A New Moth-Flame Optimization Algorithm for Discounted {0-1} Knapsack Problem

Table 3

Comparison of PSO1, PSO2, SecEGA, MFO1, and MFO2 on IDKP1–IDKP10.

Instance	OPT	Algorithm	Best	Average	Worst	StdDev	Gap	Rank
IDKP1	70106	PSO1	69471	68980	68252	288.0	1.6	4
		PSO2	69530	69117	68376	237.2	1.4	3
		SecEGA	68 663	68000	67 369	328.4	3.0	5
		MFO1	70106	70106	70106	0.0	0.0	1
		MFO2	70106	70104	70090	4.9	0.0	2
IDKP2	118268	PSO1	116710	116212	115370	354.2	1.7	4
		PSO2	117200	116516	115700	337.3	1.5	3
		SecEGA	114 434	113385	112 307	7446.7	4.1	5
		MFO1	118268			0.0	0.0	1
		MFO2	118268	118251	118230	19.3	0.0	2
IDKP3	234804	PSO1	234290	233653	232350	420.4	0.5	3
		PSO2	234390	232600	232600	389.6	0.4	4
		SecEGA	220 096	217982	216 313	835.8	7.2	5
		MFO1	234770	234748	234740	7.7	0.0	1
		MFO2	234700	234544	234360	92.3	0.1	2
IDKP4	282591	PSO1	280540	279714	277810	578.1	1.0	4
		PSO2	280770	279858	279110	486.7	1.0	3
		SecEGA	263 238	260425	258 922	933.4	7.8	5
		MFO1	282590	282587	282570	5.8	0.0	1
		MFO2	282470	282210	281940	132.1	0.1	2
IDKP5	335584	PSO1	333140	331595	329340	748.8	1.2	4
		PSO2	332710	331896	329280	691.2	1.1	3
		SecEGA	309 573	306878	304 881	907.2	8.6	5
		MFO1	335580	335580	335580	0.0	0.0	1
		MFO2	335280	335000	334780	107.2	0.2	2
IDKP6	452463	PSO1	450290	449287	447540	681.7	0.7	4
		PSO2	450880	449350	447890	683.3	0.7	3
			414 090	411367	408 788	1099.3	9.1	5
		MFO1	452430	452415	452390	9.7	0.0	1
		MFO2	451750	451293	450990	198.3	0.3	2
IDKP7	489149	PSO1	483180	481656	478830	944.5	1.5	3
		PSO2	483170	481578	479910	1034.9	1.5	4
		SecEGA	451 528	444316	442 133	1280.3	9.2	5
		MFO1	489150	489132	489120	9.7	0.0	1
		MFO2	488520	487889	487030	288.1	0.3	2
IDKP8	533841	PSO1	523300	520939	517720	1480.0	2.4	4
		PSO2	526240	521844	519190	1540.0	2.2	3
		SecEGA	490 494	481831	478 035	2215.7	9.7	5
		MFO1	533840	533825	533820	6.3	0.0	1
		MFO2	533050	532345	531940	284.3	0.3	2
IDKP9	528144	PSO1	515680	511908	507210	1937.0	3.1	4
		PSO2	516550	512575	509090	1727.0	2.9	3
		SecEGA	489 661	477001	471 848	3656.2	9.7	5
		MFO1	528140	528136	528120	7.2	0.0	1
		MFO2	527140	526734	526370	205.8	0.3	2
IDKP10	581244	PSO1	563960	560214	556100	2204.1	3.6	4
		PSO2	566670	562000	559540	1950.2	3.3	3
		SecEGA	535 541	521604	516 445	4265.1	10.3	5
		MFO1	581240	581233	581230	4.5	0.0	1
		MFO2	580620	579589	578870	365.0	0.3	2