Mathematical Problems in Engineering

Research Article

Adaptive Randomness: A New Population Initialization Method

Table 1

Comparison of convergence speed (NFC) and success rate (SR) for DE with random population initialization (DE_r), with opposition-based population initialization (DE_o), with generalized opposition-based population initialization (DE_go), and with AR-based population initialization (DE_ar).


		DE_r		DE_o		DE_go		DE_ar		ARE
		NFC	SR	NFC	SR	NFC	SR	NFC	SR

	30	49725	1	49670	1	49510	1	49505	1	1.0044	1.0033	1.0001
	30	55650	1	55735	1	55620	1	55530	1	1.0022	1.0037	1.0016
	20	121666	1	120482	1	121136	1	120314	1	1.0112	1.0014	1.0068
	30	327670	1	327185	1	324500	1	326530	1	1.0035	1.0020	0.9938
	10	230525	0.95	254545	0.95	237175	0.95	227935	0.95	1.0114	1.1167	1.0405
	30	63895	0.98	62490	0.96	62148	0.96	64725	1	0.9872	0.9655	0.9602
	30	11751	1	11645	1	11698	1	11621	1	1.0112	1.0021	1.0066
	30	97624	1	97816	1	97437	1	97411	1	1.0022	1.0042	1.0003
	2	3180	1	3150	1	3193	1	3137	1	1.0137	1.0041	1.0179
	4	13272	1	13470	1	13544	1	13255	1	1.0013	1.0162	1.0218
	2	15250	1	15488	1	15380	1	15220	1	1.0020	1.0176	1.0105
	2	4325	1	4475	1	4410	1	4215	1	1.0261	1.0574	1.0463
	30	8164	1	8157	1	8153	1	8129	1	1.0043	1.0034	1.0030
	2	2681	1	2705	1	2716	1	2678	1	1.0011	1.0101	1.0142
	4	—	0	—	0	—	0	1541	0.01	—	—	—
	10	33032	0.24	53652	0.36	50060	0.32	49760	0.36	0.6638	1.0782	1.0060
	30	250184	1	250848	1	251408	1	249712	1	1.0019	1.0045	1.0068
	30	102236	1	101268	1	102068	1	101344	1	1.0088	0.9993	1.0071
	30	—	0	—	0	—	0	—	0	—	—	—
	30	22485	1	22370	1	22402	1	22331	1	1.0069	1.0017	1.0032
	30	—	0	—	0	—	0	—	0	—	—	—
	4	—	0	—	0	—	0	—	0	—	—	—
	4	—	0	—	0	—	0	—	0	—	—	—
	4	—	0	—	0	—	0	—	0	—	—	—
	4	—	0	—	0	—	0	—	0	—	—	—
	2	7980	0.97	7923	0.96	8136	0.98	8061	0.98	0.9900	0.9829	1.0093
	2	856	1	859	1	839	1	801	1	1.0687	1.0724	1.0474
	30	172487	1	172489	1	177257	1	171543	1	1.0055	1.0055	1.0333
	2	4952	1	4781	1	4924	1	4845	1	1.0221	0.9868	1.0163
	5	—	0	21	0.02	—	0	—	0	—	—	—
	5	28396	0.99	29204	1	28974	1	28903	1	0.9825	1.0104	1.0025
	2	1567	1	1558	1	1564	1	1549	1	1.0116	1.0058	1.0097
	2	6386	1	6305	1	6309	1	6230	1	1.0250	1.0120	1.0127
	2	4110	1	4083	1	4086	1	4069	1	1.0101	1.0034	1.0042

Average values	—	68488	0.997727	69504	0.997727	68879	0.997727	68087	0.997727	1.0116	1.0152	1.0138

Note. The reported average values (the last row) are calculated only on the functions where all the algorithms have the same success rate (i.e., all SRs = 1 and one SR = 0.95).