Table 4 Comparative results of f14 to f23 for PSC-MTLBO, MTLBO, and TLBO with other meta-heuristics of benchmark suite 1.
From: Parallel sub class modified teaching learning based optimization
PSO | DE | BBO | CS | FA | GSA | ABC | AMO | TLBO | MTLBO | PSC-MTLBO | ||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
f14 | Mean | 9.9800E-01 | 9.9800E-01 | 9.9810E-01 | 9.9810E-01 | 3.0273E + 00 | 5.9533E + 00 | 9.9800E-01 | 9.9800E-01 | 2.5374E + 00 | 1.9798E + 00 | 9.9800E-01 |
Mean rank | 1 | 1 | 6 | 6 | 10 | 11 | 1 | 1 | 9 | 8 | 1 | |
SD | 1.0968E-14 | 9.8526E-16 | 4.0691E-04 | 4.8277E-04 | 1.5853E + 00 | 3.4819E + 00 | 3.7921E-16 | 3.3858E-12 | 2.2102E + 00 | 2.5021E + 00 | 3.3993E-16 | |
SD rank | 4 | 3 | 6 | 7 | 8 | 11 | 2 | 5 | 9 | 10 | 1 | |
f15 | Mean | 6.5867E-04 | 4.5400E-04 | 2.8000E-03 | 5.0310E-04 | 1.0000E-03 | 4.8000E-03 | 7.4715E-04 | 3.9738E-04 | 4.6518E-03 | 3.6749E-03 | 3.0749E-04 |
Mean rank | 5 | 3 | 8 | 4 | 7 | 11 | 6 | 2 | 10 | 9 | 1 | |
SD | 2.2775E-04 | 3.4262E-04 | 4.4000E-03 | 1.1180E-04 | 4.6002E-04 | 3.3000E-03 | 2.1481E-04 | 4.4503E-05 | 8.0340E-03 | 7.4414E-03 | 4.7444E-09 | |
SD rank | 5 | 6 | 9 | 3 | 7 | 8 | 4 | 2 | 11 | 10 | 1 | |
f16 | Mean | −1.0316E + 00 | −1.0316E + 00 | −1.0312E + 00 | −1.0316E + 00 | −1.0314E + 00 | −1.0316E + 00 | −1.0316E + 00 | −1.0316E + 00 | −1.0316E + 00 | −1.0316E + 00 | −1.0316E + 00 |
Mean rank | 6 | 6 | 11 | 1 | 10 | 1 | 6 | 6 | 1 | 1 | 1 | |
SD | 1.2775E-12 | 6.6855E-14 | 8.1085E-04 | 1.5821E-07 | 1.1000E-03 | 4.7536E-16 | 1.1269E-14 | 5.2006E-11 | 6.0000E-07 | 4.5325E-16 | 4.5325E-16 | |
SD rank | 6 | 5 | 10 | 8 | 11 | 3 | 4 | 7 | 9 | 1 | 1 | |
f17 | Mean | 3.9790E-01 | 3.9790E-01 | 3.9840E-01 | 3.9790E-01 | 3.9790E-01 | 3.9790E-01 | 3.9790E-01 | 3.9790E-01 | 3.9789E-01 | 3.9789E-01 | 3.9789E-01 |
Mean rank | 4 | 4 | 11 | 4 | 4 | 4 | 4 | 4 | 1 | 1 | 1 | |
SD | 8.2239E-12 | 0.0000E + 00 | 6.7654E-04 | 3.2449E-06 | 3.0709E-08 | 0.0000E + 00 | 5.3819E-08 | 0.0000E + 00 | 5.6656E-17 | 5.6656E-17 | 5.6656E-17 | |
SD rank | 7 | 1 | 11 | 10 | 8 | 1 | 9 | 1 | 4 | 4 | 4 | |
f18 | Mean | 3.0001E + 00 | 3.0000E + 00 | 3.0491E + 00 | 3.0013E + 00 | 3.0123E + 00 | 3.7403E + 00 | 3.0000E + 00 | 3.0018E + 00 | 5.1600E + 00 | 9.4800E + 00 | 3.0000E + 00 |
Mean rank | 4 | 1 | 8 | 5 | 7 | 9 | 1 | 6 | 10 | 11 | 1 | |
SD | 7.9627E-05 | 1.2230E-10 | 6.5000E-02 | 2.6000E-03 | 5.2600E-02 | 1.6055E + 00 | 2.6164E-05 | 5.5000E-03 | 7.4760E + 00 | 1.1769E + 01 | 0.0000E + 00 | |
SD rank | 4 | 2 | 8 | 5 | 7 | 9 | 3 | 6 | 10 | 11 | 1 | |
