Table 2 Comparisons between MPSO, PSO-sono, EAPSO, PSO-HBF, ACEPSO and MDE-DPSO on CEC2013 with 10D.
From: A hybrid differential evolution particle swarm optimization algorithm based on dynamic strategies
Fun | MPSO | PSO-sono | EAPSO | PSO-HBF | ACEPSO | MDE-DPSO |
|---|---|---|---|---|---|---|
\(f_{a1}\) | 1.3018E-05/ 1.4864E-05(<) | 0/0(>) | 0/0(>) | 2.5412E-13/ 1.0806E-13(>) | 0/0(>) | 7.3364E-07/ 1.9689E-06 |
\(f_{a2}\) | 6.5906E+04/ 7.4932E+04(<) | 1.3371E+05/ 2.9075E+05(<) | 2.8841E+04/ 1.8690E+04(<) | 1.1806E+05/ 9.8734E+04(<) | 6.0332E+05/ 3.1150E+05(<) | 2.0277E+04/ 5.2966E+04 |
\(f_{a3}\) | 4.2339E+06/ 1.8624E+07(<) | 1.6213E+05/ 7.6348E+05(<) | 3.1022E+06/ 1.2545E+07(<) | 1.7840E+08/ 4.5342E+08(<) | 1.4382E+07/ 2.2662E+07(<) | 1.6683E+04/ 5.5388E+04 |
\(f_{a4}\) | 4.7046E+01/ 4.8585E+01(<) | 7.6983E-01/ 2.0053E+00(<) | 1.8090E+03/ 1.6036E+03(<) | 1.2997E+04/ 5.2058E+03(<) | 6.0458E+03/ 4.1257E+03(<) | 4.4837E-02/ 2.0335E-01 |
\(f_{a5}\) | 9.2920E-05/ 6.9221E-05(>) | 0/0(>) | 0/0(>) | 8.1409E-12/ 3.5804E-11(>) | 1.7967E-12/ 5.6859E-12(>) | 5.5639E-04/ 2.5319E-04 |
\(f_{a6}\) | 1.0015E+01/ 9.4104E+00(<) | 8.6104E+00/ 3.8723E+00(<) | 6.5279E+00/ 4.5679E+00(<) | 1.0042E+01/ 1.4530E+01(<) | 1.2717E+01/ 1.5739E+01(<) | 6.3747E+00/ 8.4717E+00 |
\(f_{a7}\) | 3.2927E+00/ 3.3543E+00(<) | 4.8059E+00/ 5.4305E+00(<) | 3.3371E+00/ 6.7220E+00(<) | 7.1082E+01/ 3.6316E+01(<) | 2.6253E+01/ 1.1695E+01(<) | 4.3718E-02/ 8.7025E-02 |
\(f_{a8}\) | 2.0364E+01/ 6.7590E-02(<) | 2.0344E+01/ 7.1105E-02(\(\approx\)) | 2.0395E+01/ 7.5487E-02(<) | 2.0337E+01/ 8.7199E-02(\(\approx\)) | 2.0338E+01/ 7.6262E-02(\(\approx\)) | 2.0341E+01/ 7.2869E-02 |
\(f_{a9}\) | 4.7435E+00/ 1.3886E+00(<) | 4.1361E+00/ 1.4317E+00(<) | 3.0499E+00/ 1.8055E+00(<) | 9.2399E+00/ 1.5897E+00(<) | 5.4412E+00/ 1.8995E+00(<) | 1.0204E+00/ 6.5735E-01 |
\(f_{a10}\) | 5.5669E-01/ 2.4389E-01(<) | 7.3984E-01/ 5.6822E-01(<) | 1.1451E-01/ 7.2697E-02(>) | 4.1547E+00/ 3.1758E+00(<) | 3.0822E-01/ 2.0912E-01(>) | 3.3058E-01/ 8.4418E-01 |
\(f_{a11}\) | 8.6732E+00/ 4.9968E+00(<) | 6.8281E+00/ 3.2638E+00(<) | 6.2624E+00/ 3.7137E+00(<) | 5.0334E+00/ 3.1615E+00(<) | 1.7753E+00/ 1.7269E+00(>) | 2.6922E+00/ 1.4252E+00 |
\(f_{a12}\) | 1.7175E+01/ 7.6010E+00(<) | 8.3108E+00/ 4.4577E+00(\(\approx\)) | 1.0008E+01/ 4.0753E+00(<) | 8.2155E+01/ 3.2995E+01(<) | 1.0705E+01/ 5.0886E+00(<) | 8.7400E+00/ 3.4542E+00 |
\(f_{a13}\) | 3.0471E+01/ 9.5865E+00(<) | 1.5014E+01/ 7.5454E+00(<) | 2.0166E+01/ 9.7357E+00(<) | 8.4483E+01/ 3.1539E+01(<) | 1.9069E+01/ 7.6425E+00(<) | 1.2926E+01/ 5.7805E+00 |
\(f_{a14}\) | 2.9668E+02/ 8.6829E+02(<) | 3.7923E+02/ 2.0643E+02(<) | 3.1807E+02/ 3.5542E+02(<) | 2.4536E+02/ 1.2111E+02(<) | 1.2447E+02/ 1.1969E+02(>) | 1.3586E+02/ 9.7261E+01 |
