Table 34 CI–SAPF results solving truss structure and engineering design problems

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

Test examples Best mean worst Standard deviation Average number of function evaluations Average computational time \((\rm sec)\) % improvement over the best reported solution Set of parameters \(C, R\)
Test Example-1 6-Bar 4962.09 9.25E−13 2735 4.58 0 5, 0.965
4962.09
4962.09
Test Example-2
10-Bar Case 1
10-Bar Case 2
5490.60 16.65 22,654 17.87 0.0024 5, 0.965
5505.75
5534.96
5061.76 1.54 22,874 31.72 0.1099 5, 0.967
5062.22
5067.33
Test Example-3
25-Bar Case 1
25-Bar Case 2
512.81 10.16 22,588 12.21 0.6566 5, 0.955
530.88
548.61
473.47 6.80 26,796 15.95 5.3139 5, 0.955
486.74
498.06
Test Example-4 38-Bar 5891.05 2.18 69,920 40.60 0.0019* 5, 0.967
5895.38
5898.44
Test Example-5 45-Bar 14,322.29 91.77 114,525 63.17 0.1309 5, 0.97
14,455.68
14,667.10
Test Example-6 52-Bar 1894.48 11.98 101,751 52.73 0.2563 5, 0.9567
1913.97
1934.94
Test Example-7 72-Bar Case 1
72-Bar Case 2
372.41 3.25 85,500 78.61 0.3033 5, 0.955
381.53
384.63
380.18 1.69 124,080 118.52 0.0718* 5, 0.955
383.24
385.96
Test Example-8 Steeped Cantilever Beam 63,893.45 175.29 21,552 5.36 5.57e-5 5, 0.955
64,248.96
64,333.45
Test Example-9 Pressure vessel 5850.66 104.65 11,396 4.85 0.6663 5, 0.955
5960.49
6116.89
Test Example-10 Speed Reducer 2817.09 2.06 14,420 2.25 0.0165 5, 0.955
2820.32
2825.87
Test Example-11 Concrete Beam 359.21 0.08 3047 0.73 0 5, 0.955
359.24
359.47
Test Example-12 Welded Beam 1 1.55 77E−4 11,786 4.92 15.7316 5, 0.955
1.56
1.57
Test Example-13 Welded Beam 2 1.65 0.20 8740 2.08 10.0600 5, 0.955
1.88
2.08
Test Example-14 Multiple Disc Clutch 0.24 8.62E−17 671 0.23 25.0316 5, 0.955
0.24
0.24
Test Example-15 Tension Compression Spring 2.66 32E−4 3030 2.05 0 5, 0.955
2.66
2.67
Test Example-16
I Section Beam
66.26E-4 4.65E−07 7830 1.27 49.518 5, 0.955
66.26E-4
66.28E-4
Test Example-17 Cantilever Beam 1.34 1.74E−05 9581 0.91 0 5, 0.955
1.34
1.34
Test Example-18 Gear Train Design 2.7E-12 5.26E−12 8513 3.12 0 5, 0.955
3.97E-11
6.60E-10
  1. *The solution obtained using CI–SAPF is worse than other algorithms