Table 5 Performance analysis on multimodal fixed-dimension benchmark test functions.
From: Chameleon swarm algorithm with Morlet wavelet mutation for superior optimization performance
F. No. | F25 | F26 | F27 | ||||||
|---|---|---|---|---|---|---|---|---|---|
Metrics | Median | Mean | Std. dev. | Median | Mean | Std. dev. | Median | Mean | Std. dev. |
Proposed | 2.11E-34 | 2.11E-32 | 5.94E-32 | -195.62903 | -195.62903 | 3.41E-09 | -2.0218068 | -2.0218068 | 0.159154704 |
CSA | 3.36E-63 | 2.24E-62 | 5.60E-62 | -195.629 | -195.629 | 5.78E-14 | -2.02181 | -2.02181 | 1.36E-15 |
ABC | 1.29E-13 | 3.03E-13 | 3.53E-13 | -195.629 | -195.629 | 7.83E-10 | -2.02181 | -2.02181 | 9.40E-16 |
ACO | 0 | 0 | 0 | -195.629 | -195.629 | 5.78E-14 | -2.02181 | -2.02181 | 1.36E-15 |
EHO | 1.14E-06 | 1.19E-06 | 4.57E-07 | -195.617 | -195.616 | 0.007699 | -2.02181 | -2.02181 | 7.83E-06 |
EWA | 7.33E-05 | 8.33E-04 | 2.29E-03 | -195.598 | -195.539 | 0.173797 | -1.87048 | -1.82072 | 0.14998 |
GSA | 8.50E-20 | 1.08E-19 | 1.07E-19 | -195.629 | -195.629 | 5.78E-14 | -2.02114 | -2.02087 | 0.00099 |
KHA | 2.15E-11 | 4.36E-11 | 7.74E-11 | -195.629 | -195.629 | 4.67E-09 | -2.02181 | -2.02181 | 6.04E-11 |
MBO | 2.82E-12 | 8.20E-12 | 1.37E-11 | -195.629 | -195.629 | 0.000321 | -2.02166 | -2.02134 | 0.000756 |
PSO | 1.90E-157 | 1.44E-148 | 7.86E-148 | -195.629 | -195.629 | 6.14E-05 | -2.02181 | -2.02181 | 1.59E-09 |
SCA | 2.88E-158 | 6.95E-152 | 3.79E-151 | -195.629 | -195.629 | 8.44E-05 | -2.02181 | -2.02181 | 1.05E-09 |
F. No. | F28 | F29 | F30 | ||||||
|---|---|---|---|---|---|---|---|---|---|
Metrics | Median | Mean | Std. dev. | Median | Mean | Std. dev. | Median | Mean | Std. dev. |
Proposed | -106.765 | -106.765 | 2.71E-06 | -1.03163 | -1.03163 | 7.25E-10 | 0.3978874 | 0.3978874 | 2.81E-08 |
CSA | -106.765 | -106.765 | 3.82E-14 | -1.03163 | -1.03163 | 6.65E-16 | 0.397887 | 0.397887 | 0 |
ABC | -106.765 | -106.765 | 8.81E-05 | -1.03163 | -1.03163 | 1.29E-10 | 0.397887 | 0.397887 | 3.09E-11 |
ACO | -106.765 | -106.765 | 4.05E-14 | -1.03163 | -1.03163 | 6.78E-16 | 0.397887 | 0.397887 | 0 |
EHO | -106.557 | -106.524 | 0.208396 | -1.02369 | -1.01918 | 0.012386 | 0.403988 | 0.405804 | 0.007404 |
EWA | -99.6773 | -95.3087 | 11.65851 | -0.97467 | -0.88761 | 0.204595 | 0.519468 | 0.631437 | 0.299147 |
