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

Table 8

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

Instance	Measure	HHSEDA	GA	PSO	BFPA	BABC-DE
KP20	Time	1.86	12.19	4.98	3.03	26.03
	Best	1665	1657	1608	1554	1636
	Median	1665	1648	1589	1535	1618
	Worst	1660	1639	1577	1500	1607
	Mean	1664	1648	1588	1531	1619
	Std	1.00	4.19	6.89	14.69	6.59
KP21	Time	3.29	26.13	7.89	12.32	44.58
	Best	3495	3406	3266	3249	3371
	Median	3493	3379	3249	3173	3331
	Worst	3485	3357	3227	3091	3314
	Mean	3493	3379	3247	3175	3333
	Std	2.09	12.26	10.05	32.95	14.35
KP22	Time	5.09	39.78	11.87	22.98	70.96
	Best	5401	5181	4988	4933	5092
	Median	5397	5128	4951	4827	5065
	Worst	5389	5087	4923	4757	5038
	Mean	5396	5128	4954	4830	5065
	Std	3.26	24.46	16.88	44.09	13.35
KP23	Time	16.67	111.85	34.78	116.82	131.58
	Best	8695	8233	7951	7898	8323
	Median	8690	8175	7911	7784	8080
	Worst	8683	8139	7880	7692	8045
	Mean	8690	8179	7912	7785	8087
	Std	3.39	25.68	17.55	48.25	49.59
KP24	Time	35.88	229.82	66.59	353.11	148.32
	Best	12164	11344	11007	10926	11368
	Median	12157	11288	10957	10800	11178
	Worst	12146	11245	10920	10753	11141
	Mean	12156	11290	10956	10817	11186
	Std	4.06	22.77	24.28	65.24	44.81
KP25	Time	95.82	593.82	146.32	1136.50	343.02
	Best	17581	16232	15782	15645	16079
	Median	17570	16169	15697	15487	15987
	Worst	17563	16055	15635	15376	15932
	Mean	17570	16162	15699	15495	15988
	Std	5.00	40.73	31.62	77.33	38.30
KP26	Time	105.6	832.52	198.75	1205.96	500.89
	Best	21000	19219	18743	18659	19149
	Median	20984	19182	18692	18494	19025
	Worst	20965	19147	18628	18388	18969
	Mean	20981	19180	18691	18493	19027
	Std	8.51	21.42	26.26	79.56	41.01
KP27	Time	176.70	1419.12	318.23	2414.70	1426.00
	Best	26379	24107	23487	23455	24220
	Median	26358	24024	23401	23162	23820
	Worst	26342	23964	23344	23015	23769
	Mean	26359	24022	23406	23182	23851
	Std	9.14	45.73	39.86	111.00	106.67
KP28	Time	348.5	2133.43	616.43	6333.80	2677.90
	Best	34545	31453	30653	30579	31258
	Median	34515	31312	30586	30331	31098
	Worst	34492	31211	30523	30154	31057
	Mean	34516	31314	30587	30331	31117
	Std	11.45	66.13	32.72	101.25	51.79

Bold shows the best result.