Table 13 Comparisons between CO,HBA,ARO,OMA,EDO,WOA-LFDE and MDE-DPSO on CEC2013 with 50D.
From: A hybrid differential evolution particle swarm optimization algorithm based on dynamic strategies
Fun | CO | HBA | ARO | OMA | EDO | WOA-LFDE | MDE-DPSO |
|---|---|---|---|---|---|---|---|
\(f_{a1}\) | 1.0700E-12/ 2.1472E-13(>) | 1.1834E+00/ 2.5845E+00(<) | 2.5661E-09/ 1.7039E-08(>) | 1.2379E-01/ 5.1295E-01(<) | 3.9997E+04/ 1.0958E+04(<) | 4.7191E-07/ 1.0805E-06(>) | 4.1957E-04/ 1.3511E-04 |
\(f_{a2}\) | 1.0335E+06/ 3.6529E+05(>) | 8.9756E+07/ 1.2267E+08(<) | 3.0543E+06/ 1.3441E+06(>) | 2.3870E+07/ 9.6217E+06(<) | 1.0719E+07/ 5.3058E+06(>) | 1.5262E+06/ 5.7847E+05(>) | 1.3700E+07/ 2.2149E+07 |
\(f _{a3}\) | 1.9015E+09/ 2.6350E+09(<) | 1.5681E+11/ 6.0028E+11(<) | 5.9223E+08/ 4.7404E+08(>) | 1.0930E+10/ 1.2578E+10(<) | 3.3032E+10/ 9.7108E+09(<) | 3.9403E+09/ 3.2098E+09(<) | 6.4477E+08/ 3.1638E+09 |
\(f_{a4}\) | 8.5620E+03/ 2.4054E+03(<) | 1.7773E+04/ 5.7465E+03(<) | 4.9478E+03/ 2.4447E+03(<) | 4.5169E+04/ 1.1925E+04(<) | 3.9715E+04/ 9.8340E+03(<) | 4.2085E+03/ 3.4658E+03(<) | 5.1416E+00/ 4.1948E+00 |
\(f_{a5}\) | 6.8680E-12/ 1.1587E-11(>) | 8.0647E+00/ 4.6229E+01(<) | 3.5347E-06/ 2.2035E-05(>) | 1.1612E+00/ 5.0271E+00(<) | 2.1183E+03/ 1.2885E+03(<) | 3.3077E-04/ 8.3321E-04(>) | 1.6223E-02/ 1.9968E-03 |
\(f_{a6}\) | 4.8609E+01/ 1.6045E+01(<) | 1.0511E+02/ 5.7389E+01(<) | 7.3832E+01/ 2.9069E+01(<) | 1.1318E+02/ 5.0088E+01(<) | 1.4205E+03/ 6.5564E+02(<) | 8.5496E+01/ 2.4797E+01(<) | 4.5759E+01/ 2.1256E+01 |
\(f_{a7}\) | 2.0344E+02/ 3.7016E+01(<) | 2.9736E+02/ 2.7362E+02(<) | 1.0027E+02/ 1.9067E+01(<) | 1.9116E+02/ 6.6891E+01(<) | 1.2092E+02/ 1.8986E+01(<) | 3.2642E+02/ 5.0150E+02(<) | 2.7823E+01/ 8.3646E+00 |
\(f_{a8}\) | 2.1115E+01/ 4.5453E-02(\(\approx\)) | 2.1130E+01/ 4.0391E-02(\(\approx\)) | 2.1136E+01/ 4.2086E-02(\(\approx\)) | 2.1127E+01/ 3.1698E-02(\(\approx\)) | 2.1132E+01/ 3.4922E-02(\(\approx\)) | 2.1122E+01/ 3.8981E-02(\(\approx\)) | 2.1130E+01/ 4.1759E-02 |
