Table 38 Comparison of CI–SAPF and CI–SAPF–CBO for engineering design problems using Wilcoxon’s rank sum test at \(\alpha =0.05\)

From: Cohort intelligence with self-adaptive penalty function approach hybridized with colliding bodies optimization algorithm for discrete and mixed variable constrained problems

  Test examples Steeped Beam Pressure vessel Speed Reducer Concrete Beam Welded Beam 1 Welded Beam 2 Multiple Disc Clutch Tension Compression Spring I Section Beam Steeped Beam 2 Gear Train Design
FunctionvValues Test statistic − 1.175361821 − 0.199589743 3.740459631 − 0.51745489 5.10062677 − 0.798358973 0 0.118275403 − 6.1651054 0.554415953 − 4.124854692
P value 0.119924996 0.420900725 0.999908158 0.302419326 0.999999831 0.212331102 0.5 0.547075277 3.52181E-10 0.710352895 1.85484E−05
h-value 0 0 0 0 0 0 0 0 1 0 1
CPU time Test statistic − 3.474339973 0.088706553 − 3.903088311 6.652991439 3.577830951 − 3.223004741 0.443532763 − 0.140452041 5.056273493 − 2.542921172 1.508011393
P value 0.000256056 0.535342438 4.74865E−05 1 0.999826771 0.000634267 0.671309786 0.444151421 0.999999786 0.005496501 0.934224194
h-value 1 0 1 0 0 1 0 0 0 1 0
Function evaluations Test statistic − 1.995897432 − 0.539631528 0.842712249 − 0.591377017 6.652991439 − 6.652991439 0.443532763 − 0.384395061 3.829166184 − 1.478442542 1.700208923
P value 0.022972544 0.294725585 0.800305302 0.277133918 1 1.43597E-11 0.671309786 0.35034283 0.999935711 0.069644683 0.955454183
h-value 1 0 0 0 0 1 0 0 0 0 0