f19 | Mean | −3.8628E + 00 | −3.8628E + 00 | −3.8627E + 00 | −3.8628E + 00 | −3.8613E + 00 | −3.8625E + 00 | −3.8628E + 00 | −3.8628E + 00 | −2.7286E + 00 | −3.8319E + 00 | −3.8628E + 00 |
Mean rank | 1 | 1 | 7 | 1 | 9 | 8 | 1 | 1 | 11 | 10 | 1 | |
SD | 3.1270E-12 | 2.3042E-15 | 1.4077E-04 | 1.4043E-05 | 3.7000E-03 | 3.8767E-04 | 1.3654E-10 | 1.3669E-15 | 1.5766E + 00 | 1.5460E-01 | 9.0649E-16 | |
SD rank | 4 | 3 | 7 | 6 | 9 | 8 | 5 | 2 | 11 | 10 | 1 | |
f20 | Mean | −3.2554E + 00 | −3.2174E + 00 | −3.2833E + 00 | −3.3210E + 00 | −3.2741E + 00 | −3.3220E + 00 | −3.3220E + 00 | −3.3220E + 00 | −3.1467E + 00 | −3.2789E + 00 | −3.3220E + 00 |
Mean rank | 9 | 10 | 6 | 5 | 8 | 1 | 1 | 1 | 11 | 7 | 1 | |
SD | 6.0200E-02 | 3.9400E-02 | 5.6300E-02 | 7.5186E-04 | 7.2300E-02 | 4.7967E-16 | 8.5733E-10 | 5.0850E-06 | 3.7278E-01 | 5.8637E-02 | 9.0649E-16 | |
SD rank | 9 | 6 | 7 | 5 | 10 | 1 | 3 | 4 | 11 | 8 | 2 | |
f21 | Mean | −7.6393E + 00 | −1.0153E + 01 | −5.4381E + 00 | −9.7256E + 00 | −6.5633E + 00 | −4.7840E + 00 | −1.0153E + 01 | −1.0059E + 01 | −7.3120E + 00 | −5.8022E + 00 | −9.0815E + 00 |
Mean rank | 6 | 1 | 10 | 4 | 8 | 11 | 2 | 3 | 7 | 9 | 5 | |
SD | 3.2359E + 00 | 8.1382E-06 | 3.6051E + 00 | 2.8460E-01 | 3.8155E + 00 | 1.4761E + 00 | 1.3000E-03 | 2.4910E-01 | 2.8581E + 00 | 3.1657E + 00 | 1.7468E + 00 | |
SD rank | 9 | 1 | 10 | 4 | 11 | 5 | 2 | 3 | 7 | 8 | 6 | |
f22 | Mean | −7.3602E + 00 | −1.0403E + 01 | −7.7759E + 00 | −9.8624E + 00 | −1.0403E + 01 | −6.5797E + 00 | −1.0401E + 01 | −1.0390E + 01 | −7.5069E + 00 | −6.1173E + 00 | −9.4385E + 00 |
Mean rank | 9 | 1 | 7 | 5 | 2 | 10 | 3 | 4 | 8 | 11 | 6 | |
SD | 3.3035E + 00 | 2.5631E-06 | 3.3125E + 00 | 3.2910E-01 | 7.0965E-04 | 3.8073E + 00 | 4.6000E-03 | 2.9700E-02 | 3.0994E + 00 | 3.0230E + 00 | 1.9563E + 00 | |
SD rank | 9 | 1 | 10 | 5 | 2 | 11 | 3 | 4 | 8 | 7 | 6 | |
f23 | Mean | −8.9611E + 00 | −1.0536E + 01 | −9.3514E + 00 | −9.7534E + 00 | −1.0230E + 01 | −8.2651E + 00 | −1.0534E + 01 | −1.0499E + 01 | −7.0532E + 00 | −7.6819E + 00 | −1.0536E + 01 |
Mean rank | 8 | 2 | 7 | 6 | 5 | 9 | 3 | 4 | 11 | 10 | 1 | |
SD | 2.8381E + 00 | 3.9747E-06 | 2.6288E + 00 | 4.9130E-01 | 1.5332E + 00 | 2.8868E + 00 | 5.4000E-03 | 1.4280E-01 | 3.1958E + 00 | 3.1608E + 00 | 3.6260E-15 | |
SD rank | 8 | 2 | 7 | 5 | 6 | 9 | 3 | 4 | 11 | 10 | 1 | |
Average mean rank | 5.3 | 3.0 | 8.1 | 4.1 | 7.0 | 7.5 | 2.8 | 3.2 | 7.9 | 7.7 | 1.9 | |
Overall mean rank | 6 | 3 | 11 | 5 | 7 | 8 | 2 | 4 | 10 | 9 | 1 | |
Average SD rank | 6.5 | 3 | 8.5 | 5.8 | 7.9 | 6.6 | 3.8 | 3.8 | 9.1 | 7.9 | 2.4 | |
Overall SD rank | 6 | 2 | 10 | 5 | 8 | 7 | 3 | 3 | 11 | 8 | 1 | |
Overall friedman rank | 6 | 3 | 11 | 5 | 7 | 8 | 2 | 4 | 10 | 9 | 1 | |
