Adaptive Randomness: A New Population Initialization Method

Table 2

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
	30	Mean	8.81228  − 009	8.81301  − 009	8.79674  − 009	8.77417   − 009
		Std. Dev.	1.10323  − 009	8.84418  − 010	1.08043  − 009	8.7124  − 010
	30	Mean	9.04527  − 009	9.10281  − 009	9.06893  − 009	8.92437   − 009
		Std. Dev.	7.96893  − 010	6.70026  − 010	7.70684  − 010	7.79631  − 010
	20	Mean	9.34818  − 009	9.39706  − 009	9.38949  − 009	9.33293   − 009
		Std. Dev.	5.33216  − 010	4.83679  − 010	5.58047  − 010	5.48986  − 010
	30	Mean	9.26684  − 009	9.32035  − 009	9.3298  − 009	9.11962   − 009
		Std. Dev.	7.17271  − 010	6.50894  − 010	5.82968  − 010	7.65305  − 010
	10	Mean	0.049748	0.049748	0.049748	0.049748
		Std. Dev.	0.22248	0.22248	0.22248	0.22248
	30	Mean	0.000172542	0.00029585	0.000320462	8.80458   − 009
		Std. Dev.	0.00122635	0.00146403	0.00159228	1.20596  − 009
	30	Mean	6.24585  − 009	6.62518  − 009	6.86516  − 009	6.20522   − 009
		Std. Dev.	2.32947  − 009	2.28414  − 009	2.42006  − 009	2.35472  − 009
	30	Mean	9.3102  − 009	9.33032  − 009	9.2814  − 009	9.25572   − 009
		Std. Dev.	4.90595  − 010	5.23764  − 010	6.79597  − 010	5.84208  − 010
	2	Mean	4.46327  − 009	4.39462  − 009	4.67599  − 009	4.31941   − 009
		Std. Dev.	2.95843  − 009	3.02071  − 009	2.72012  − 009	2.98226  − 009
	4	Mean	6.27386  − 009	6.25378  − 009	6.40042  − 009	5.92566   − 009
		Std. Dev.	2.57066  − 009	2.69058  − 009	2.27469  − 009	2.58577  − 009
	2	Mean	4.72646  − 009	4.63412  − 009	4.47891  − 009	3.90594   − 009
		Std. Dev.	3.03952  − 009	2.74639  − 009	3.01052  − 009	2.94237  − 009
	2	Mean	4.65101  − 008	4.65101  − 008	4.65101  − 008	4.65101  − 008
		Std. Dev.	0	0	0	0
	30	Mean	0	0	0	0
		Std. Dev.	0	0	0	0
	2	Mean	5.04676  − 009	4.58853  − 009	4.67473  − 009	4.51194   − 009
		Std. Dev.	2.87757  − 009	3.1021  − 009	2.83989  − 009	2.96938  − 009
	4	Mean	0.00967981	0.0121192	0.0154611	0.0047311
		Std. Dev.	0.0461986	0.048523	0.0506461	0.0142838
	10	Mean	0.0320855	0.0287587	0.0247149	0.0239915
		Std. Dev.	0.023079	0.0368454	0.0268588	0.0306438
	30	Mean	9.16118  − 009	9.11199  − 009	9.30319  − 009	9.10653   − 009
		Std. Dev.	8.92376  − 010	8.15186  − 010	7.58129  − 010	8.8449  − 010
	30	Mean	9.34244  − 009	9.38564  − 009	9.42362  − 009	9.22727   − 009
		Std. Dev.	5.34739  − 010	4.09769  − 010	4.70872  − 010	7.64185  − 010
	30	Mean	1.73273	2.07072	1.40319	1.38389
		Std. Dev.	1.11967	2.26245	1.01423	1.17433
	30	Mean	0	0	0	0
		Std. Dev.	0	0	0	0
	30	Mean	0.000697643	0.000727313	0.000740714	0.000656965
		Std. Dev.	0.00020979	0.000291491	0.000261093	0.0001786
	4	Mean	0.00405371	0.00405371	0.00405371	0.00405371
		Std. Dev.	8.89894  − 019	8.44228  − 019	8.89894  − 019	8.44228  − 019