Table 39 Comparison of CI–SAPF and CI–SAPF–CBO for test 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 Dynamic problem (maximization) Transportation problem Multistage problem (maximization) Rosen-suzuki test problem convex programming problem (minimization) Knapsack problem (maximization) Integer Linear problem (a) (maximization) Integer Linear problem (b) (maximization) Non-convex integer problem (formulation 1) Non-convex integer problem (formulation 2) Global nonlinear mixed discrete programming Three-bar truss design problem
Function values Test statistic 0 0.229158594 − 2.217663813 -0.236550807 -0.598769229 -0.827927823 0.221766381 1.108831906 1.552364669 0 − 0.221766381
P value 0.5 0.590627173 0.013288882 0.406502644 0.274663392 0.203855688 0.587752124 0.866248648 0.939712504 0.5 0.412247876
h-value 0 0 1 0 0 0 0 0 0 0 0
CPU time Test statistic − 6.608638162 -5.056273493 6.638207013 − 6.652991439 -4.169207968 -3.636968653 1.330598288 − 3.740459631 0.029568851 − 6.652991439 3.977010438
P value 1.93936E−11 2.13764E−07 1 1.43597E−11 1.5283E−05 0.000137933 0.908339387 9.1842E-05 0.511794546 1.43597E−11 0.999965106
h-value 1 1 0 1 1 1 0 1 0 1 0
Function evaluations Test statistic − 1.463658116 − 0.206981956 6.652991439 5.632866085 0.044353276 0.421356124 3.348672357 − 0.399179486 − .076398847 − 6.431225057 6.652991439
P value 0.071643692 0.418011975 1 0.999999991 0.517688597 0.663252474 0.999594001 0.344880479 6.14557E-10 6.32898E−11 1
h-value 0 0 0 0 0 0 0 0 1 1 0