A Novel Discrete Global-Best Harmony Search Algorithm for Solving 0-1 Knapsack Problems

Table 4

Comparison among three algorithms on solving 0-1 knapsack problems with small or median sizes.

No.	Dim.	maxFEs	Approach	Best	Worst	Median	Mean	Std.	SR
Kp1	10	1𝑒3	GHS	295	293	295	294.9	0.3136	48/50
			NGHS	295	295	295	295	0	50/50
			DGHS	295	295	295	295	0	50/50
Kp2	20	1𝑒3	GHS	1024	1018	1024	1023.7	1.1876	48/50
			NGHS	1024	995	1024	1018.6	8.0585	28/50
			DGHS	1024	1024	1024	1024	0	50/50
Kp3	4	1𝑒3	GHS	35	35	35	35	0	50/50
			NGHS	35	35	35	35	0	50/50
			DGHS	35	35	35	35	0	50/50
Kp4	4	1𝑒3	GHS	23	23	23	23	0	50/50
			NGHS	23	23	23	23	0	50/50
			DGHS	23	23	23	23	0	50/50
Kp5	15	1𝑒3	GHS	481.0694	466.3380	481.0694	479.8091	3.3263	42/50
			NGHS	481.0694	437.9345	481.0694	479.1293	6.5594	41/50
			DGHS	481.0694	481.0694	481.0694	481.0694	0	50/50
Kp6	10	1𝑒3	GHS	52	52	52	52	0	50/50
			NGHS	52	51	52	51.9400	0.2399	47/50
			DGHS	52	52	52	52	0	50/50
Kp7	7	1𝑒3	GHS	107	105	107	106.8	0.6060	45/50
			NGHS	107	107	107	107	0	50/50
			DGHS	107	107	107	107	0	50/50
Kp8	23	1𝑒3	GHS	9766	9744	9756.5	9756.2	5.3816	0/50
			NGHS	9767	9760	9765	9764.3	2.2950	15/50
			DGHS	9767	9767	9767	9767	0	50/50
Kp9	5	1𝑒3	GHS	130	130	130	130	0	50/50
			NGHS	130	130	130	130	0	50/50
			DGHS	130	130	130	130	0	50/50
Kp10	20	1𝑒3	GHS	1025	1019	1025	1024.1	2.1030	43/50
			NGHS	1025	979	1025	1020.8	8.2048	31/50
			DGHS	1025	1025	1025	1025	0	50/50
Kp11	50	1𝑒3	GHS	2985	2837	2935	2932.5	35.9802	0/50
			NGHS	3087	2943	3002	3006.5	29.2779	0/50
			DGHS	3119	3114	3119	3118.7	0.9355	41/50
		5𝑒3	GHS	3073	2955	3022	3018.9	28.1109	0/50
			NGHS	3104	3039	3077	3076.7	16.0329	0/50
			DGHS	3119	3119	3119	3119	0	50/50
Kp12	100	1𝑒3	GHS	24551	22867	23630.5	23648.6	382.0742	0/50
			NGHS	25817	24209	24974	25028	361.3838	0/50
			DGHS	26559	26534	26541	26544	10.6246	16/50
		5𝑒3	GHS	25448	24343	24891	24881	262.5590	0/50
			NGHS	26418	25686	26102	26102	165.5934	0/50
			DGHS	26559	26536	26559	26553	8.6175	33/50
		1𝑒4	GHS	26079	24806	25296	25304	219.1038	0/50
			NGHS	26428	25896	26282	26264	105.0596	0/50
			DGHS	26559	26547	26559	26556	5.0214	39/50
		2𝑒4	GHS	26091	25151	25685	25683	223.8487	0/50
			NGHS	26489	26242	26366	26367	59.8389	0/50
			DGHS	26559	26547	26559	26558	3.2886	46/50
		3𝑒4	GHS	26172	25379	25816	25833	166.5229	0/50
			NGHS	26559	26265	26424	26420	63.9882	1/50
			DGHS	26559	26547	26559	26558.5	2.3754	48/50
		4𝑒4	GHS	26326	25643	25947	25954	142.3878	0/50
			NGHS	26547	26354	26441	26445	46.2120	0/50
			DGHS	26559	26559	26559	26559	0	50/50