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

Table 9

Comparison of BPSO8, SecEGA, and FirEGA on WDKP1–WDKP10.

Index	Instance	OPT	Algorithm	Best	Average	Worst	Std. dev	Gap
1	WDKP1	83098	FirEGA	82803	82693	82592	52.04	0.49
			SecEGA	80014	79022	78096	473.67	4.91
			BPSO8	83090	83014.1	82649	82.14	0.10
2	WDKP2	138215	FirEGA	137704	137584	137356	63.23	0.46
			SecEGA	133315	132276	131337	415.62	4.30
			BPSO8	138110	137830.0	137270	161.59	0.28
3	WDKP3	256616	FirEGA	254120	253657	253307	173.01	1.15
			SecEGA	238331	235721	234025	873.58	8.14
			BPSO8	256360	255778.7	254850	325.67	0.33
4	WDKP4	315657	FirEGA	313966	312849	311998	484.76	0.89
			SecEGA	293640	290851	288764	950.06	7.86
			BPSO8	315040	314340.7	313360	471.89	0.42
5	WDKP5	428490	FirEGA	426311	424548	423058	798.53	0.92
			SecEGA	393617	390014	387992	1059.83	8.98
			BPSO8	427390	426349.7	424950	640.64	0.50
6	WDKP6	466050	FirEGA	463185	461672	457718	1107.57	0.94
			SecEGA	429208	425112	423269	1058.37	8.78
			BPSO8	464040	463228.3	461980	487.82	0.61
7	WDKP7	547683	FirEGA	544019	541949	538126	1224.68	1.05
			SecEGA	501557	496134	493845	1230.94	9.41
			BPSO8	545270	544006.7	542140	779.24	0.67
8	WDKP8	576959	FirEGA	573427	571559	563253	1495.36	0.94
			SecEGA	530971	523203	520350	2157.09	9.32
			BPSO8	574290	572652.7	571520	693.20	0.75
9	WDKP9	650660	FirEGA	647477	644820	630086	2056.06	0.90
			SecEGA	598343	586770	583854	2315.5	9.82
			BPSO8	646910	645133.0	642980	923.83	0.85
10	WDKP10	678947	FirEGA	675452	673008	668239	1441.96	0.88
			SecEGA	620230	606215	609964	3090.86	10.72
			BPSO8	675460	673135.3	670990	1171.04	0.86