 2.43175E+03 3.36714E+03 3.39359E+03 2.90019E+03 2.84405E+03 2.59662E+03 3.23052E+03
Std 9.72631E+01 1.23286E+02 4.22618E+02 3.75556E+02 2.11052E+02 1.69063E+02 1.56777E+02 1.55392E+02
F23 Avg 2.61524E+03 2.61524E+03 2.61525E+03 2.61578E+03 2.61542E+03 2.61981E+03 2.62137E+03 2.72030E+03
Std 1.33518E-12 1.56165E-12 4.26698E-03 2.35254E-01 9.01591E-02 2.09472E+00 3.12716E+00 2.30333E+01
F24 Avg 2.63172E+03 2.63409E+03 2.67252E+03 2.67515E+03 2.60444E+03 2.60261E+03 2.60001E+03 2.60000E+03
Std 4.99888E+00 6.97270E+00 2.61344E+01 2.70422E+01 5.54186E+00 1.76688E+00 4.09949E-03 4.86976E-09
F25 Avg 2.71090E+03 2.70493E+03 2.73140E+03 2.73293E+03 2.71885E+03 2.71553E+03 2.71040E+03 2.70000E+03
Std 2.18201E+00 1.97306E+00 1.68219E+01 2.03315E+01 1.04665E+01 1.32286E+01 2.38993E+00 1.46262E-13
F26 Avg 2.71689E+03 2.70371E+03 2.71710E+03 2.70382E+03 2.70048E+03 2.70374E+03 2.70074E+03 2.70330E+03
Std 3.78166E+01 1.81900E+01 3.77753E+01 1.82564E+01 1.04485E-01 1.81813E+01 1.77235E-01 2.40891E-01
F27 Avg 3.17902E+03 3.18694E+03 3.88180E+03 4.01990E+03 3.65205E+03 3.61347E+03 3.11040E+03 3.44727E+03
Std 7.65075E+01 8.62136E+01 4.88491E+02 4.22291E+02 3.44449E+02 3.35484E+02 3.81213E+00 2.49340E+02
F28 Avg 3.71995E+03 3.72157E+03 5.78038E+03 5.33833E+03 4.53855E+03 4.54990E+03 3.82833E+03 5.47109E+03
Std 3.49325E+01 9.73647E+01 1.23292E+03 6.78767E+02 3.70275E+02 5.20391E+02 1.44019E+02 2.06620E+02
F29 Avg 4.01888E+03 3.94449E+05 1.30666E+07 3.96821E+07 6.71592E+06 6.31911E+06 1.87950E+06 2.20942E+07
Std 2.06796E+02 2.14040E+06 1.59102E+07 4.36528E+07 3.76641E+06 4.59685E+06 4.25118E+06 8.85299E+06
F30 Avg 5.26737E+03 5.55292E+03 1.86083E+04 3.44395E+04 1.33490E+04 2.61403E+04 2.79065E+04 4.18805E+05
Std 6.28726E+02 1.10322E+03 3.14675E+04 7.26489E+04 1.43735E+04 2.10759E+04 9.57433E+03 1.18249E+05