Adaptive Randomness: A New Population Initialization Method

Table 3

Comparison among the 4 DE algorithms on test problems , where “Mean” indicates the mean function error value and “Std. Dev.” stands for the standard deviation. The best results among the four algorithms are shown in boldface.

			DEr	DEo	DEgo	DEar
	4	Mean	10.1876	10.1876	10.1876	10.1876
		Std. Dev.	5.46751  − 015	5.46751  − 015	5.31347  − 015	5.31347  − 015
	4	Mean	10.4503	10.4503	10.4503	10.4503
		Std. Dev.	1.8225  − 015	1.8225  − 015	1.8225  − 015	1.8225  − 015
	4	Mean	10.6103	10.6103	10.6103	10.6103
		Std. Dev.	1.8225  − 015	1.8225  − 015	1.8225  − 015	1.8225  − 015
	2	Mean	0.03	0.04	0.02	0.02
		Std. Dev	0.171447	0.196946	0.140705	0.140705
	2	Mean	2.72741  − 009	2.94925  − 009	2.78605  − 009	2.63247   − 009
		Std. Dev.	2.76876  − 009	2.8458  − 009	2.79248  − 009	2.76724  − 009
	30	Mean	9.28689  − 009	9.28566  − 009	9.28304  − 009	9.27877   − 009
		Std. Dev.	6.31616  − 010	5.9591  − 010	6.40915  − 010	6.07695  − 010
	2	Mean	4.63641  − 009	4.15234  − 009	4.89748  − 009	3.94368   − 009
		Std. Dev.	3.24716  − 009	3.01035  − 009	2.81979  − 009	2.7603  − 009
	5	Mean	0.0452575	0.0437805	0.043716	0.0430663
		Std. Dev.	0.0220521	0.0262655	0.0233605	0.0220867
	5	Mean	0.00523817	6.93483  − 009	7.14794  − 009	6.31104   − 009
		Std. Dev.	0.0523817	2.25948  − 009	2.13661  − 009	2.19293  − 009
	2	Mean	0	0	0	0
		Std. Dev.	0	0	0	0
	2	Mean	4.70104  − 009	4.89609  − 009	4.7038  − 009	4.44655   − 009
		Std. Dev.	2.89836  − 009	2.82738  − 009	3.08112  − 009	2.68808  − 009
	2	Mean	4.75055  − 009	4.73653  − 009	4.52236  − 009	4.23427   − 009
		Std. Dev.	2.96249  − 009	3.10385  − 009	3.18058  − 009	2.89249  − 009