Different Transfer Functions for Binary Particle Swarm Optimization with a New Encoding Scheme for Discounted {0-1} Knapsack Problem

Table 10

Comparison of BPSO8, SecEGA, and FirEGA on UDKP1–UDKP10.

Index	Instance	OPT	Algorithm	Best	Average	Worst	Std. dev	Gap
1	UDKP1	85740	FirEGA	80593	79103	77935	690.01	7.74
			SecEGA	78287	76807	75156	798.95	10.42
			BPSO8	85740	85590.0	85347	102.30	0.17
2	UDKP2	163744	FirEGA	155039	151662	149875	1044.95	7.38
			SecEGA	148043	145548	143833	883.43	11.11
			BPSO8	163560	163061.7	162260	314.45	0.42
3	UDKP3	269393	FirEGA	246698	240886	237980	1491.97	10.58
			SecEGA	228823	225492	222486	1353.58	16.30
			BPSO8	268430	267008.7	265560	681.78	0.89
4	UDKP4	347599	FirEGA	321605	317319	314486	1426.85	8.71
			SecEGA	305796	299978	297606	1435.46	13.70
			BPSO8	346120	343789.0	341800	924.93	1.10
5	UDKP5	442644	FirEGA	405409	399620	395367	1692.23	9.72
			SecEGA	376147	370808	367574	1611.71	16.23
			BPSO8	437870	435053.0	431500	1572.94	1.71
6	UDKP6	536578	FirEGA	486556	478726	474015	2233.61	10.78
			SecEGA	447438	442499	438809	1765.28	17.53
			BPSO8	530600	527004.7	523880	1877.81	1.78
7	UDKP7	635860	FirEGA	568119	560948	556938	2441.8	11.78
			SecEGA	529753	521401	518407	1813.04	18.00
			BPSO8	627350	621875.3	617290	2120.14	2.20
8	UDKP8	650206	FirEGA	590137	585286	580684	2078.87	9.99
			SecEGA	550645	546678	543836	1449.36	15.92
			BPSO8	637900	634388.3	629600	2121.45	2.43
9	UDKP9	718532	FirEGA	655172	649636	645012	2023.64	9.59
			SecEGA	613581	602215	605835	2003.75	16.19
			BPSO8	704350	699156.3	693320	3132.54	2.70
10	UDKP10	779460	FirEGA	712270	706575	701545	2013.43	9.35
			SecEGA	665459	658908	655645	1723.8	15.47
			BPSO8	767550	756768.3	749330	3865.48	2.91