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Table 4 Statistical comparisons of proposed Vs other algorithms for UBFs

From: An advanced hybrid meta-heuristic algorithm for solving small- and large-scale engineering design optimization problems

Vs Criteria Algorithm
Traditional algorithms DE variants PSO variants Hybrid variants Proposed algorithms
EO HHO JADE SHADE HEPSO RPSOLF PSOSCALF FAPSO aPSO haDEPSO
aDE Better 21 15 20 13 21 21 18 14 15 0
  Equal 2 8 3 9 2 2 5 9 8 16
  Worst 0 0 0 1 0 0 0 0 0 7
  R+ 313 416 345 355 329 465 323 377 342 315
  R 152 49 120 130 136 79 142 88 123 150
  p value 5.2e−10 5.6e−10 8.2e−10 5.8e−10 6.2e−10 6.9e−07 4.3e−09 6.2e−11 5.1e−10 6.9e−07
  t test a a a a+ a a a a+ a+ a+
  Decision + + + + + + +
Vs   EO HHO JADE SHADE HEPSO RPSOLF PSOSCALF FAPSO aDE haDEPSO
aPSO Better 21 11 20 13 20 19 19 15 0 0
  Equal 2 4 2 9 2 2 3 4 7 8
  Worst 0 8 1 1 1 2 1 4 16 15
  R+ 387 293 335 305 312 323 382 300 350 400
  R 78 172 130 160 153 142 83 165 115 65
  p value 5.3e−10 5.1e−09 6.2e−10 4.6e−08 5.7e−10 5.1e−09 5.6e−10 5.8e−10 6.2e−09 5.3e−10
  t test a a a a+ a a+ a+ a+ a a+
  Decision + + + + + + +
Vs   EO HHO JADE SHADE HEPSO RPSOLF PSOSCALF FAPSO aDE aPSO
haDEPSO Better 0 14 20 13 20 20 15 14 8 15
  Equal 6 7 3 10 3 3 8 9 15 8
  Worst 17 2 0 0 0 0 0 0 0 0
  R+ 294 321 329 367 330 313 377 293 323 304
  R 171 144 136 98 135 152 88 172 142 161
  p value 5.1e−10 6.2e−10 4.6e−08 5.7e−10 5.1e−07 5.1e−10 5.3e−08 6.2e−09 4.6e−10 5.7e−07
  t test a a a a+ a a+ a+ a a+ a
  Decision + + + + + + +