\(f_{a9}\) | 5.9116E+01/ 3.9722E+00(<) | 7.1841E+01/ 4.5882E+00(<) | 5.6723E+01/ 5.8265E+00(<) | 5.6959E+01/ 5.7054E+00(<) | 6.2146E+01/ 3.2081E+00(<) | 6.6751E+01/ 3.9199E+00(<) | 3.1836E+01/ 3.7026E+00 |
\(f_{a10}\) | 3.2171E-01/ 1.5901E-01(<) | 5.8948E+01/ 1.4256E+02(<) | 4.2661E-01/ 2.1232E-01(<) | 7.7104E+01/ 4.5629E+01(<) | 2.5999E+03/ 1.1121E+03(<) | 1.1358E+00/ 3.1099E+00(<) | 1.5105E-01/ 7.8201E-02 |
\(f_{a11}\) | 5.7025E+00/ 3.6024E+00(>) | 1.3992E+02/ 1.7348E+02(<) | 1.0358E+02/ 3.9055E+01(<) | 5.1832E+02/ 8.1500E+01(<) | 7.8161E+02/ 1.3114E+02(<) | 3.5500E+02/ 8.7445E+01(<) | 6.3366E+01/ 1.7053E+01 |
\(f_{a12}\) | 7.4354E+02/ 1.4515E+02(<) | 7.2912E+02/ 1.1674E+02(<) | 3.6060E+02/ 6.2948E+01(<) | 5.4998E+02/ 1.0693E+02(<) | 9.0543E+02/ 1.7728E+02(<) | 9.1387E+02/ 1.6814E+02(<) | 9.6860E+01/ 1.8914E+01 |
\(f_{a13}\) | 6.5738E+02/ 8.2167E+01(<) | 9.1724E+02/ 1.1704E+02(<) | 5.0393E+02/ 7.8129E+01(<) | 5.9346E+02/ 8.2768E+01(<) | 8.7636E+02/ 1.6193E+02(<) | 9.9006E+02/ 1.3180E+02(<) | 2.3412E+02/ 4.6378E+01 |
\(f_{a14}\) | 6.2668E+02/ 2.2102E+02(>) | 7.8905E+03/ 3.6993E+03(<) | 9.5690E+02/ 2.9819E+02(>) | 1.1638E+04/ 1.2165E+03(<) | 1.1436E+04/ 5.8084E+02(<) | 3.5404E+03/ 1.1253E+03(>) | 4.0840E+03/ 1.0320E+03 |
\(f_{a15}\) | 8.7820E+03/ 9.0804E+02(<) | 1.2576E+04/ 1.5496E+03(<) | 8.9190E+03/ 1.4148E+03(<) | 1.3674E+04/ 7.0629E+02(<) | 1.2758E+04/ 5.0779E+02(<) | 9.1760E+03/ 1.0709E+03(<) | 7.4896E+03/ 2.0874E+03 |
\(f_{a16}\) | 1.9915E+00/ 5.9876E-01(\(\approx\)) | 2.9867E+00/ 6.2152E-01(<) | 1.9084E+00/ 6.1856E-01(\(\approx\)) | 3.3522E+00/ 2.5969E-01(<) | 3.0054E+00/ 3.2777E-01(<) | 2.1686E+00/ 5.8764E-01(<) | 1.9457E+00/ 1.0652E+00 |
\(f_{a17}\) | 5.5036E+01/ 1.4892E+00(>) | 2.4627E+02/ 4.3608E+01(<) | 1.1195E+02/ 5.1474E+01(>) | 6.1597E+02/ 1.2749E+02(<) | 1.1288E+03/ 1.4336E+02(<) | 6.6668E+02/ 1.1799E+02(<) | 1.4693E+02/ 2.4120E+01 |
\(f_{a18}\) | 9.9580E+02/ 1.7766E+02(<) | 9.7809E+02/ 1.1160E+02(<) | 3.9364E+02/ 8.1904E+01(<) | 6.9949E+02/ 1.0573E+02(<) | 1.1688E+03/ 1.3221E+02(<) | 1.0960E+03/ 2.9139E+02(<) | 1.6110E+02/ 2.5338E+01 |
