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

Table 5

Comparison with HS variants for high dimensional instances with no correlation.

Instance	Measure	HHSEDA	ABHS	NGHS	DBHS	BHS
KP11	Time	1.935	11.96	0.21	0.22	0.18
	Best	6423	6423	6131	5634	6423
	Median	6419.5	6401	5952.5	5292.5	6400.5
	Worst	6399	6388	5774	5130	6385
	Mean	6416.6	6402.8	5947.3	5313.3	6402.8
	Std	7.8375	9.2165	106.28	116.23	9.93
KP12	Time	3.61	28.25	0.32	116.23	0.35
	Best	12960	12954	11955	10514	12949
	Median	12955	12904	11541	98160	12935
	Worst	12947	12859	10734	96094	12864
	Mean	1295.5	12899	11561	99002	12930
	Std	4.0	20.98	239.34	210.50	18.17
KP13	Time	5.76	43.44	0.41	0.50	0.55
	Best	19540	19493	17425	14721	19531
	Median	19534	19445	16776	14190	19496
	Worst	19513	19366	15272	13910	19373
	Mean	19531	19441	16738	14259	19490
	Std	7.56	29.62	520.38	227.00	29.55
KP14	Time	20.31	191.96	1.24	1.60	1.88
	Best	32078	31958	27562	23398	32049
	Median	32059	31911	26387	22656	31998
	Worst	32031	31816	25597	22313	31941
	Mean	32056	31896	26471	22703	31996
	Std	10.5297	41.48	551.19	248.62	26.0169
KP15	Time	47.10	580.85	2.57	3.33	3.57
	Best	44942	44800	37004	31081	44882
	Median	44927	44720	35279	30538	44857
	Worst	44909	44658	33680	30135	44782
	Mean	44926	44721	35314	30569	44851
	Std	9.6472	38.69	723.59	242.94	24.83
KP16	Time	126.62	2009.00	5.4792	7.19	10.27
	Best	64604	64482	50864	44615	64498
	Median	64572	64358	41956	43500	64457
	Worst	64551	64288	47371	42910	64395
	Mean	64572	64360	49006	43516	64457
	Std	13.35	66.34	922.25	427.87	23.25
KP17	Time	133.21	2398.70	6.72	8.19	12.75
	Best	77005	76515	59281	51597	76888
	Median	76956	76337	57093	51065	76812
	Worst	76889	76207	56115	50662	76635
	Mean	76953	76350	57341	51104	76797
	Std	29.00	85.40	907.81	266.76	57.07
KP18	Time	366.72	5715.70	11.94	14.43	22.14
	Best	96364	95971	72914	64451	96233
	Median	96302	95667	70298	63545	96084
	Worst	96246	95385	68266	62826	95985
	Mean	96299	95660	70304	63553	96091
	Std	27.20	122.51	1313.4	457.11	56.51
KP19	Time	545.24	14870.00	25.56	27.06	36.64
	Best	127260	126568	93953	84341	126978
	Median	127194	126438	91522	83182	126860
	Worst	127105	126250	88857	82488	126710
	Mean	127190	126430	91195	83306	126870
	Std	31.85	78.81	1437	475.07	56.78

Bold shows the best result.