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

Table 10

Comparison with non-HS variants for high dimensional instances with high correlation.

Instance	Measure	HHSEDA	GA	PSO	BFPA	BABC-DE
KP29	Time	1.8048	12.1582	4.612	3.4190	14.1013
	Best	1769	1761	1733	1695	1757
	Median	1768	1754	1722	1669	1748
	Worst	1766	1747	1710	1644	1742
	Mean	1781	1753.9	1721.8	1667.73	1748.2
	Std	0.8277	3.99	4.96	10.21	3.5785
KP30	Time	3.58	23.31	9.76	12.35	23.02
	Best	3857	3794	3722	3662	3785
	Median	3855	3773.5	3706	3617.5	3772.5
	Worst	3851	3753	3696	3591	3763
	Mean	3854.6	3772	3707.4	3622.26	3773.23
	Std	1.35	10.25	6.27	19.68	5.63
KP31	Time	4.98	34.78	10.96	24.96	31.00
	Best	5498	5377	5285	5213	5391
	Median	5494	5352	5265.5	5163	5367
	Worst	5487	5321	5254	5119	5355
	Mean	5493.6	5309.3	5266.4	5169.73	5367.63
	Std	2.64	14.42	8.09	24.25	8.88
KP32	Time	17.58	127.7	32.95	112.26	68.62
	Best	9435	9167	9021	8953	9189
	Median	9430	9140	9007	8870	9167
	Worst	9424	9094	8991	8830	9146
	Mean	9429.8	9138.1	9006.7	8875.2	9165.3
	Std	2.48	16.76	7.43	27.08	11.01
KP33	Time	38.80	268.4	73.93	297.6	198.70
	Best	13214	12732	12570	12446	12782
	Median	13210	12702	12529	12360	12747
	Worst	13204	12677	12508	12293	12728
	Mean	13209	12703	12530	12362	12751
	Std	3.41	14.41	10.39	36.37	14.56
KP34	Time	92.94	549	164.93	888.2	420
	Best	19051	18303	18041	17871	18371
	Median	19042	18259	18012	17809	18339
	Worst	19028	18220	17993	17722	18312
	Mean	19043	18258	18011	17809	18338
	Std	5.01	20.55	12.41	38.38	16.83
KP35	Time	108.29	815.68	179.69	120.2	432.4
	Best	22700	21771	21510	21330	21904
	Median	22685	21723	21457	21216.5	21836.5
	Worst	22674	21678	21422	21101	21805
	Mean	22685	21723	21455.5	21219.26	21842.2
	Std	5.42	25.14	15.96	46.48	24.85
KP36	Time	195.27	1224	316.33	2416.5	746.8
	Best	28175	26944	26613	26441	27042
	Median	28166	26877	26561	26287	2699.6
	Worst	28151	26821	26534	26208	26938
	Mean	28165	26873	26562	26290	26997
	Std	6.45	30.60	20.78	49.73	25.63
KP37	Time	361.39	2078.4	596.38	6315.5	2283
	Best	38021	36318	35935	35697	36524
	Median	38003	36256	35873	35540.5	36420
	Worst	37985	36188	35850	35477	36361
	Mean	38003	36250	35880	35557	36427
	Std	7.97	32.20	23.01	53.27	36.33

Bold shows the best result.