GSA | -106.765 | -106.687 | 0.333367 | -1.03163 | -1.03163 | 5.61E-16 | 0.397887 | 0.397887 | 0 |
KHA | -106.765 | -106.765 | 4.31E-09 | -1.03163 | -1.03163 | 1.59E-10 | 0.397887 | 0.397887 | 9.52E-10 |
MBO | -106.762 | -106.754 | 0.023937 | -1.03159 | -1.0314 | 0.000505 | 0.397905 | 0.397922 | 5.48E-05 |
PSO | -106.747 | -106.738 | 0.02994 | -1.03162 | -1.03161 | 1.26E-05 | 0.398202 | 0.398307 | 0.000391 |
SCA | -106.745 | -106.737 | 0.028856 | -1.03162 | -1.03162 | 1.38E-05 | 0.398185 | 0.398302 | 3.90E-04 |
F. No. | F31 | F32 | F33 | ||||||
|---|---|---|---|---|---|---|---|---|---|
Metrics | Median | Mean | Std. dev. | Median | Mean | Std. dev. | Median | Mean | Std. dev. |
Proposed | 3 | 3 | 2.81E-09 | -3.862782 | -3.862782 | 7.72E-08 | -3.322 | -3.26650591 | 0.060329422 |
CSA | 3 | 3 | 6.12E-16 | -3.86278 | -3.86278 | 2.68E-15 | -3.322 | -3.28214 | 0.057338 |
ABC | 3.00005 | 3.00021 | 0.000453 | -3.86278 | -3.86278 | 3.78E-10 | -3.32195 | -3.32194 | 3.70E-05 |
ACO | 3 | 3 | 1.25E-15 | -3.86278 | -3.86278 | 2.71E-15 | -3.32199 | -3.27443 | 0.05924 |
EHO | 3.135808 | 3.192015 | 0.173313 | -3.83639 | -3.83114 | 0.019951 | -2.83397 | -2.81893 | 0.143102 |
EWA | 20.88954 | 20.48409 | 13.54759 | -3.75671 | -3.74107 | 0.100396 | -2.49959 | -2.39237 | 0.519278 |
GSA | 3 | 3 | 2.36E-15 | -3.86278 | -3.86278 | 2.44E-15 | -3.322 | -3.322 | 1.39E-15 |
KHA | 3 | 3 | 6.79E-09 | -3.86278 | -3.86278 | 9.17E-10 | -3.322 | -3.27422 | 0.059526 |
MBO | 3.004415 | 5.721823 | 14.78531 | -3.86218 | -3.86172 | 0.001306 | -3.20289 | -3.25594 | 0.060095 |
PSO | 3 | 3 | 9.84E-06 | -3.85482 | -3.85683 | 0.003227 | -3.01043 | -3.0077 | 0.160297 |
SCA | 3 | 3 | 6.99E-06 | -3.85474 | -3.85641 | 0.003118 | -3.01438 | -3.03234 | 9.49E-02 |
F. No. | F34 | F35 | F36 | ||||||
|---|---|---|---|---|---|---|---|---|---|
Metrics | Median | Mean | Std. dev. | Median | Mean | Std. dev. | Median | Mean | Std. dev. |
Proposed | -2.0626119 | -2.062611 | 3.58E-10 | 1 | 1 | 2.26E-15 | 90.66391828 | 91.73547588 | 4.461266533 |
CSA | -2.06261 | -2.06261 | 9.03E-16 | 1 | 1 | 2.55E-15 | 180.3276 | 180.3276 | 0 |
ABC | -2.06261 | -2.06261 | 5.09E-12 | 1.000146 | 1.000167 | 0.00014 | 180.2127 | 181.39 | 1.575748 |
ACO | -2.06261 | -2.06261 | 9.03E-16 | 1 | 1 | 0 | 180.031 | 181.432 | 1.66114 |
EHO | -2.06257 | -2.06255 | 6.94E-05 | 1.001608 | 1.001698 | 0.000707 | 180.3276 | 180.3276 | 0 |
