Research Article
A Multistrategy-Integrated Learning Sparrow Search Algorithm and Optimization of Engineering Problems
Table 4
Comparisons of IHSSA and other seven algorithms for 14 test functions.
| | Function | Algorithm | Avg | Std | Best | Run time |
| | F1 | WOA | 6.47271E-97 | 2.45955E-96 | 1.4869E-104 | 0.00114 | | GWO | 9.58408E-41 | 1.61375E-40 | 1.85345E-42 | 0.001135 | | PSO | 4.51174E-11 | 6.25117E-11 | 1.31715E-12 | 0.003173933 | | TLBO | 2.29067E-85 | 1.79774E-85 | 2.6797E-86 | 0.0051 | | SSA | 0 | 0 | 0 | 0.001907 | | CSSA | 0 | 0 | 0 | 0.002318533 | | LSSA | 0 | 0 | 0 | 0.002167 | | GSSA | 3.826E-123 | 1.4763E-122 | 0 | 0.003030333 | | YSSA | 0 | 0 | 0 | 0.0024253 | | IHSSA | 0 | 0 | 0 | 0.00231 |
| | F2 | WOA | 14907.66827 | 7290.613484 | 5245.501087 | 0.000753 | | GWO | 2.01843E-11 | 4.84067E-11 | 2.37886E-15 | 0.001054 | | PSO | 6.159248452 | 3.416561147 | 2.274329699 | 0.003053 | | TLBO | 1.49173E-15 | 1.26326E-15 | 1.28014E-16 | 0.005033 | | SSA | 4.9592E-290 | 0 | 0 | 0.001873 | | CSSA | 0 | 0 | 0 | 0.001958 | | LSSA | 0 | 0 | 0 | 0.002093 | | GSSA | 1.03442E-88 | 1.13315E-87 | 0 | 0.002994 | | YSSA | 0 | 0 | 0 | 0.00206 | | IHSSA | 0 | 0 | 0 | 0.001953 |
| | F3 | WOA | 34.68527033 | 29.6668357 | 4.83669E-05 | 0.000001 | | GWO | 2.5165E-10 | 2.80518E-10 | 3.92494E-11 | 0.000071 | | PSO | 0.210838877 | 0.155290345 | 0.057831908 | 0.002197 | | TLBO | 2.30203E-34 | 1.48485E-34 | 3.57945E-35 | 0.004141 | | SSA | 2.9952E-193 | 0 | 0 | 0.000924 | | CSSA | 0 | 0 | 0 | 0.00118 | | LSSA | 0 | 0 | 0 | 0.001134 | | GSSA | 4.87917E-90 | 2.20121E-89 | 0 | 0.002007 | | YSSA | 0 | 0 | 0 | 0.001297 | | IHSSA | 0 | 0 | 0 | 0.001171 |
| | F4 | WOA | 28.72457614 | 0.198079568 | 27.98805166 | 0.000752 | | GWO | 1.62822E+35 | 6.51934E+35 | 38250907192 | 0.001087 | | PSO | 3.24434E+87 | 4.65939E+86 | 2.29319E+87 | 0.002976 | | TLBO | 420.4775663 | 1327.016075 | 21.95591078 | 0.004966 | | SSA | 1.3694E-05 | 3.77399E-05 | 1.36288E-09 | 0.001724 | | CSSA | 6.06157E-06 | 1.48998E-05 | 1.03023E-08 | 0.001897 | | LSSA | 5.93493E-06 | 1.14239E-05 | 0 | 0.001974 | | GSSA | 5.11701E-07 | 5.04167E-07 | 1.6666E-14 | 0.002881 | | YSSA | 1.50157E-05 | 3.02452E-05 | 2.37868E-09 | 0.002006 | | IHSSA | 2.40169E-07 | 8.20733E-07 | 0 | 0.001887 |
