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

Table 7

Comparison of BPSO8, SecEGA, and FirEGA on IDKP1–IDKP10.

Index	Instance	OPT	Algorithm	Best	Average	Worst	Std. dev	Gap
1	IDKP1	70106	FirEGA	70106	70099	70090	7	0.01
			SecEGA	68663	68000	67369	328	3.00
			BPSO8	69950	69761	69521	109	0.49
2	IDKP2	118268	FirEGA	118169	117869	117625	102.59	0.34
			SecEGA	114434	113385	112307	7446.67	4.13
			BPSO8	118000	117418.0	117040	228.83	0.72
3	IDKP3	234804	FirEGA	234497	233997	233666	175.42	0.34
			SecEGA	220096	217982	216313	835.83	7.16
			BPSO8	234540	234253.7	233800	192.52	0.23
4	IDKP4	282591	FirEGA	282148	280695	278881	827.63	0.67
			SecEGA	263238	260425	258922	933.4	7.84
			BPSO8	281560	280953.3	280220	328.28	0.58
5	IDKP5	335584	FirEGA	335004	333484	329621	1173.9	0.63
			SecEGA	309573	306878	304881	907.19	8.55
			BPSO8	334330	333380.7	332480	479.64	0.66
6	IDKP6	452463	FirEGA	451680	449863	446704	1161.52	0.58
			SecEGA	414090	411367	408788	1099.31	9.08
			BPSO8	451390	450455.0	448980	563.12	0.44
7	IDKP7	489149	FirEGA	488009	485592	476385	2294.28	0.73
			SecEGA	451528	444316	442133	1280.31	9.17
			BPSO8	485920	484205.7	482400	879.02	1.01
8	IDKP8	533841	FirEGA	533035	529984	514196	2308.11	0.72
			SecEGA	490494	481831	478035	2215.66	9.74
			BPSO8	528450	526356.7	524150	1268.72	1.40
9	IDKP9	528144	FirEGA	526410	523982	511651	2216.13	0.79
			SecEGA	489661	477001	471848	3656.22	9.68
			BPSO8	522140	518834.7	515480	1726.89	1.76
10	IDKP10	581244	FirEGA	578903	576772	568903	1905.18	0.77
			SecEGA	535541	521604	516445	4265.07	10.26
			BPSO8	572260	569364.7	566140	1446.41	2.04