Table 6 Outcomes on multimodal benchmark functions with fixed dimensions (F14 to F23).
Algorithms | Metric | F14 | F15 | F16 | F17 | F18 | F19 | F20 | F21 | F22 | F23 |
---|---|---|---|---|---|---|---|---|---|---|---|
PO | Mean | −2.878e−06 | 0.15182 | −0.31136 | 4.5667 | −0.5 | 0.50963 | 0.48301 | 1.0001 | 1.0002 | 4 |
Std | 0.039299 | 0.036599 | 0.56745 | 10.9012 | 0.70711 | 0.36809 | 0.39528 | 2.8094e−05 | 4.1593e−05 | 0.0006310 | |
Rank | 11 | 4 | 2 | 2 | 1 | 10 | 8 | 1 | 1 | 2 | |
CPO-1 | Mean | −31.9783 | 0.1605 | 0.3114 | 2.7083 | −0.5 | 0.50946 | 0.34694 | 4.0001 | 4.0001 | 4.0001 |
Std | 0.0002385 | 0.037731 | 0.56746 | 0.61277 | 0.70711 | 0.36833 | 0.18924 | 0.0018993 | 0.0006964 | 0.0006257 | |
Rank | 2 | 8 | 4 | 1 | 1 | 9 | 6 | 3 | 2 | 3 | |
CPO-2 | Mean | −31.9783 | 0.13678 | 0.31159 | 4.5667 | −0.5 | 0.50977 | 0.34494 | 4.0001 | 4.0001 | 4.0001 |
Std | 1.1397e−05 | 0.040622 | 0.567 | 10.9012 | 0.70711 | 0.36786 | 0.19009 | 3.9159e−05 | 0.0006292 | 0.0006306 | |
Rank | 3 | 1 | 6 | 2 | 1 | 11 | 5 | 3 | 2 | 3 | |
CPO-3 | Mean | −0.027781 | 0.15227 | 0.31142 | 2.7083 | −0.5 | 0.5078 | 0.48542 | 3.9974 | 4.0001 | 4.0001 |
Std | 1.9254e−05 | 0.035161 | 0.56743 | 0.61277 | 0.70711 | 0.37099 | 0.28411 | 0.096006 | 0.0006287 | 0.0006296 | |
Rank | 10 | 5 | 5 | 1 | 1 | 5 | 9 | 2 | 2 | 3 | |
CPO-4 | Mean | −31.9784 | 1.9508 | −0.31128 | 5.9499 | −0.5 | 0.50748 | 0.34508 | 4.0002 | 4.0001 | 4.0001 |
Std | 0.0011457 | 1.8121 | 0.56761 | 4.9142 | 0.70711 | 0.37151 | 0.19014 | 0.14338 | 0.0006289 | 0.0006306 | |
Rank | 1 | 11 | 3 | 3 | 1 | 3 | 4 | 4 | 2 | 3 | |
CPO-5 | Mean | −23.9784 | 0.18232 | −0.31141 | 5.9499 | −0.5 | 0.50881 | 0.3447 | 1.0001 | 4.0001 | 4.0566 |
Std | 11.3023 | 0.046545 | 0.56746 | 4.9142 | 0.70711 | 0.36938 | 0.19037 | 1.4364e−05 | 0.0006428 | 0.14926 | |
Rank | 8 | 9 | 1 | 3 | 1 | 7 | 2 | 1 | 2 | 6 | |
CPO-6 | Mean | −31.9783 | 0.15354 | −0.31141 | 2.7083 | −0.5 | 0.50774 | 0.50153 | 1.0001 | 4.0001 | 3.9999 |
Std | 1.1409e−06 | 0.034451 | 0.56746 | 0.61277 | 0.70711 | 0.37109 | 0.30168 | 4.953e−05 | 0.0006276 | 0.02663 | |
Rank | 4 | 6 | 1 | 1 | 1 | 4 | 10 | 1 | 2 | 1 | |
CPO-7 | Mean | −31.9783 | 0.18419 | −0.31141 | 5.9499 | −0.5 | 0.50933 | 0.34383 | 4.0001 | 4.0001 | 4.0003 |
Std | 8.1103e−05 | 0.047206 | 0.56746 | 4.9142 | 0.70711 | 0.36858 | 0.19075 | 5.3883e−05 | 0.0006334 | 0.025795 | |
Rank | 5 | 10 | 1 | 3 | 1 | 8 | 1 | 3 | 2 | 4 | |
CPO-8 | Mean | −0.027789 | 0.1604 | 0.3114 | 2.7083 | −0.5 | 0.50815 | 0.3448 | 4.0001 | 4.0001 | 4.0009 |
Std | 1.7353e−06 | 0.036725 | 0.56747 | 0.61277 | 0.70711 | 0.37043 | 0.19017 | 5.5582e−05 | 0.0006269 | 0.029768 | |
Rank | 9 | 7 | 4 | 1 | 1 | 6 | 3 | 3 | 2 | 5 | |
CPO-9 | Mean | −31.9783 | 0.14465 | 0.31143 | 2.7083 | −0.5 | 0.50706 | 0.44414 | 1.0001 | 4.0001 | 4.0001 |
Std | 2.5676e−06 | 0.036943 | 0.56743 | 0.61277 | 0.70711 | 0.37219 | 0.27642 | 1.4268e−05 | 0.00062777 | 0.00063165 | |
Rank | 9 | 2 | 6 | 1 | 1 | 2 | 7 | 1 | 2 | 3 | |
CPO-10 | Mean | −31.9783 | 0.15 | −0.31141 | 5.9499 | −0.5 | 0.49752 | 0.34508 | 1.0001 | 4.0001 | 4.0001 |
Std | 1.5314e−05 | 0.034803 | 0.56745 | 4.9142 | 0.70711 | 0.38771 | 0.18987 | 1.122e−05 | 0.0006807 | 0.0006313 | |
Rank | 7 | 3 | 1 | 3 | 1 | 1 | 4 | 1 | 2 | 3 |