EWA | -2.06207 | -2.05512 | 0.021859 | 1.067353 | 1.177343 | 0.298134 | 180.7353 | 180.8577 | 0.48185 |
GSA | -2.06261 | -2.06261 | 9.03E-16 | 1 | 1 | 1.05E-05 | 180.3276 | 180.3277 | 0.000182 |
KHA | -2.06261 | -2.06261 | 2.64E-11 | 1.000001 | 1.000007 | 1.15E-05 | 180.9794 | 182.3246 | 1.11834 |
MBO | -2.06261 | -2.06261 | 2.31E-13 | 1 | 1 | 3.69E-07 | 180.3276 | 180.3276 | 0 |
PSO | -2.06261 | -2.06261 | 4.68E-06 | 1 | 1 | 0 | 180.3276 | 180.3276 | 0 |
SCA | -2.06261 | -2.06261 | 6.70E-06 | 1 | 1 | 0 | 180.3276 | 180.3276 | 0 |
F. No. | F37 | F38 | F39 | ||||||
|---|---|---|---|---|---|---|---|---|---|
Metrics | Median | Mean | Std. dev. | Median | Mean | Std. dev. | Median | Mean | Std. dev. |
Proposed | -4.31E + 07 | -9.8E + 07 | 1.41E + 084 | -42.944387 | -42.944387 | 6.66E-08 | 4.85E-05 | 4.85E-05 | 1.23E-14 |
CSA | -24.1568 | -24.1568 | 1.03E-14 | -42.9444 | -42.9444 | 3.61E-14 | 4.85E-05 | 4.85E-05 | 1.41E-20 |
ABC | -24.1568 | -24.1568 | 2.66E-10 | -42.9444 | -42.9444 | 2.50E-12 | 4.85E-05 | 4.85E-05 | 6.14E-17 |
ACO | -24.1568 | -24.1549 | 0.00968 | -42.9444 | -42.9444 | 3.61E-14 | 4.85E-05 | 4.85E-05 | 1.38E-20 |
EHO | -24.0661 | -24.0457 | 0.081798 | -42.8615 | -42.8367 | 0.098118 | 4.85E-05 | 4.85E-05 | 1.52E-09 |
EWA | -11.3453 | -13.1553 | 6.227318 | -42.4701 | -40.2579 | 3.145068 | 4.85E-05 | 4.86E-05 | 2.36E-07 |
GSA | -24.1568 | -24.148 | 0.043026 | -42.92 | -42.8443 | 0.155228 | 4.84E-05 | 4.84E-05 | 1.37E-20 |
KHA | -24.1568 | -24.1568 | 1.55E-09 | -42.7208 | -42.7208 | 0.227429 | 4.85E-05 | 4.85E-05 | 2.49E-16 |
MBO | -24.1568 | -24.1568 | 3.00E-11 | -42.9438 | -42.9418 | 0.004484 | 4.85E-05 | 4.85E-05 | 5.45E-18 |
PSO | -24.1464 | -24.142 | 0.013467 | -42.9438 | -42.9434 | 0.000925 | 4.85E-05 | 4.85E-05 | 1.56E-10 |
SCA | -24.1359 | -24.1308 | 0.020502 | -42.9436 | -42.9432 | 0.001581 | 4.85E-05 | 4.85E-05 | 1.91E-10 |
F. No. | F40 | F41 | F42 | ||||||
|---|---|---|---|---|---|---|---|---|---|
Metrics | Median | Mean | Std. dev. | Median | Mean | Std. dev. | Median | Mean | Std. dev. |
Proposed | -0.0004414 | -0.000428 | 0.000110794 | 0.225177603 | 0.236948535 | 0.072175916 | -1 | -1 | 2.95E-08 |
CSA | -0.08478 | -0.08478 | 2.82E-17 | 0.00118 | 0.00118 | 0 | -1 | -1 | 0 |
ABC | -0.00135 | -0.00147 | 0.000477 | 0.085066 | 0.086875 | 0.018614 | -0.2743 | -0.38552 | 0.351841 |
