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

Table 6

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

Instance	Measure	HHSEDA	GA	PSO	BFPA	BABC-DE
KP11	Time	1.94	NA	4.01	3.17	7.57
	Best	6423	NA	6385	5294	6423
	Median	6419.5	NA	6254	4537.5	6421
	Worst	6399	NA	6131	4227	6413
	Mean	6416.6	NA	6269.2	4555.8	6419.7
	Std	7.8375	NA	62.83	223.97	3.35
KP12	Time	3.61	NA	6.52	12.12	11.01
	Best	12960	NA	11820	9436	12921
	Median	12955	NA	11612	8626	12890
	Worst	12947	NA	11479	8303	12875
	Mean	1295.5	NA	11637	8671.4	12892
	Std	4.0	NA	91.23	283	12.84
KP13	Time	5.76	42.38	10.58	23.98	15.60
	Best	19540	19405	17104	13363	19461
	Median	19534	19127	16437	12754	19396
	Worst	19513	18870	16240	12148	19363
	Mean	19531	19123	16521	12747	19402
	Std	7.56	124.90	217.87	318.92	22.29
KP14	Time	20.31	124.40	33.41	104.26	47.13
	Best	32078	30686	26621	21067	31807
	Median	32059	30169	25756	20560	31711
	Worst	32031	29911	25424	19725	31667
	Mean	32056	30193	25824	20553	31716
	Std	10.5297	186.70	262.49	294.5	33.76
KP15	Time	47.10	222.26	66.95	298.56	224.20
	Best	44942	41261	35517	29888	44401
	Median	44927	40851	34771	28457	44339
	Worst	44909	40473	34367	27568	44269
	Mean	44926	40847	34792	28473	44339
	Std	9.6472	208.89	251.70	594.92	29.85
KP16	Time	126.62	551.19	154.20	875.33	491.93
	Best	64604	57392	48859	41551	64115
	Median	64572	56320	48261	40188	63749
	Worst	64551	55726	47711	39461	63691
	Mean	64572	56427	48301	40331	63760
	Std	13.35	443.72	286.87	631.65	72.79
KP17	Time	133.21	708.01	178.14	1176.40	614.70
	Best	77005	66543	57432	49109	76026
	Median	76956	65757	56459	47714	75872
	Worst	76889	65148	56035	46718	75788
	Mean	76953	65757	56577	47828	75886
	Std	29.00	321.30	351.11	575.4	58.32
KP18	Time	366.72	1209.30	301.62	2342.5	1239.90
	Best	96364	81365	70362	61597	95144
	Median	96302	80220	69588	59600	94969
	Worst	96246	79387	68785	58551	94910
	Mean	96299	80263	69619	59826	94979
	Std	27.20	506.60	342.00	787.9	51.80
KP19	Time	545.24	2452.50	562.59	1958.60	5568.00
	Best	127260	103904	90984	80234	125521
	Median	127194	102779	90092	78365	125341
	Worst	127105	101843	89519	76813	125228
	Mean	127190	10271	90097	78388	125350
	Std	31.85	554.35	315.43	813.21	68.36

Bold shows the best result.