A Review of Surrogate Assisted Multiobjective Evolutionary Algorithms

Table 2

Summary of features of the reviewed works.

Reference	Year	CLS	Op		MC	AM	MOEA	ENG	SYNT
Choi et al. [14]	2004	NEC	✕	GM	✕	KRG	NSGA-II	✓ (17, 2)	✕
Lian and Liou [16]	2005	NEC	✕	GM	✕	PRS	GA	✓ (8, 2)	✕
Gonzalez et al. [18]	2006	NEC	✕	GM	✕	KRG	HAPEA	✓ (53, 2)	✕
Goel et al. [20]	2007	NEC	✕	GM	✕	PRS	NSGA-II	✓ (4, 4)	✕
Liao et al. [21]	2008	NEC	✕	GM	✕	PRS	NSGA-II	✓ (5, 3)	✕
Husain and Kim [22]	2010	NEC	✕	GM		KRG	NSGA-II	✓ (3, 2)	✕
Nain and Deb [34]	2002	FEC	✕	GM	✕	ANN	NSGA-II	✕	✓ (39, 2)
D’Angelo and Minisci [35]	2005	FEC	✕	GM	✕	KRG	MOPED	✓ (5, 2)	✕
Voutchkov and Keane [37]	2006	FEC	✕	GM		KRG	NSGA-II	✕	✓ (10, 2)
Isaacs et al. [38]	2007	FEC	✕	LM	✕	RBF	NSGA-II	✕	✓ (10, 2)
Todoroki and Sekishiro [39]	2008	FEC	✕	GM	✕	KRG	MOGA	✓ (7, 2)	✕
Liu et al. [41]	2008	FEC	✕	LM	✕	PRS	MOGA	✓ (3, 2)	✓ (3, 2)
Fonseca et al. [42]	2010	FEC	✕	GM	✕	FIT^1	NSGA-II	✕	✓ (30, 3)
Zapotecas Martínez and Coello Coello [43]	2013	FEC	✕	GM	✕	RBF	MOEA/D	✓ (12, 2)	✓ (30, 2)
Stander [45]	2013	FEC	✕	GM	✕	RBF	NSGA-II	✓ (7, 2)	✓ (30, 2)
Gaspar-Cunha and Vieira [46]	2005	AEC	✕	GM	✕	ANN	GA	✓ (4, 2)	✓ (30, 2)
Sreekanth and Datta [47]	2010	AEC	✕	GM		GP	NSGA-II	✓ (33, 2)	✕
Rosales-Perez et al. [48]	2013	AEC	✕	GM	✕	SVM	GA	✕	✓ (30, 2)
Gaspar-Cunha et al. [46, 51]	2005	IFR	✕	GM	✕	ANN	GA	✓ (4, 2)	✓ (30, 2)
Chafekar et al. [49]	2005	IFR	✓	GM	✕	PRS	OEGADO	✓ (6, 2)	✓ (30, 3)
Emmerich et al. [52]	2006	IFR	✓	GM	✕	KRG	NSGA-II	✓ (5, 3)	✓ (10, 2)
Knowles [53]	2006	IFR	✓	GM	✕	KRG	EGO	✕	✓ (10, 3)
Adra et al. [55]	2007	IFR	✓	GM	✕	ANN	NSGA-II, SPEA2	✕	✓ (30, 2)
Georgopoulou and Giannakoglou [56]	2009	IFR	✓	LM	✕	RBF	SPEA2	✓ (13, 2) (20, 2)	✓ (30, 2)
Loshchilov et al. [57]	2010	IFR	✓	GM	✕	CUST^2	NSGA-II, MO-CMA-ES	✕	✓ (30, 2)
Zhang et al. [58]	2010	IFR	✓	GM	✕	KRG	MOEA/D	✕	✓ (8, 2) (6, 3)
Zapotecas Martínez and Coello Coello [59, 60]	2010	IFR	✓	GM	✕	SVM	DE	✕	✓ (30, 2)
Arias-Montaño et al. [61]	2012	IFR	✓	GM	✕	RBF^3	MODE-LD+SS	✓ (12, 3)	✕
Pilát and Neruda [63, 68]	2011	IFR	✓	LM		PRS	NSGA-II, -IBEA	✕	✓ (15, 2)
Pilát and Neruda [64, 65]	2012	IFR	✓	LM		PRS, SVR	SBMO-ES	✕	✓ (30, 2)
Pilát and Neruda [66]	2013	IFR	✓	LM		PRS, SVM, ANN	NSGA-II, -IBEA	✕	✓ (30, 2) (20, 15)
Bittner and Hahn [67]	2013	IFR	✓	GM	✕	KRG	PSO	✓ (11, 3)	✓ (10, 2)

CLS: classification. Op: the proposal can be incorporated as an independent operator.
: local or global surrogate model. AM: adopted surrogate model approach.
MC: surrogate model comparison. ENG/SYNT: engineering or synthetic problems.
Accuracy. The Suitability of the surrogate model technique to be coupled into MOEA.
Fitness inheritance and fitness imitation.
Customized metamodeling technique.
RBF with multiple kernels.