ACO | -0.00023 | -0.00308 | 0.015429 | 0.40729 | 0.34216 | 0.19321 | -1 | -1 | 0 |
EHO | -0.00033 | -0.00033 | 8.30E-05 | 0.299955 | 0.319105 | 0.064923 | -0.97574 | -0.96931 | 0.023361 |
EWA | -0.00018 | -0.00019 | 6.03E-05 | 0.518583 | 0.538881 | 0.165609 | -0.0821 | -0.28969 | 0.360464 |
GSA | -0.00721 | -0.00734 | 0.000887 | 0.012586 | 0.012677 | 0.001616 | -1 | -1 | 0 |
KHA | -0.00032 | -0.00033 | 6.76E-05 | 0.31831 | 0.330702 | 0.066606 | -1 | -0.93333 | 0.253707 |
MBO | -0.00147 | -0.00153 | 0.000427 | 0.071294 | 0.073001 | 0.016403 | -1 | -1 | 2.79E-12 |
PSO | -0.05622 | -0.47053 | 0.50395 | 0.379077 | 0.275878 | 0.219059 | -0.99968 | -0.99928 | 0.001 |
SCA | -0.00023 | -0.26699 | 0.44958 | 0.415254 | 0.305494 | 0.218981 | -0.99969 | -0.99958 | 0.000406 |
F. No. | F43 | F44 | F45 | ||||||
|---|---|---|---|---|---|---|---|---|---|
Metrics | Median | Mean | Std. dev. | Median | Mean | Std. dev. | Median | Mean | Std. dev. |
Proposed | 0.06447 | 0.06447 | 2.89E-10 | 6.33E-09 | 1.02E-08 | 1.11E-08 | 1.42E-07 | 2.33E-07 | 2.68E-07 |
CSA | 0.06447 | 0.06447 | 5.65E-17 | 5.19E-62 | 2.09E-61 | 3.16E-61 | 0 | 1.58E-31 | 3.21E-31 |
ABC | 0.06447 | 0.06447 | 6.35E-17 | 0.005392 | 0.0068 | 0.005398 | 6.53E-09 | 3.16E-08 | 7.23E-08 |
ACO | 0.06447 | 0.06447 | 4.82E-17 | 1.22E-05 | 1.75E-03 | 4.97E-03 | 0 | 0 | 0 |
EHO | 0.064678 | 0.064827 | 0.000361 | 2.360286 | 2.952881 | 1.908784 | 0.015626 | 0.027624 | 0.023508 |
EWA | 0.067695 | 0.070012 | 0.007023 | 1.328246 | 2.232653 | 2.055741 | 0.424127 | 0.972663 | 1.938851 |
GSA | 0.06447 | 0.06447 | 5.04E-17 | 0.001635 | 0.010816 | 0.031779 | 7.12E-20 | 1.17E-19 | 1.15E-19 |
KHA | 0.06447 | 0.06447 | 1.13E-12 | 5.27E-09 | 0.000189 | 0.001033 | 1.73E-11 | 5.40E-11 | 7.20E-11 |
MBO | 0.06447 | 0.06447 | 1.18E-12 | 0.074933 | 0.251114 | 0.424296 | 0.000758 | 0.007305 | 0.013659 |
PSO | 0.064473 | 0.064476 | 4.85E-06 | 0.000602 | 0.001295 | 0.001885 | 0.0042 | 0.006728 | 0.007226 |
SCA | 0.064475 | 0.064478 | 7.28E-06 | 0.000434 | 0.000853 | 0.001007 | 0.003451 | 0.004811 | 0.003892 |
F. No. | F46 | F47 | F48 | ||||||
|---|---|---|---|---|---|---|---|---|---|
Metrics | Median | Mean | Std. dev. | Median | Mean | Std. dev. | Median | Mean | Std. dev. |
Proposed | -19.2085 | -19.2085 | 31070.34351 | -0.99999 | -0.99999 | 5.82E-06 | -10.8723 | -10.868999 | 0.007508046 |