| | F5 | WOA | 0 | 0 | 0 | 0.000587 | | GWO | 1.581667461 | 2.939452422 | 0 | 0.001086 | | PSO | 45.60347387 | 12.12604405 | 24.87396229 | 0.003016 | | TLBO | 6.383023506 | 4.955050004 | 0 | 0.005033 | | SSA | 0 | 0 | 0 | 0.001767 | | CSSA | 0 | 0 | 0 | 0.001891 | | LSSA | 0 | 0 | 0 | 0.001917 | | GSSA | 0 | 0 | 0 | 0.0028 | | YSSA | 0 | 0 | 0 | 0.002885 | | IHSSA | 0 | 0 | 0 | 0.00188 |
| | F6 | WOA | 5.15143E-15 | 2.16807E-15 | 8.88178E-16 | 0.000032 | | GWO | 2.6823E-14 | 3.63147E-15 | 1.86517E-14 | 0.000032 | | PSO | 0.343589201 | 0.596942294 | 1.24699E-06 | 0.002345 | | TLBO | 0.031044156 | 0.170035847 | 4.44089E-15 | 0.004333 | | SSA | 8.88178E-16 | 0 | 8.88178E-16 | 0.001045 | | CSSA | 8.88178E-16 | 0 | 8.88178E-16 | 0.001243 | | LSSA | 8.88178E-16 | 0 | 8.88178E-16 | 0.001302 | | GSSA | 8.88178E-16 | 1.00293E-31 | 8.88178E-16 | 0.002071 | | YSSA | 8.88178E-16 | 1.00293E-31 | 8.88178E-16 | 0.001365 | | IHSSA | 8.88178E-16 | 0 | 8.88178E-16 | 0.001232 |
| | F7 | WOA | 0.00420253 | 0.012960719 | 0 | 0.000702 | | GWO | 0.001780922 | 0.004128695 | 0 | 0.000986 | | PSO | 0.017048805 | 0.019184635 | 6.22012E-11 | 0.002873 | | TLBO | 0 | 0 | 0 | 0.004866 | | SSA | 0 | 0 | 0 | 0.001613 | | CSSA | 0 | 0 | 0 | 0.001893 | | LSSA | 0 | 0 | 0 | 0.001803 | | GSSA | 0 | 0 | 0 | 0.002723 | | YSSA | 0 | 0 | 0 | 0.001993 | | IHSSA | 0 | 0 | 0 | 0.001885 |
| | F8 | WOA | 749.0614488 | 1053.51792 | 0.142228645 | 0.001887 | | GWO | 5984.325616 | 512.034691 | 5075.836656 | 0.001087 | | PSO | 5822.761982 | 781.2113436 | 3040.698318 | 0.002733 | | TLBO | 5050.58229 | 1189.147899 | 3306.384094 | 0.004777 | | SSA | 3958.182107 | 712.2420957 | 2389.812363 | 0.001487 | | CSSA | 1619.35044 | 977.2374638 | 217.1401425 | 0.001995 | | LSSA | 4878.962977 | 846.4505234 | 3517.371964 | 0.001683 | | GSSA | 678.1120161 | 1382.220669 | 0.000381827 | 0.002487 | | YSSA | 2178.636278 | 2045.618662 | 0.000381827 | 0.002057 | | IHSSA | 3377.438965 | 1620.549772 | 0.000815262 | 0.001987 |
| | F9 | WOA | 1.2342E-117 | 5.3288E-117 | 2.672E-142 | 0.000885 | | GWO | 0 | 0 | 0 | 0.001102 | | PSO | 7.15959E-48 | 2.6399E-47 | 6.0523E-53 | 0.002666 | | TLBO | 6.1741E-183 | 0 | 1.5723E-188 | 0.004666 | | SSA | 0 | 0 | 0 | 0.001424 | | CSSA | 0 | 0 | 0 | 0.001911 | | LSSA | 0 | 0 | 0 | 0.001614 | | GSSA | 0 | 0 | 0 | 0.002457 | | YSSA | 0 | 0 | 0 | 0.002011 | | IHSSA | 0 | 0 | 0 | 0.001902 |
