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Table 6 Comparison of the best solution obtained from various studies for optimization problems

From: Hybrid inner-outer algorithm for solving real-world mechanical optimization problems

   Present work TSA GA-PSO-SQP CI GAMS ABC
I-O array (TD) (5%, 4%, 1.875%)
Speed reducer X1= 3.6 3.49631 NA 3.5 NA NA 3.499
X2= 0.7 0.7 0.7 0.7
X3= 17 17 17 17
X4= 7.3 7.3 7.3 7.3
X5= 8.05 7.79862 7.7153 7.8
X6= 3.4 3.3311 3.35 3.3502
X7= 5.5 5.28843 5.286 5.2878
F(x)= 3195.21 2991.1355 2994.44355 2997.05841
Pressure vessel X1= 6.1875 5.56875 NA 0.880944 0.81249 NA 0.8125
X2= 0.0625 0.0625 0.433702 0.4375 0.4375
X3= 105 99.75 45.634248 42.098446 42.098446
X4= 10 10 137.24998 176.636 176.63659
F(x)= 86236.6608 66916.8895 5798.7989 6059.7144 6059.71434
Gear train X1= 60 57 NG NA NA NA 49
X2= 12 13 NG 16
X3= 36 37 NG 19
X4= 60 58 NG 43
F(x)= 0.00058949 0. 147E-5 3.0389E−12 0
Disc brake design X1= 55   NA NA NA 55 NA
X2= 75   75
X3= 1000   1561.39914
X4= 2   2
F(x)= 0.1274   0.1274