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

Table 7

Comparison with HS variants for high dimensional instances with low correlation.

Instance	Measure	HHSEDA	ABHS	NGHS	DBHS	BHS
KP20	Time	1.86	11.71	0.20	0.47	0.28
	Best	1665	1665	1627	1536	1665
	Median	1665	1663	1588	1523	1661
	Worst	1660	1656	1561	1506	1654
	Mean	1664	1662	1593	1523	1661
	Std	1.00	2.52	15.77	7.28	2.48
KP21	Time	3.29	37.86	0.38	1.13	0.53
	Best	3495	3491	3376	3190	3494
	Median	3493	3486	3300	3146	3489
	Worst	3485	3473	3242	3126	3479
	Mean	3493	3484	3306	3148	3489
	Std	2.09	5.09	37.64	12.99	3.56
KP22	Time	5.09	33.24	0.45	2.09	0.88
	Best	5401	5387	5111	4887	5398
	Median	5397	5374	5022	4823	5388
	Worst	5389	5352	4907	4793	5377
	Mean	5396	5372	5019	4824	5387
	Std	3.26	9.08	45.89	18.58	5.33
KP23	Time	16.67	211.81	1.34	7.92	4.29
	Best	8695	8658	8207	7786	8690
	Median	8690	8646	8010	7745	8677
	Worst	8683	8615	7905	7711	8664
	Mean	8690	8639	8019	7743	8677
	Std	3.39	14.89	72.61	18.46	6.19
KP24	Time	35.88	556.70	2.62	19.83	9.93
	Best	12164	12112	11299	10800	12158
	Median	12157	12080	11113	10741	12141
	Worst	12146	12042	10949	10706	12132
	Mean	12156	12079	11115	10744	12142
	Std	4.06	18.80	69.93	20.70	6.11
KP25	Time	95.82	1201.27	6.66	54.26	37.79
	Best	17581	17430	15985	15510	17572
	Median	17570	17380	15858	15420	17556
	Worst	17563	15112	15749	15369	17534
	Mean	17570	17245	15857	15425	17556
	Std	5.00	32.94	67.40	31.06	8.97
KP26	Time	105.6	2497.86	6.90	56.79	30.54
	Best	21000	20798	19075	18422	20971
	Median	20984	20741	18894	18367	20959
	Worst	20965	20662	18753	18323	20939
	Mean	20981	20742	18896	18366	20957
	Std	8.51	40.93	87.64	27.11	8.45
KP27	Time	176.70	5811.06	11.76	106.15	37.01
	Best	26379	26146	23859	23180	26343
	Median	26358	26101	23604	23070	26326
	Worst	26342	26048	23409	23022	26311
	Mean	26359	26097	23619	23078	26326
	Std	9.14	33.98	121.78	47.06	11.48
KP28	Time	348.5	13514	22.64	207.45	76.04
	Best	34545	34267	31113	30277	34489
	Median	34515	34206	30807	30158	34479
	Worst	34492	34154	30617	30141	34455
	Mean	34516	34213	30824	30177	34476
	Std	11.45	41.81	120.20	40.94	11.66

Bold shows the best result.