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

Table 5

Comparison of PSO1, PSO2, SecEGA, MFO1, and MFO2 on WDKP1–WDKP10.

Instance	OPT	Algorithm	Best	Average	Worst	StdDev	Gap	Rank
WDKP1	83098	PSO1	82998	82764	82465	140.5	18.1	4
		PSO2	83002	82797	82549	125.7	18.1	3
		SecEGA	80014	79022	78096	473.7	4.9	5
		MFO1	82962	82894	82848	22.5	18.2	1
		MFO2	82950	82862	82798	34.8	18.2	2
WDKP2	138215	PSO1	137880	137278	136770	254.2	16.1	4
		PSO2	137860	137381	136780	247.2	16.2	3
		SecEGA	133315	132276	131337	415.6	4.3	5
		MFO1	137920	137873	137850	22.0	16.6	1
		MFO2	137890	137795	137720	40.7	16.5	2
WDKP3	256616	PSO1	256160	255362	254210	422.3	8.8	4
		PSO2	255990	255386	254670	356.3	8.8	3
		SecEGA	238331	235721	234025	873.6	8.1	5
		MFO1	255970	255891	255820	28.4	9.0	1
		MFO2	255660	255463	255260	90.0	8.8	2
WDKP4	315657	PSO1	314790	313860	313010	434.8	11.1	4
		PSO2	314750	314108	313390	399.3	11.2	3
		SecEGA	293640	290851	288764	950.1	7.9	5
		MFO1	315040	314980	314930	28.0	11.5	1
		MFO2	314630	314400	314190	125.6	11.3	2
WDKP5	428490	PSO1	426910	425683	424470	701.9	26.8	4
		PSO2	426680	425736	424520	501.1	26.9	3
		SecEGA	393617	390014	387992	1059.8	9.0	5
		MFO1	427710	427666	427620	23.0	27.4	1
		MFO2	427260	426687	426270	214.5	27.1	2
WDKP6	466050	PSO1	463690	462092	460590	641.3	2.1	4
		PSO2	463350	462284	460930	583.1	2.2	3
		SecGA	429208	425112	423269	1058.4	8.8	5
		MFO1	464880	464819	464760	28.9	2.7	1
		MFO2	463820	463485	463080	203.2	2.4	2
WDKP7	547683	PSO1	544700	542724	538860	1154.9	11.0	4
		PSO2	544730	542765	539860	922.5	11.0	3
		SecEGA	501557	496134	493845	1230.9	9.4	5
		MFO1	546500	546425	546380	29.8	11.7	1
		MFO2	545300	544705	544110	295.4	11.4	2
WDKP8	576959	PSO1	572530	570187	567530	1216.6	6.8	4
		PSO2	571870	570226	568570	825.3	6.8	3
		SecEGA	530971	523203	520350	2157.1	9.3	5
		MFO1	575590	575463	575360	45.5	7.8	1
		MFO2	574520	573672	572880	299.1	7.5	2
WDKP9	650660	PSO1	643950	641272	638210	1501.3	21.4	4
		PSO2	645140	641658	638230	1502.3	21.5	3
		SecEGA	598343	586770	583854	2315.5	9.8	5
		MFO1	648760	648672	648600	35.9	22.8	1
		MFO2	647040	646510	646030	268.1	22.4	2
WDKP10	678967	PSO1	672380	668923	666420	1429.2	15.1	3
		PSO2	671880	668830	665740	1553.1	15.1	4
		SecEGA	620230	606215	609964	3090.9	10.7	5
		MFO1	677450	677388	677330	34.5	16.5	1
		MFO2	676110	675115	674680	284.2	16.2	2