International Journal of Aerospace Engineering

Research Article

Enhanced Hybrid Differential Evolution for Earth-Moon Low-Energy Transfer Trajectory Optimization

Table 9

Comparisons of mean error and standard deviation between DEMR and other six algorithms on CEC2005 functions.


Func.	DEMR	CMA-ES	LBBO	GL-25	SaDE	MPEDE	SHADE

F1		⁺	⁺	⁺	⁻	⁻	⁻
F2		⁺	⁺	⁺	⁺	⁺	⁺
F3		⁺	⁺	⁻	⁻	3⁺	⁺
F4		⁻	⁻	⁺	⁺	⁺	⁺
F5		⁺	⁼	2⁻	⁺	⁺	0⁺
F6		⁼	⁼	⁻	⁻	⁻	⁺
F7		⁺	⁺	⁺	⁺	⁺	⁺
F8		⁼	⁼	⁻	⁻	⁻	⁻
F9		⁻	⁺	⁻	⁻	⁻	⁻
F10		⁻	⁻	⁼	⁼	⁼	⁺
F11		⁺	⁼	⁻	⁺	⁼	⁺
F12		⁻	⁻	⁻	⁻	⁻	⁻
F13		⁻	⁻	⁻	⁻	⁻	⁼
F14		⁻	⁼	⁻	⁺	⁼	⁺
F15		⁻	⁼	⁻	⁺	⁺	⁼
F16		⁻	⁻	⁼	⁼	⁼	9⁺
F17		4⁻	⁻	⁺	⁺	⁼	⁺
F18		⁻	⁻	⁻	⁻	⁻	⁻
F19		⁻	⁻	⁻	⁻	⁻	⁻
F20		⁻	⁻	⁻	⁻	⁻	⁻
F21		⁻	⁻	⁻	⁻	⁻	⁻
F22		⁼	⁼	⁼	⁼	⁼	⁻
F23		⁻	⁻	⁻	⁻	⁼	⁼
F24		⁼	⁺	⁻	⁺	⁺	⁺
F25		⁻	⁺	⁺	⁺	⁺	⁺
⁺		6	7	6	10	8	13
⁻		15	11	16	12	10	9
⁼		4	7	3	3	7	3

indicates that the intermediate results are reported at when the algorithms obtain the global optimum; “−,” “+,” and “=”denote that the performance of this algorithm is, respectively, worse than, better than, and similar to DEMR according to the Wilcoxon rank-sum test at .