| | F10 | WOA | 0.754881452 | 1.386931349 | 0.001459345 | 0.000757 | | GWO | 0.600742635 | 1.39373905 | 2.53554E-05 | 0.000965 | | PSO | 0.000892468 | 0.000922365 | 1.42838E-06 | 0.002883 | | TLBO | 3.78444E-06 | 9.24279E-06 | 3.07036E-08 | 0.004883 | | SSA | 4.82652E-08 | 1.02745E-07 | 2.87751E-13 | 0.001633 | | CSSA | 6.06071E-08 | 1.74794E-07 | 4.9792E-14 | 0.001969 | | LSSA | 1.87914E-06 | 3.82252E-06 | 0 | 0.001777 | | GSSA | 9.6035E-07 | 1.483E-06 | 2.07901E-28 | 0.002665 | | YSSA | 5.06037E-08 | 9.41366E-08 | 2.87751E-13 | 0.002075 | | IHSSA | 1.78222E-08 | 5.32296E-08 | 3.72464E-15 | 0.001965 |
| | F11 | WOA | 6.5603E-78 | 3.17192E-77 | 9.75895E-90 | 0.00132 | | GWO | 6.77957E-66 | 2.37196E-65 | 2.19507E-70 | 0.000106 | | PSO | 1.0187E+26 | 2.21398E+25 | 4.6921E+25 | 0.002255 | | TLBO | 4.82046E-85 | 5.52867E-85 | 1.68795E-86 | 0.004233 | | SSA | 0 | 0 | 0 | 0.000977 | | CSSA | 0 | 0 | 0 | 0.001212 | | LSSA | 0 | 0 | 0 | 0.001273 | | GSSA | 0 | 0 | 0 | 0.002087 | | YSSA | 0 | 0 | 0 | 0.001338 | | IHSSA | 0 | 0 | 0 | 0.001206 |
| | F12 | WOA | 6.6988E+16 | 9.54778E+16 | 39646.29751 | 0.000265 | | GWO | 2.61392E+15 | 3.73552E+15 | 1.47252E+14 | 0.000282 | | PSO | 2.38287E+43 | 1.23114E+43 | 4.17747E+42 | 0.002377 | | TLBO | 9.02546E+14 | 4.72246E+14 | 2.97075E+14 | 0.004306 | | SSA | 0 | 0 | 0 | 0.000983 | | CSSA | 0 | 0 | 0 | 0.001293 | | LSSA | 0 | 0 | 0 | 0.001166 | | GSSA | 0 | 0 | 0 | 0.001983 | | YSSA | 0 | 0 | 0 | 0.001412 | | IHSSA | 0 | 0 | 0 | 0.001282 |
| | F13 | WOA | 0.7 | 0 | 0 | 0.001367 | | GWO | 0.8 | 2.006884702 | 0 | 0.000958 | | PSO | 1.22453E+20 | 2.91996E+19 | 5.79476E+19 | 0.003133 | | TLBO | 4.87463304 | 0.988415075 | 2.761251106 | 0.005187 | | SSA | 0 | 0 | 0 | 0.001922 | | CSSA | 0 | 0 | 0 | 0.002064 | | LSSA | 0 | 0 | 0 | 0.002097 | | GSSA | 0 | 0 | 0 | 0.002965 | | YSSA | 0 | 0 | 0 | 0.002185 | | IHSSA | 0 | 0 | 0 | 0.002057 |
| | F14 | WOA | 591670353.7 | 3240707887 | 1.967264854 | 0.000187 | | GWO | 5.22374E+34 | 1.32705E+35 | 5.04003E+32 | 0.000466 | | PSO | 1.94575E+60 | 2.11926E+59 | 1.42718E+60 | 0.002175 | | TLBO | 0.320134144 | 0.127010931 | 0.093171452 | 0.00516 | | SSA | 5.14521E-10 | 1.83095E-09 | 2.07524E-20 | 0.000983 | | CSSA | 3.47974E-10 | 7.18343E-10 | 9.49837E-14 | 0.001377 | | LSSA | 1.00461E-06 | 2.21303E-06 | 1.49976E-32 | 0.001183 | | GSSA | 1.45943E-07 | 2.58657E-07 | 7.98889E-19 | 0.002022 | | YSSA | 2.20337E-07 | 6.82432E-07 | 1.49976E-32 | 0.001485 | | IHSSA | 1.96838E-10 | 7.70225E-10 | 2.39969E-14 | 0.001365 |
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