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

Journal of Electrical Systems and Information Technology

Table 13 Optimum results for tension/compression spring design problem

Algorithms	Optimal values for variables			Optimal cost
Algorithms	d(\({x}_{1}\))	D(\({x}_{2}\))	N(\({x}_{3}\))	Optimal cost
GSA	0.050276	0.323680	13.525410	0.012702
CPSO	0.051728	0.357644	11.244543	0.012674
CDE	0.051609	0.354714	11.410831	0.012670
SCA	0.052160	368,159	10.648442	0.012669
EO	0.0516199100	0.355054381	11.387967	0.012666
PSOSCANMS	0.05072	0.334801	10.79431	0.012475
PSO	0.051728	0.357644	11.244543	0.0126747
HS	0.051154	0.349871	12.076432	0.0126706
DE	0.051609	0.354714	11.410831	0.0126702
AFA	5.167E−02	3.562E−01	1.132E+01	0.012624
GWO	0.05169	0.356737	11.28885	0.012666
WCA	0.0517208702	0.3579276279	11.1912042488	0.012630231
Modified DE	0.051688	0.356692	11.290483	0.012665
QPSO	0.051515	0.352529	11.538862	0.012665
SHO	0.051144	0.343751	12.0955	0.012674000
HS	0.05025	0.316351	15.23960	0.012776352
EPO	0.051087	0.342908	12.0898	0.012656987
aDE	0.05012	0.328431	11.49631	0.012552
aPSO	0.05012	0.328431	11.49631	0.012568
haDEPSO	0.05012	0.328431	11.49631	0.012475