A Hybrid Harmony Search Algorithm with Distribution Estimation for Solving the 0-1 Knapsack Problem

Table 3

Comparison with harmony search algorithm variants for low dimensional instances.

Instance	Measure	HHSEDA	BHS	DBHS	NGHS	ABHS
KP1	Best	130	130	130	130	130
	Median	130	130	130	130	130
	Worst	130	130	130	130	130
	Mean	130	130	130	130	130
	Std	0	0	0	0	0
KP2	Best	107	107	107	107	107
	Median	107	107	107	107	107
	Worst	107	105	107	107	107
	Mean	107	106.93	107	107	107
	Std	0	0.3651	0	0	0
KP3	Best	23	23	23	23	23
	Median	23	23	23	23	23
	Worst	23	23	23	23	23
	Mean	23	23	23	23	23
	Std	0	0	0	0	0
KP4	Best	35	35	35	35	35
	Median	35	35	35	35	35
	Worst	35	35	35	35	35
	Mean	35	35	35	35	35
	Std	0	0	0	0	0
KP5	Best	1025	1025	1017	1025	1025
	Median	1025	1025	961	1012.50	1025
	Worst	1025	1019	913	1025	1025
	Mean	1025	1024.80	963.73	1004.80	1025
	Std	0	1.10	27.09	22.89	0
KP6	Best	52	52	52	52	52
	Median	52	52	52	52	52
	Worst	52	52	52	51	52
	Mean	52	52	52	51.93	52
	Std	0	0	0	0.2537	0
KP7	Best	295	295	295	295	295
	Median	295	295	295	295	295
	Worst	295	293	295	287	295
	Mean	295	294.7	295	293.87	295
	Std	0	0.6513	0	2.3154	0
KP8	Best	1024	1024	1010	1024	1024
	Median	1024	1024	960	1016	1024
	Worst	1024	1018	920	940	1024
	Mean	1024	1023.4	959.87	999.87	1024
	Std	0	1.8308	22.41	28.11	0
KP9	Best	481.07	481.07	481.07	481.07	481.07
	Median	481.07	481.07	481.16	481.07	481.07
	Worst	481.07	481.07	437.93	481.01	481.07
	Mean	481.07	481.07	469.13	481.50	481.07
	Std	0	0	10.61	26.19	0
KP10	Best	9767	9767	9764	9767	9767
	Median	9767	9767	9758	9764	9767
	Worst	9767	9763	9752	9755	9767
	Mean	9767	9766.7	9758.1	9763.6	9767
	Std	0	0.8769	3.20	3.4601	0