\(f_{a15}\) | 8.7796E+02/ 2.7079E+02(<) | 5.9371E+02/ 2.6744E+02(<) | 1.3204E+03/ 4.0819E+02(<) | 1.1982E+03/ 2.6421E+02(<) | 5.0890E+02/ 4.0545E+02(>) | 5.7733E+02/ 2.5062E+02 |
\(f_{a16}\) | 1.0671E+00/ 1.8933E-01(<) | 6.4899E-01/ 2.9389E-01(>) | 1.2216E+00/ 2.8380E-01(<) | 4.4543E-01/ 1.8618E-01(>) | 1.0898E+00/ 1.5647E-01(<) | 7.6139E-01/ 2.7808E-01 |
\(f_{a17}\) | 2.9138E+01/ 7.3084E+00(<) | 1.7474E+01/ 4.2745E+00(<) | 2.4265E+01/ 8.0439E+00(<) | 1.0256E+01/ 2.1239E+00(>) | 1.1571E+01/ 1.7563E+00(>) | 1.2792E+01/ 1.4399E+00 |
\(f_{a18}\) | 3.3173E+01/ 6.6018E+00(<) | 1.6714E+01/ 3.7478E+00(>) | 3.6451E+01/ 5.9602E+00(<) | 6.8188E+01/ 2.4593E+01(<) | 1.3659E+01/ 2.2447E+00(>) | 1.8001E+01/ 3.4874E+00 |
\(f_{a19}\) | 1.1563E+00/ 3.3626E-01(<) | 9.5495E-01/ 4.2218E-01(<) | 8.0509E-01/ 2.8500E-01(<) | 1.3725E+00/ 5.8023E-01(<) | 6.9250E-01/ 1.7606E-01(\(\approx\)) | 6.6019E-01/ 1.9277E-01 |
\(f_{a20}\) | 3.7675E+00/ 3.3626E-01(<) | 2.7010E+00/ 5.9110E-01(<) | 3.2352E+00/ 4.7747E-01(<) | 3.9471E+00/ 5.3062E-01(<) | 3.8734E+00/ 2.2275E-01(<) | 2.0585E+00/ 3.7788E-01 |
\(f_{a21}\) | 4.0019E+02/ 3.5948E-12(<) | 4.0019E+02/ 0.0000E+00(<) | 3.8449E+02/ 5.4358E+01(>) | 3.9234E+02/ 3.9246E+01(\(\approx\)) | 3.7272E+02/ 6.9576E+01(>) | 3.9627E+02/ 2.8033E+01 |
\(f_{a22}\) | 6.4573E+02/ 3.5164E+02(<) | 3.4543E+02/ 1.6980E+02(<) | 2.9956E+02/ 2.5633E+02(<) | 4.0494E+02/ 1.4949E+02(<) | 1.7217E+02/ 6.8202E+01(<) | 1.3998E+02/ 9.5252E+01 |
\(f_{a23}\) | 7.5136E+02/ 3.0240E+02(<) | 5.5238E+02/ 3.0914E+02(<) | 1.0982E+03/ 5.7985E+02(<) | 1.6034E+03/ 3.0219E+02(<) | 6.8046E+02/ 3.9764E+02(<) | 5.4094E+02/ 2.8161E+02 |
\(f_{a24}\) | 2.0665E+02/ 1.5713E+01(<) | 2.0963E+02/ 5.6375E+00(<) | 2.0758E+02/ 1.4991E+01(<) | 2.2799E+02/ 1.5311E+01(<) | 2.1797E+02/ 3.2557E+00(<) | 2.0263E+02/ 1.3197E+01 |
\(f_{a25}\) | 2.0776E+02/ 4.8881E+00(<) | 2.0370E+02/ 1.3510E+01(<) | 2.0954E+02/ 6.0039E+00(<) | 2.2599E+02/ 1.2278E+01(<) | 2.1878E+02/ 3.8371E+00(<) | 2.0242E+02/ 3.0595E+00 |
\(f_{a26}\) | 1.5004E+02/ 6.5985E+01(<) | 1.5800E+02/ 5.5081E+01(<) | 2.0093E+02/ 7.0086E+01(<) | 2.0238E+02/ 3.2322E+01(<) | 1.9933E+02/ 5.0714E+00(<) | 1.3669E+02/ 4.3341E+01 |
\(f_{a27}\) | 3.3539E+02/ 6.3599E+01(>) | 3.6885E+02/ 1.0178E+02(<) | 4.2545E+02/ 1.0504E+02(<) | 4.7207E+02/ 1.0584E+02(<) | 5.4489E+02/ 2.0211E+01(<) | 3.3741E+02/ 4.4985E+01 |
\(f_{a28}\) | 3.0636E+02/ 8.9930E+01(>) | 2.8824E+02/ 4.7527E+01(>) | 3.1984E+02/ 9.4665E+01(\(\approx\)) | 7.7721E+02/ 2.7307E+02(<) | 3.0000E+02/ 6.1280E-13(>) | 3.1511E+02/ 7.6376E+01 |
>/\(\approx\)/< | 3/0/25 | 5/2/21 | 4/1/23 | 4/2/22 | 10/2/16 | -/-/- |
