Research Article
A Novel Segmentation Method for Furnace Flame Using Adaptive Color Model and Hybrid-Coded HLO
Table 1
Results of AHcHLO, HcHLO, ASHLO, IAHLO, SFPSO, and ALPSO on the benchmark functions.
| | Fun | Metric | AHcHLO | HcHLO | ASHLO | IAHLO | SFPSO | ALPSO |
| | F1 | Best | 87.500000 | 87.500000 | 87.500000 | 87.500000 | 87.500000 | 87.500000 | | Mean | 87.500000 | 87.500000 | 87.500000 | 87.500000 | 87.500000 | 87.500000 | | Std | 0.00E + 00 | 3.02E − 08 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | | t-test | — | — | 0 | 0 | 0 | 0 | | -test | — | — | 0 | 0 | 0 | 0 |
| | F2 | Best | 7.667180 | 7.667181 | 7.667180 | 7.667180 | 7.667180 | 7.667180 | | Mean | 7.667180 | 7.667194 | 7.667180 | 7.667180 | 7.667180 | 7.667180 | | Std | 1.78E − 15 | 4.76E − 06 | 1.78E − 15 | 1.78E − 15 | 1.78E − 15 | 1.78E − 15 | | t-test | — | — | 0 | 0 | 0 | 0 | | -test | — | — | 0 | 0 | 0 | 0 |
| | F3 | Best | 4.579582 | 4.579587 | 4.579636 | 4.580169 | 4.579592 | 4.670711 | | Mean | 4.579584 | 4.579597 | 4.611342 | 4.611562 | 4.589737 | 5.017949 | | Std | 1.65E − 06 | 3.02E − 06 | 7.17E − 02 | 5.14E − 02 | 4.27E − 02 | 2.26E − 01 | | t-test | — | — | 1 | 1 | 1 | 1 | | -test | — | — | 1 | 1 | 1 | 1 |
| | F4 | Best | 2.000000 | 2.000000 | 2.000001 | 2.000001 | 2.000001 | 2.000000 | | Mean | 2.000000 | 2.000000 | 2.000001 | 2.001420 | 2.000001 | 2.002490 | | Std | 0.00E + 00 | 2.81E − 07 | 4.44E − 16 | 1.40E − 02 | 4.44E − 16 | 2.35E − 02 | | t-test | — | — | 1 | 0 | 1 | 0 | | -test | — | — | 1 | 1 | 1 | 0 |
| | F5 | Best | 2.124468 | 2.124470 | 2.124469 | 2.124469 | 2.124469 | 2.124468 | | Mean | 2.124488 | 2.124470 | 2.133572 | 2.142858 | 2.124567 | 2.133234 | | Std | 2.03E − 04 | 6.42E − 07 | 6.07E − 02 | 8.48E − 02 | 2.42E − 04 | 6.07E − 02 | | t-test | — | — | 0 | 1 | 1 | 0 | | -test | — | — | 1 | 1 | 1 | 0 |
| | F6 | Best | 1.076543 | 1.076546 | 1.102035 | 1.108898 | 1.103897 | 1.077931 | | Mean | 1.076544 | 1.081757 | 1.241141 | 1.239521 | 1.235834 | 1.129488 | | Std | 5.25E − 06 | 2.97E − 02 | 6.82E − 02 | 6.54E − 02 | 6.22E − 02 | 3.02E − 02 | | t-test | — | — | 1 | 1 | 1 | 1 | | -test | — | — | 1 | 1 | 1 | 1 |
| | F7 | Best | 99.239640 | 99.239635 | 99.239640 | 99.239640 | 99.239640 | 99.239640 | | Mean | 99.239640 | 99.241553 | 102.469891 | 101.291827 | 99.325068 | 99.240113 | | Std | 1.42E − 14 | 1.71E − 03 | 3.91E + 00 | 3.32E + 00 | 8.50E − 01 | 3.47E − 03 | | t-test | — | — | 1 | 1 | 0 | 0 | | -test | — | — | 1 | 1 | 0 | 1 |
