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

Table 9

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

Instance	Measure	HHSEDA	ABHS	NGHS	DBHS	BHS
KP29	Time	1.80	12.54	0.25	0.49	0.29
	Best	1769	1769	1735	1687	1769
	Median	1768	1765	1716	1677	1766
	Worst	1766	1759	1658	1671	1761
	Mean	1781	1765	1711	1677	1766
	Std	0.8277	2.43	17.09	4.67	1.94
KP30	Time	3.58	22.98	0.38	1.14	0.66
	Best	3857	3851	3743	3660	3854
	Median	3855	3844	3714	3641	3849
	Worst	3851	3831	3674	3626	3837
	Mean	3854.6	3843	3713.5	3642	3847
	Std	1.3544	4.89	15.19	6.41	4.11
KP31	Time	4.98	34.13	0.59	1.88	1.11
	Best	5498	5486	5321	5206	5491
	Median	5494	5471	5279	5192	5479
	Worst	5487	5454	5246	5181	5462
	Mean	5493.6	5470	5278	5193	5479
	Std	2.6351	7.11	19.68	7.26	6.75
KP32	Time	17.58	227.23	1.66	7.55	3.99
	Best	9435	9409	9088	8932	9426
	Median	9430	9376	9033	8909	9418
	Worst	9424	9346	8962	8884	9400
	Mean	9429.8	9378	9027	8907	9417
	Std	2.4786	15.43	28.78	12.68	5.82
KP33	Time	38.80	564.62	3.32	19.33	8.87
	Best	13214	13174	12611	12458	13203
	Median	13210	13133	12548	12401	13192
	Worst	13204	13095	12480	12383	13183
	Mean	13209	13133	12548	12404	13192
	Std	3.4108	18.14	31.60	16.06	5.52
KP34	Time	92.95	2072.70	6.92	52.96	23.85
	Best	19051	18982	18148	17876	19037
	Median	19042	18945	18039	17849	19018
	Worst	19028	18906	17941	17831	19002
	Mean	19043	18940	18039	17853	19018
	Std	5.0062	19.19	43.37	12.87	8.16
KP35	Time	108.29	2483.3	8.5626	52.02	22.79
	Best	22700	22468	21618	21325	22674
	Median	22685	22397	21513	21286	22654
	Worst	22674	22342	21412	21249	22638
	Mean	22685	22407	21511	21286	22653
	Std	5.4241	31.78	48.56	16.05	8.27
KP36	Time	195.27	529.5	13.94	132.70	40.38
	Best	28175	27851	26704	26458	28149
	Median	28166	27835	26585	26362	28132
	Worst	28151	27799	26477	26335	28118
	Mean	28165	27827	26584	26368	28133
	Std	6.4505	23.03	60.65	26.21	8.17
KP37	Time	361.39	13765	28.79	291.19	81.75
	Best	38021	37654	36032	35699	37983
	Median	38003	37617	35911	35651	37964
	Worst	37985	37597	35757	35617	37943
	Mean	38003	37626	35906	35650	37964
	Std	7.9658	23.59	70.29	23.79	8.76

Bold shows the best result.