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Table 7 Best design variables for four benchmark engineering design problems

From: Improved Differential Evolution with Shrinking Space Technique for Constrained Optimization

Engineering problems

Method

Best design variable

x best

Best function values

f best

Weld-beam design

ATMDE

0.244 368 975, 6.217 519 715, 8.291 471 390, 0.244 368 975

2.380 956 580

AATM

0.244 106 586, 6.220 903 633, 8.298 161 229,0.244 382 231

2.382 326

Spring design

ATMDE

0.356 717 739, 0.051 689 061, 11.288 965 783 04

0.012 665 232

AATM

0.359 690 411, 0.051 813 095, 11.119 252 680

0.012 668 261

Speed reducer design

ATMDE

3.50, 0.7, 17, 7.309 819 903, 7.715 173 384 44, 3.350 233 018 67, 5.286 521 228 48

2 994.473 624

AATM

3.500 016 221, 0.700 001 177, 17.000 029 883, 7.300 297 290, 7.716 049 465, 3.350 239 798, 5.286 660 476 6

2 994.516 778

Three-bar truss design

ATMDE

0.788 675 135, 0.408 248 289

263.895 843

AATM

0.788 681 755, 0.408 229 565

263.895 843