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

Table 8

Comparison of BPSO8, SecEGA, and FirEGA on SDKP1–SDKP10

Index	Instance	OPT	Algorithm	Best	Average	Worst	Std. dev	Gap
1	SDKP1	94459	FirEGA	93235	93171	93070	42.15	1.36
			SecEGA	89769	88832	87463	594.91	5.96
			BPSO8	94363	94181.6	93897	113.74	0.29
2	SDKP2	160805	FirEGA	159159	159004	158859	61.54	1.12
			SecEGA	153821	152059	150753	489.39	5.44
			BPSO8	160570	160136.0	159780	182.33	0.42
3	SDKP3	238248	FirEGA	235454	235241	235043	79.86	1.26
			SecEGA	224997	223580	221918	543.38	6.16
			BPSO8	237370	236778.3	235960	314.48	0.62
4	SDKP4	340027	FirEGA	336353	335963	335709	122.41	1.20
			SecEGA	318510	315513	313747	851.14	7.21
			BPSO8	338240	337433.0	336210	495.98	0.76
5	SDKP5	463033	FirEGA	452900	447587	444255	1974.99	3.34
			SecEGA	420238	416964	413933	1291.65	9.95
			BPSO8	459970	458292.0	457130	802.76	1.02
6	SDKP6	466097	FirEGA	459254	458893	458584	162.94	1.55
			SecEGA	430738	427304	425504	1031.12	8.32
			BPSO8	462650	461310.7	459880	680.64	1.03
7	SDKP7	620446	FirEGA	599361	592279	579673	3949.03	4.54
			SecEGA	561224	556083	552007	1926.26	10.37
			BPSO8	614830	613182.7	610700	984.83	1.17
8	SDKP8	670697	FirEGA	661276	660104	659367	426.06	1.58
			SecEGA	611644	606263	603774	1446.94	9.61
			BPSO8	665230	663681.7	661500	925.22	1.05
9	SDKP9	739121	FirEGA	729135	727544	727064	343.67	1.57
			SecEGA	674885	667900	664580	1614.04	9.64
			BPSO8	732910	730950.3	728990	1024.07	1.11
10	SDKP10	765317	FirEGA	756205	753394	750757	985.46	1.56
			SecEGA	708935	695557	691994	2956.08	9.12
			BPSO8	758110	756337.3	753730	1038.86	1.17