A Hybrid Lightning Search Algorithm-Simplex Method for Global Optimization

Table 8

Best results of the spring design example by different methods.

Reference	Method	Optimum variables
		Coello [19]	GA	0.051480		0.351661	11.632201	0.0127048
Coello and Montes [20]	GA	0.051989	0.363965	10.890522	0.0126810
Montes and Coello [21]	ES	0.051643	0.355360	11.397926	0.012698
Parsopoulos and Vrahatis [22]	UPSO	NA	NA	NA	0.01312
He and Wang [23]	CPSO	0.051728	0.357644	11.244543	0.0126747
Huang et al. [24]	CDE	0.051609	0.354714	11.410831	0.0126702
Mahdavi et al. [25]	IHS	0.05115438	0.34987116	12.0764321	0.0126706
Akay and Karaboga [26]	ABC	0.051749	0.358179	11.203763	0.012665
Mirjalili [27]	MFO	0.051994457	0.36410932	10.868421862	0.0126669
Mirjalili et al. [28]	GWO	0.05169	0.356737	11.28885	0.012666
Baykasoğlu and Ozsoydan [29]	AFA	0.0516674837	0.3561976945	11.3195613646	0.0126653049
Gandomi et al. [30]	BA	0.05169	0.35673	11.2885	0.01267
Present study	LSA-SM	0.05170453	0.3570899	11.26718	0.01266524

ES: evolution strategies; UPSO: unified particle swarm optimization; CPSO: coevolutionary particle swarm optimization; CDE: coevolutionary differential evolution; IHS: improved harmony search; MFO: moth-flame optimization algorithm; AFA: adaptive firefly algorithm; NA: there is no relevant data.