| | F8 | Best | 3.557461 | 3.557466 | 3.558204 | 3.557911 | 3.607595 | 3.570644 | | Mean | 3.559827 | 3.558935 | 3.585373 | 3.592501 | 3.607832 | 3.665221 | | Std | 6.56E − 03 | 4.88E − 03 | 3.88E − 02 | 4.15E − 02 | 6.88E − 04 | 6.32E − 02 | | t-test | — | — | 1 | 1 | 1 | 1 | | -test | — | — | 1 | 1 | 1 | 1 |
| | F9 | Best | −32217.430000 | −32217.42778 | −32217.430000 | −32217.430000 | −32217.430000 | −32217.430000 | | Mean | −32217.430000 | −32217.42778 | −32217.430000 | −32217.430000 | −32217.430000 | −32217.430000 | | Std | 3.64E − 12 | 2.19E − 11 | 3.64E − 12 | 3.64E − 12 | 3.64E − 12 | 3.64E − 12 | | t-test | — | — | 0 | 0 | 0 | 0 | | -test | — | — | 0 | 0 | 0 | 0 |
| | F10 | Best | −0.808844 | −0.808844 | −0.808844 | −0.808844 | −0.808844 | −0.726114 | | Mean | −0.808844 | −0.808844 | −0.808440 | −0.808775 | −0.807086 | 0.767928 | | Std | 2.22E − 16 | 3.25E − 11 | 2.95E − 03 | 6.84E − 04 | 5.63E − 03 | 1.65E + 00 | | t-test | — | — | 0 | 0 | 1 | 1 | | -test | — | — | 0 | 0 | 1 | 1 |
| | F11 | Best | −0.974565 | −0.974565 | −0.974565 | −0.974565 | −0.974565 | −0.974565 | | Mean | −0.974565 | −0.974565 | −0.974565 | −0.974255 | −0.974565 | −0.961576 | | Std | 1.11E − 16 | 1.56E − 15 | 1.11E − 16 | 2.12E − 03 | 1.11E − 16 | 1.27E − 02 | | t-test | — | — | 0 | 0 | 0 | 1 | | -test | — | — | 0 | 1 | 0 | 1 |
| | F12 | Best | −1.000000 | −0.999892 | −1.000000 | −1.000000 | −1.000000 | −1.000000 | | Mean | −1.000000 | −0.999821 | −1.000000 | −1.000000 | −−1.000000 | −0.999999 | | Std | 0.00E + 00 | 9.54E − 06 | 4.01E − 08 | 1.40E − 08 | 0.00E + 00 | 3.22E − 06 | | t-test | — | — | 1 | 0 | 0 | 1 | | -test | — | — | 1 | 0 | 0 | 1 |
| | F13 | Best | 5850.383000 | 5850.438514 | 5850.961000 | 5850.522000 | 6090.693000 | 5903.295000 | | Mean | 5974.989830 | 5908.944814 | 6010.429390 | 5980.964330 | 6104.016650 | 6347.670080 | | Std | 1.08E + 02 | 1.01E + 02 | 1.11E + 02 | 1.21E + 02 | 4.94E + 01 | 2.92E + 02 | | t-test | — | — | 1 | 0 | 1 | 1 | | -test | — | — | 1 | 0 | 1 | 1 |
| | F14 | Best | −75.134170 | −75.134137 | −75.132390 | −75.133670 | −75.133990 | −75.131530 | | Mean | −75.134170 | −75.134137 | −74.880659 | −74.919266 | −74.958547 | −72.689203 | | Std | 2.84E − 14 | 1.11E − 07 | 8.38E − 02 | 1.11E − 01 | 1.37E − 01 | 2.65E + 00 | | t-test | — | — | 1 | 1 | 1 | 1 | | -test | — | — | 1 | 1 | 1 | 1 |
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The best numbers are given in bold, and the lower values of results indicate better optimization ability.
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