\(f_{a19}\) | 8.3968E+00/ 2.3467E+00(>) | 2.8749E+03/ 2.0240E+04(<) | 6.1893E+00/ 1.2946E+00(>) | 3.2359E+02/ 2.9976E+02(<) | 9.1953E+04/ 8.3754E+04(<) | 2.2762E+02/ 2.3168E+02(<) | 2.6418E+01/ 1.4896E+01 |
\(f_{a20}\) | 2.3833E+01/ 9.2365E-01(<) | 2.4268E+01/ 5.2928E-01(<) | 2.1831E+01/ 1.1793E+00(<) | 2.2839E+01/ 7.1336E-01(<) | 2.2640E+01/ 5.9069E-01(<) | 2.4452E+01/ 1.9861E-01(<) | 1.9828E+01/ 7.2314E-01 |
\(f_{a21}\) | 8.9786E+02/ 3.4599E+02(<) | 9.5919E+02/ 1.7855E+02(<) | 9.5971E+02/ 1.4294E+02(<) | 8.1150E+02/ 3.4597E+02(<) | 3.9943E+03/ 2.4130E+02(<) | 8.8612E+02/ 2.6582E+02(<) | 7.4209E+02/ 4.0346E+02 |
\(f_{a22}\) | 7.0981E+02/ 2.4544E+02(>) | 8.7389E+03/ 3.6585E+03(<) | 8.5935E+02/ 3.0245E+02(>) | 1.1882E+04/ 1.6133E+03(<) | 1.2033E+04/ 5.9870E+02(<) | 5.5675E+03/ 1.3683E+03(<) | 4.1192E+03/ 9.5181E+02 |
\(f_{a23}\) | 1.0891E+04/ 1.6866E+03(<) | 1.4376E+04/ 1.6315E+03(<) | 1.0214E+04/ 1.3423E+03(<) | 1.3408E+04/ 1.0081E+03(<) | 1.3059E+04/ 4.2726E+02(<) | 1.0970E+04/ 1.4378E+03(<) | 8.1780E+03/ 2.7352E+03 |
\(f_{a24}\) | 3.6737E+02/ 1.0866E+01(<) | 5.0431E+02/ 6.6646E+01(<) | 3.6558E+02/ 1.3069E+01(<) | 3.8759E+02/ 1.3039E+01(<) | 3.8094E+02/ 7.2385E+00(<) | 4.0699E+02/ 1.4818E+01(<) | 2.9885E+02/ 2.6556E+01 |
\(f_{a25}\) | 3.9594E+02/ 1.3159E+01(<) | 4.8794E+02/ 3.7242E+01(<) | 3.9064E+02/ 1.3097E+01(<) | 3.9877E+02/ 1.5727E+01(<) | 3.9364E+02/ 1.0539E+01(<) | 4.3561E+02/ 1.9093E+01(<) | 3.8459E+02/ 3.4698E+00 |
\(f_{a26}\) | 3.4458E+02/ 1.2723E+02(<) | 4.9413E+02/ 4.4228E+01(<) | 4.1785E+02/ 8.8591E+01(<) | 4.2025E+02/ 6.8370E+01(<) | 3.2960E+02/ 1.3213E+02(<) | 4.5778E+02/ 6.5655E+01(<) | 2.9276E+02/ 8.7019E+01 |
\(f_{a27}\) | 1.9369E+03/ 1.1900E+02(<) | 2.5436E+03/ 1.9277E+02(<) | 1.8849E+03/ 1.4056E+02(<) | 1.8721E+03/ 1.2047E+02(<) | 2.0358E+03/ 8.0954E+01(<) | 2.1950E+03/ 1.3951E+02(<) | 1.1261E+03/ 7.2770E+01 |
\(f_{a28}\) | 2.2438E+03/ 2.0621E+03(<) | 5.9746E+03/ 1.6817E+03(<) | 1.4825E+03/ 1.7827E+03(<) | 3.6924E+03/ 2.2386E+03(<) | 4.6777E+03/ 1.6970E+03(<) | 7.5373E+03/ 1.5657E+03(<) | 1.2328E+03/ 1.6049E+03 |
>/\(\approx\)/< | 8/2/18 | 0/1/27 | 8/2/18 | 0/1/27 | 1/1/26 | 4/1/23 | -/-/- |
