Large-Scale Portfolio Optimization Using Multiobjective Evolutionary Algorithms and Preselection Methods

Table 1

The numerical results of various algorithms (FEs = 20000).

⁢Algorithms	⁢Methods	⁢S-1			⁢S-2
		Best risk	Best return	Best compromise solution	Best risk	Best return	Best compromise solution
⁢NSGAII	1000 stocks
	Risk
	Return	1.0007	1.0021	1.0014	1.0002	1.0113	1.0098
	P-1 (200 stocks)
	Risk
	Return	1.0017	1.0082	1.0061	1.0010	1.0113	1.0091
	P-2 (200 stocks)
	Risk
	Return	1.0022	1.0087	1.0063	1.0011	1.0113	1.0095
⁢MODE-SS	1000 stocks
	Risk
	Return	1.0012	1.0037	1.0031	1.0004	1.0113	1.0093
	P-1 (200 stocks)
	Risk
	Return	1.0018	1.0085	1.0071	1.0011	1.0113	1.0094
	P-2 (200 stocks)
	Risk
	Return	1.0024	1.0091	1.0077	1.0006	1.0113	1.0092
⁢MODE-NDS	1000 stocks
	Risk
	Return	1.0016	1.0067	1.0060	1.0004	1.0113	1.0092
	P-1 (200 stocks)
	Risk
	Return	1.0017	1.0082	1.0060	1.0013	1.0113	1.0093
	P-2 (200 stocks)
	Risk
	Return	1.0018	1.0081	1.0062	1.0011	1.0113	1.0094
⁢MOCLPSO	1000 stocks
	Risk
	Return	1.0016	1.0059	1.0042	1.0010	1.0113	1.0096
	P-1 (200 stocks)
	Risk
	Return	1.0025	1.0071	1.0059	1.0003	1.0113	1.0096
	P-2 (200 stocks)
	Risk
	Return	1.0025	1.0070	1.0060	1.0009	1.0113	1.0089
⁢NMOEA/D	1000 stocks
	Risk
	Return	1.0012	1.0098	1.0075	1.0017	1.0113	1.0093
	P-1 (200 stocks)
	Risk
	Return	1.0018	1.0105	1.0087	1.0022	1.0113	1.0095
	P-2 (200 stocks)
	Risk
	Return	1.0015	1.0106	1.0089	1.0010	1.0113	1.0094