Minimization of the Total Traveling Distance and Maximum Distance by Using a Transformed-Based Encoding EDA to Solve the Multiple Traveling Salesmen Problem

Table 2

The total average distance of the three algorithms.

Instance	One-chromosome				TPGA
	Min	Mean	Max	StDev	Min	Mean	Max	StDev	Min	Mean	Max	StDev	Min	Mean	Max	StDev
att48	39195	64157	104400	20065	47960	88032	142234	29831	42765	73320	119821	26312	42446	73416	121381	26676
berlin52	9355	12574	18389	2534	10693	16034	23586	3884	9654	14087	20647	3756	9410	14173	21140	3856
bier127	208466	253086	330415	32864	261954	332874	433197	47074	220310	253968	328622	18768	214928	255589	311903	18317
ch130	13488	17246	23859	3019	17602	24176	32313	3785	12781	15893	19262	1644	12020	15813	18983	1582
eil101	1021.6	1343.3	1832.4	233.2	1328.1	1829.7	2441.7	326.1	1024.4	1270.4	1625.4	183.7	943.9	1256.9	1624.1	197.1
eil51	511.2	738.2	1147.4	190.7	614	963.5	1450.8	260.7	497.2	771.2	1195.1	243.6	491.9	772.6	1186	245.7
eli76	721.8	1036.2	1457.1	226.1	1035.6	1460.9	2151.2	331.4	771.2	1082.3	1640.5	280.4	760	1087	1610.3	285.4
gr96	862	1355.4	2026.5	348.6	1291.9	1972.6	2968.2	519.3	911.3	1396.9	2260.3	405.3	900.2	1396.4	2257.7	421.3
kroa150	70880	89392	121337	14485	91575	124442	164472	18229	62801	78955	104886	8744	60914	77017	93631	7330
kroa200	99818	121945	164443	16620	136530	172730	223643	23919	90234	110421	145046	13832	86536	109347	141175	12517
kroB100	40570	57373	82441	11490	56782	83671	118140	17817	41476	54609	74861	10195	40070	54504	78913	10802
kroB150	69561	90636	122612	15676	98376	128704	171691	20984	62532	79664	93700	8023	63013	79136	97548	8422
kroB200	95106	119595	156774	15559	129137	170888	220721	25313	85875	111429	146582	13879	88753	111071	142722	12021
kroC100	40573	59920	90359	13754	61044	85942	128239	17762	37895	54879	77495	12239	40453	54072	78388	12654
kroD100	36251	57801	85497	12768	55413	85475	129610	19920	40864	56408	82342	12689	40074	56230	81408	12490
kroE100	42230	59632	84089	11448	59108	87720	128825	19932	41706	57851	80784	11665	39912	57714	85800	12747
lin105	30104	45726	71980	12090	41504	70560	107157	19321	30822	48377	79901	14521	30116	48700	77804	15158
lin318	212259	244247	307006	22524	271844	341953	447096	43659	182437	230828	311132	38487	183700	231180	318757	39493
mtsp100	42551	58361	87622	12581	57443	85849	123128	19325	42190	56268	81858	12583	39444	56187	83089	13184
mtsp150	84018	105130	139427	15595	110196	144405	184927	20654	76189	94674	115786	9230	76317	93618	118046	8784
mtsp51	524.7	744.9	1107.2	192.9	600.5	960.9	1436.8	265	514.1	771.5	1188	239.1	506.4	776.3	1198.2	241.1
pr124	150254	235652	346625	51913	244964	349702	507277	74210	133373	202203	298646	49945	134543	200514	296597	50491
pr136	225315	304074	428602	58108	300700	446351	634173	89691	223163	286062	383137	50634	200711	287362	390805	52720
pr144	205204	278907	414337	56813	289835	425899	587282	85838	194333	251995	327206	39986	198892	250551	323671	39774
pr152	279221	375123	530527	76952	380235	559885	790537	115996	207562	304803	409260	58957	217451	302093	403995	58259
pr226	465922	598166	796733	87652	645486	890751	1223229	146404	329781	488266	687780	83403	343841	489202	698623	85134
pr264	285262	373461	479017	37923	385908	527207	698832	78944	172047	230943	311573	33215	173869	230313	314209	36013
pr299	241958	295390	381982	33177	343357	432610	585709	60203	218292	272548	337654	28996	220328	272507	341877	27987
pr76	164907	249381	389365	73419	231932	363181	560341	107747	175830	268514	434977	84973	168656	269631	440088	88178
rat195	6740	8679	12038	1491	9573	12711	16873	2107	7200.4	8721.7	10212.1	884.8	7059.3	8739.1	10285.1	887.8
rat99	2149.2	3295.3	5008.3	913.2	3148	4989	7707	1417	2270	3672	5940	1198	2279	3651	5924	1221
rd400	82572	91903	104639	4786	101925	114910	135460	9463	53411	80713	117869	20490	53204	82324	119892	21221
st70	1023.9	1487.8	2264.9	372	1309.4	2163.9	3315.9	609.2	939.3	1594.3	2594	530.9	972.7	1606.4	2641.4	537
tsp225	13022	16756	22477	2559	18365	24630	32360	4086	13615	16592	20431	1548	13417	16775	20124	1553
Average	95930	126303	173878	21187	131434	182519	252133	33230	82825	112163	154056	19785	82557	112010	154332	20041