Table 9 Performance of algorithms on the applied engineering problems*.
Optimizers | Best | Mean | Worst | Standard deviation |
|---|---|---|---|---|
(a) Three-bar truss problem | ||||
LF-FA51 | 282.84 | 283.20 | NA | 1.1 |
SCA52 | 263.89584 | 263.90336 | 263.96976 | 1.3E-02 |
mGWO53 | 263.8961 | NA | NA | NA |
SFO10 | 263.89592 | NA | NA | NA |
FA51 | 282.84 | 287.84 | NA | 4.94 |
iLSHADε54 | 2.64E + 02 | 2.64E + 02 | 2.65E + 02 | 4.47E-01 |
DE-QL55 | 2.638958E + 02 | 2.638958E + 02 | 2.638958E + 02 | 1.640928E-14 |
VMCH56 | 2.64E + 02 | 2.64E + 02 | 2.64E + 02 | 1.16E-14 |
IUDE54 | 2.64E + 02 | 2.64E + 02 | 2.64E + 02 | 0.00E + 00 |
εMAgES54 | 2.64E + 02 | 2.64E + 02 | 2.64E + 02 | 0.00E + 00 |
IVYA50 | 263.89584 | 263.90581 | 263.9460 | 0.0126 |
HSI-MA | 263.89585 | 263.89591 | 263.8960 | 3.5962E-05 |
(b) Pressure vessel optimization problem | ||||
HAIS-GA57 | 6832.584 | 7187.314 | 8012.615 | 276 |
DHOA58 | 6103.842 | NA | NA | NA |
EO59 | 6059.7143 | 6668.114 | 7544.4925 | 566.24 |
CPSO60 | 6061.0777 | 6147.1332 | 6363.8041 | 86.4545 |
RFO61 | 6113.3195 | NA | NA | NA |
NHAIS-GA62 | 6061.1229 | 6743.0848 | 7368.0602 | 457.99 |
UPSO63 | 6154.70 | 8016.37 | 9387.77 | 745.869 |
MMLA64 | 6059.71433 | 6347.730290 | 6891.504402 | 188.3245 |
DE-QL55 | 8.077438E + 03 | 1.085138E + 04 | 1.355810E + 04 | 1.459232E + 03 |
VMCH56 | 6.07E + 03 | 6.06E + 03 | 6.37E + 03 | 6.23E + 01 |
IVYA50 | 6059.7143 | 6286.8871 | 7544.4925 | 4.35E + 02 |
HSI-MA | 6013.5247 | 6046.7688 | 6069.18038 | 2.02E + 01 |
(c) Tension/compression spring design | ||||
DDAO65 | 0.0129065 | 0.0151829 | 0.0173199 | 1.26E-03 |
mGWO53 | 0.012668 | NA | NA | NA |
UPSO63 | 0.01312 | 0.02294 | NA | 7.20E-03 |
G-QPSO43 | 0.012665 | 0.013524 | 0.017759 | 1.268E-03 |
MFO66 | 0.012753902 | 0.014023657 | 0.017236590 | 0.001390 |
GCHHO67 | 0.0126653 | NA | NA | NA |
PFA68 | 0.0126653 | NA | NA | NA |
HGA69 | 0.012668 | 0.013481 | 0.016155 | NA |
COOT70 | 0.0126653 | NA | NA | NA |
MVO66 | 0.012816930 | 0.014464372 | 0.017839737 | 0.001622 |
(l + λ)-ES71 | 0.012689 | 0.013165 | NA | 3.9E-04 |
INFO72 | 0.012666 | NA | NA | NA |
IVYA50 | 0.0126653 | 0.0134604 | 0.0159532 | 3.62E-04 |
HSI-MA | 0.0126692 | 0.0126864 | 0.0127130 | 1.03E-05 |
(d) Piston lever optimal design | ||||
ISA73 | 8.4 | 226.5 | 610.6 | 111.2 |
HPSO-Q48 | 129 | 151 | 168 | 13.4 |
DE48 | 159 | 187 | 199 | 14.2 |
PSO48 | 122 | 166 | 294 | 51.7 |
IVYA50 | 8.41269832 | 145.6892 | 286.2716 | 125.37 |
HSI-MA | 8.41269832 | 30.0327 | 54.1626 | 8.41 |
(e) Tubular column design | ||||
LS-LF-FA51 | 26.50 | 26.58 | NA | 0.19 |
AD-IFA51 | 26.50 | 26.54 | NA | 0.07 |
DBB-BC49 | 26.49954 | 26.50117 | NA | 2.0E-03 |
LF-FA51 | 26.50 | 27.46 | NA | 1.36 |
ISA73 | 26.531 | 26.531 | 26.532 | 0.00017 |
FA51 | 26.52 | 28.74 | NA | 2.08 |
IVYA50 | 26.499497 | 26.499617 | 26.502314 | 1.45E-04 |
HSI-MA | 19.597955 | 19.602311 | 19.607113 | 2.50E-03 |