CSA | -19.2085 | -19.2085 | 4.57E-15 | -0.96353 | -0.96353 | 0 | -10.8723 | -10.869 | 0.007508 |
ABC | -19.2085 | -19.2085 | 3.72E-10 | -0.96353 | -0.96353 | 3.92E-13 | -10.8723 | -10.8723 | 7.06E-11 |
ACO | -19.2085 | -19.2084 | 2.74E-04 | -0.96353 | -0.96353 | 0 | -10.8723 | -10.8723 | 2.21E-09 |
EHO | -19.1904 | -19.176 | 0.035102 | -0.96348 | -0.96346 | 7.70E-05 | -10.8692 | -10.8695 | 0.00184 |
EWA | -17.0841 | -15.965 | 3.548643 | -0.95901 | -0.95425 | 0.011804 | -10.8147 | -10.7669 | 0.113016 |
GSA | -19.2085 | -19.1985 | 0.014989 | -0.96339 | -0.96329 | 0.000228 | -10.8649 | -10.8624 | 0.010089 |
KHA | -19.2085 | -19.2085 | 5.87E-10 | -0.96353 | -0.96353 | 1.08E-11 | -10.8723 | -10.8644 | 0.00987 |
MBO | -19.2084 | -19.2074 | 0.001899 | -0.96353 | -0.96353 | 2.16E-14 | -10.8723 | -10.8714 | 0.001805 |
PSO | -19.2035 | -19.2004 | 0.008389 | -0.96352 | -0.96352 | 1.56E-05 | -10.8723 | -10.8723 | 2.94E-07 |
SCA | -19.2031 | -19.2009 | 0.007262 | -0.96352 | -0.96352 | 2.07E-05 | 10.8723 | -10.8723 | 3.92E-07 |
F. No. | F49 | F50 | F51 | ||||||
|---|---|---|---|---|---|---|---|---|---|
Metrics | Median | Mean | Std. dev. | Median | Mean | Std. dev. | Median | Mean | Std. dev. |
Proposed | -186.731 | -186.731 | 9.47E-05 | -10.5364 | -10.2783333 | 1.411185639 | 1.97E-35 | 1.41E-34 | 3.19E-34 |
CSA | -186.731 | -186.731 | 3.81E-14 | -10.5364 | -9.02633 | 2.579842 | 2.29E-64 | 8.22E-64 | 1.82E-63 |
ABC | -186.731 | -186.731 | 6.01E-05 | -10.5305 | -10.5247 | 0.010206 | 1.78E-12 | 1.06E-11 | 3.48E-11 |
ACO | -186.652 | -186.561 | 0.189325 | -10.5364 | -9.56257 | 2.56129 | 3.4e-315 | 2.4e-311 | 1.4e-310 |
EHO | -186.201 | -186.085 | 0.478853 | -4.95503 | -5.3281- | 1.17823 | 4.77E-08 | 4.94E-08 | 2.27E-08 |
EWA | -163.845 | -152.86 | 32.1348 | -2.26778 | -2.37761 | 1.178693 | 1.55E-06 | 3.40E-05 | 9.46E-05 |
GSA | -185.427 | -185.171 | 1.287655 | -10.5364 | -10.5364 | 1.86E-15 | 2.92E-21 | 4.85E-21 | 5.40E-21 |
KHA | -186.731 | -186.731 | 7.49E-07 | -10.5364 | -7.78394 | 3.709944 | 1.78E-12 | 2.54E-12 | 2.93E-12 |
MBO | -186.729 | -186.718 | 0.020366 | -2.87114 | -4.47229 | 2.898341 | 3.01E-13 | 1.81E-12 | 3.85E-12 |
PSO | -186.647 | -186.592 | 0.137766 | -5.01782 | -5.17974 | 1.641081 | 1.63E-155 | 4.87E-145 | 2.66E-144 |
SCA | -186.638 | -186.513 | 0.274842 | -4.95368 | -4.99818 | 0.417868 | 1.94E-154 | 2.35E-146 | 9.10E-146 |
