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

Table 4

Comparison of PSO1, PSO2, SecEGA, MFO1, and MFO2 on SDKP1–SDKP10.

Instance	OPT	Algorithm	Best	Average	Worst	StdDev	Gap	Rank
SDKP1	94459	PSO1	94219	93874	93489	184.3	33.9	4
		PSO2	94205	93999	93703	130.5	34.1	3
		SecEGA	89 769	88832	87463	594.9	6.0	5
		MFO1	94286	94274	94258	12.6	34.5	1
		MFO2	94286	94222	94121	43.2	34.4	2
SDKP2	160805	PSO1	160280	159531	158810	360.1	34.9	4
		PSO2	160090	159617	159030	307.4	35.0	3
		SecEGA	153 821	152059	150753	489.4	5.4	5
		MFO1	159980	159895	159800	47.3	35.2	1
		MFO2	159840	159667	159390	93.9	35.0	2
SDKP3	238248	PSO1	237340	236389	235320	440.2	0.7	3
		PSO2	237300	236428	235620	371.4	0.7	1
		SecEGA	224 997	223580	221918	543.4	6.2	5
		MFO1	236530	236404	236310	51.8	0.7	2
		MFO2	236140	235855	235600	128.8	0.4	4
SDKP4	340027	PSO1	337960	337013	335880	585.0	19.3	1
		PSO2	337860	336811	335890	508.3	19.2	3
		SecEGA	318 510	315513	313 747	851.1	7.2	5
		MFO1	336980	336865	336800	39.0	19.2	2
		MFO2	336390	335989	335730	172.9	18.9	4
SDKP5	463033	PSO1	459780	458216	456130	728.5	36.5	3
		PSO2	459420	458086	456840	615.1	36.5	4
		SecEGA	420 238	416964	413 933	1291.7	10.0	5
		MFO1	460190	460096	460010	45.5	37.1	1
		MFO2	459240	458554	458240	225.4	36.6	2
SDKP6	466097	PSO1	462350	460874	459340	677.1	1.9	2
		PSO2	462000	460989	459690	602.6	1.9	1
		SecGA	430 738	427304	425 504	1031.1	8.3	5
		MFO1	461000	460862	460750	64.3	1.9	3
		MFO2	460060	459245	458780	226.8	1.5	4
SDKP7	620446	PSO1	614510	612746	610360	1059.2	25.3	4
		PSO2	614780	612902	610930	928.1	25.3	3
		SecEGA	561 224	556083	552 007	1926.3	10.4	5
		MFO1	615900	615756	615630	69.2	25.9	1
		MFO2	613930	613268	612870	281.1	25.4	2
SDKP8	670697	PSO1	663730	661988	659770	984.4	24.0	4
		PSO2	664250	662529	660340	992.7	24.1	2
		SecEGA	611 644	606263	603 774	1446.9	9.6	5
		MFO1	664750	664590	664450	76.0	24.5	1
		MFO2	662910	662053	661640	303.5	24.0	3
SDKP9	739121	PSO1	731830	730283	727770	1058.9	38.3	3
		PSO2	732320	730619	728570	1060.1	38.3	2
		SecEGA	674 885	667900	664 580	1614.0	9.6	5
		MFO1	731630	731502	731360	68.3	38.5	1
		MFO2	728790	728306	727650	315.5	37.9	4
SDKP10	765317	PSO1	756580	755021	753220	806.2	29.9	2
		PSO2	757430	754798	752470	1402.8	29.9	3
		SecEGA	708 935	695557	691 994	2956.1	9.1	5
		MFO1	756190	755966	755650	120.7	30.1	1
		MFO2	753740	753027	752270	336.6	29.6	4