A Global Multilevel Thresholding Using Differential Evolution Approach

Table 3

The average of mean number of generation (NG_AM) and ranks of the methods.

No.; maxGen.		FODPSO	DPSO	PSO	ABC	Rank-DE	DE	O(rand)R-DE	O(0.9)R-DE	O(0.8)R-DE	O(0.7)R-DE	O(0.6)R-DE	O(0.5)R-DE	O(0.4)R-DE	O(0.3)R-DE	O(0.2)R-DE	O(0.1)R-DE	O(0.0)R-DE
𝑛=2; 𝐺=50	NGAM	18.337	15.713	13.218	13.202	10.538	14.713	10.117	6.394	6.903	7.636	8.208	9.147	9.261	9.901	10.709	11.631	20.850
	Rank	16	15	13	12	9	14	8	1	2	3	4	5	6	7	10	11	17
𝑛=3; 𝐺=100	NGAM	35.200	36.210	27.479	33.210	19.488	29.049	18.958	10.492	12.296	13.587	14.807	16.969	17.107	18.100	19.546	21.749	44.192
	Rank	15	16	12	14	9	13	8	1	2	3	4	5	6	7	10	11	17
𝑛=4; 𝐺=150	NGAM	45.391	58.683	49.596	63.251	31.060	48.130	29.595	14.733	18.526	20.885	22.815	26.632	26.456	28.058	30.175	33.499	72.100
	Rank	12	15	14	16	10	13	8	1	2	3	4	6	5	7	9	11	17
𝑛=5; 𝐺=200	NGAM	55.664	81.877	87.441	108.131	44.157	69.088	41.283	19.508	24.524	28.097	30.963	36.935	36.748	38.647	41.455	45.631	100.693
	Rank	12	14	15	17	10	13	8	1	2	3	4	6	5	7	9	11	16
𝑛=6; 𝐺=300	NGAM	NA(2)	100.664	141.937	157.328	61.935	99.700	56.405	24.623	32.687	38.167	42.608	51.003	50.281	52.089	55.729	61.748	138.716
	Rank	17	13	15	16	11	12	9	1	2	3	4	6	5	7	8	10	14
𝑛=7; 𝐺=400	NGAM	NA(1)	NA(1)	192.267	236.928	86.938	142.096	75.340	29.763	41.691	49.408	56.193	67.619	67.063	69.696	74.389	83.326	184.371
	Rank	17	16	14	15	11	12	9	1	2	3	4	6	5	7	8	10	13
𝑛=8; 𝐺=600	NGAM	NA(7)	NA(6)	NA(2)	NA(1)	117.092	198.986	100.944	33.967	51.573	62.263	74.523	91.836	89.666	95.198	102.552	115.583	244.880
	Rank	17	16	15	14	11	12	8	1	2	3	4	6	5	7	9	10	13
𝑛=9; 𝐺=800	NGAM	NA(11)	NA(13)	NA(12)	NA(3)	151.004	264.253	125.299	41.228	63.742	79.432	90.201	113.530	110.416	114.397	122.555	137.538	299.492
	Rank	17	16	15	14	11	12	9	1	2	3	4	6	5	7	8	10	13
𝑛=10; 𝐺=1000	NGAM	NA(11)	NA(16)	NA(16)	NA(7)	NA(1)	321.373	147.770	NA(3)	73.564	91.121	105.020	132.968	128.999	132.691	141.825	157.997	356.546
	Rank	17	16	15	14	12	10	8	13	1	2	3	6	4	5	7	9	11
𝑛=11; 𝐺=1500	NGAM	NA(16)	NA(17)	NA(19)	NA(9)	NA(1)	405.090	185.020	NA(3)	NA(2)	NA(2)	127.135	162.822	157.184	160.123	175.152	198.522	434.877
	Rank	17	16	15	14	12	8	6	13	10	10	1	4	2	3	5	7	9
𝑛=12; 𝐺=2000	NGAM	NA(18)	NA(20)	NA(20)	NA(9)	278.743	535.542	229.965	NA(4)	NA(5)	135.266	160.047	205.266	197.386	203.814	222.094	251.535	574.104
	Rank	17	16	15	14	12	8	6	13	11	10	1	4	2	3	5	7	9
𝑛=13; 𝐺=3000	NGAM	NA(20)	NA(19)	NA(20)	NA(14)	NA(3)	NA(3)	275.860	NA(12)	NA(5)	NA(1)	NA(1)	NA(1)	NA(1)	261.522	278.082	316.468	726.521
	Rank	17	16	15	14	12	9	2	13	11	10	6	6	6	1	3	4	5
𝑛=14; 𝐺=4000	NGAM	NA(20)	NA(20)	NA(20)	NA(14)	NA(4)	NA(4)	330.194	NA(11)	NA(8)	NA(4)	NA(1)	NA(2)	296.414	NA(1)	331.626	385.951	889.711
	Rank	17	16	15	14	12	9	1	13	11	10	7	8	6	5	2	3	4
𝑛=15; 𝐺=5000	NGAM	NA(20)	NA(20)	NA(20)	NA(19)	NA(13)	NA(5)	399.228	NA(11)	NA(10)	NA(8)	NA(6)	363.506	362.665	383.788	417.958	481.830	1086.001
	Rank	17	16	15	14	13	8	1	12	11	10	9	7	6	5	2	3	4
𝑛=16; 𝐺=6000	NGAM	NA(20)	NA(20)	NA(20)	NA(18)	NA(10)	NA(8)	NA(4)	NA(18)	NA(11)	NA(9)	NA(5)	NA(1)	NA(2)	447.570	491.772	552.856	1374.438
	Rank	17	16	15	14	12	9	4	13	11	10	8	6	7	5	1	2	3
Avg for; 𝑛=2 to 16	𝑛max,; NA(𝑥); NGAM	5,; NA(146),; 38.648	6,; NA(152),; 58.629	7,; NA(149),; 85.323	7,; NA(94),; 102.008	9,; NA(32),; 88.995	12,; NA(20),; 193.456	15,; NA(4),; 144.713	9,; NA(62),; 22.589	10,; NA(41),; 36.167	10,; NA(24),; 52.586	12,; NA(13),; 66.593	12,; NA(4),; 106.519	12,; NA(3),; 119.204	13,; NA(1),; 143.971	16,; NA(0),; 167.708	16,; NA(0),; 190.391	16,; NA(0),; 436.499
	Rank	17	16	15	14	12	9	4	13	11	10	8	7	6	5	1	2	3