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

Table 3

Maximum distance of the three compared algorithms.

Instance	One-chromosome				TPGA
	Minimum	Mean	Maximum	StDev	Min	Mean	Max	StDev	Min	Mean	Max	StDev	Min	Mean	Max	StDev
att48	13668	16178	23013	2972	13678	18440	31915	4870	13668	14650	18185	1489	13668	14687	19252	1570
berlin52	2440	3267.4	5506	913.3	2440	3671	6885	1253	2440	2850.3	4357.3	566.9	2440	2838.5	4020.1	543.1
bier127	28890	68194	127487	32040	34697	88175	160235	42537	24007	50498	105182	29541	24007	50441	107861	29014
ch130	2119	4685	8530	2088	2472	6288	11699	2968	1177	3113	6777	2002	1177	3112	6718	1962
eil101	156	349.3	621	145.4	178	438.4	811	201.2	107.2	234.3	504.2	132.3	108	236.2	505	130.5
eil51	109	173.23	301	54.08	109	195.7	352	76.63	108.89	137.98	245.88	39.32	108.89	137.24	238.07	38.33
eli76	140	261.84	451	99.51	141	318.8	576	141	124.28	189.96	369.26	79.58	124.42	190.91	350.25	79.71
gr96	181	341.1	572	120.4	204	434.3	834	182.4	169.74	249.33	479.74	92.83	169.74	253.24	461.39	97.9
kroa150	10877	24701	43153	11241	12890	33802	65152	16075	5395	15378	34924	10129	5395	15389	34281	9933
kroa200	13968	34060	63613	16286	18234	47219	85907	22693	6221	21580	48028	15050	6271	21647	48262	15043
kroB100	7492	15510	27325	6333	8623	19895	35162	8710	6699	10503	20761	4546	6699	10480	19748	4563
kroB150	11170	24615	43288	11044	13835	33480	66963	15396	5750	15271	36168	9535	5750	15220	32456	9289
kroB200	14455	33215	60208	15652	17701	46330	89048	22545	6698	21760	50222	15170	6697	21740	51004	14895
kroC100	7686	15738	27000	6322	8456	20534	39549	9018	5750	10031	20252	4830	5750	9858	19638	4549
kroD100	8035	15495	26648	6166	8676	20215	37334	8865	6357	10374	20636	4679	6357	10395	19507	4606
kroE100	8321	15860	27766	6208	8896	20891	36552	8846	7038	10946	20938	4631	7038	11058	21363	4766
lin105	6687	11982	21810	4386	7334	15608	27895	6384	6375	8802	15930	3060	6375	8816	15539	3017
lin318	26565	65155	117892	32195	34679	91301	170309	45253	10175	44867	106246	33540	10266	45772	107495	34536
mtsp100	7805	15625	28178	6230	8670	20291	36571	8799	6357	10519	22419	4920	6357	10380	20549	4554
mtsp150	12427	28944	51754	13383	14710	38711	71653	18645	5352	18495	42674	12571	5306	18188	39861	12141
mtsp51	110	171.37	278	53.43	109	194.65	367	73.71	108.89	136.71	214.08	36.13	108.89	138.23	238.87	38.52
pr124	31977	65199	119940	26367	38626	89080	179180	40189	22594	38131	77415	19053	22594	38281	75941	18940
pr136	38778	81809	146217	34977	47037	110777	209589	51156	25731	53626	113915	30275	25731	53285	120554	29799
pr144	37745	79364	147984	33520	46297	108344	196336	49131	24313	49939	115229	29812	24313	49548	107708	28633
pr152	48531	101819	178569	41889	59013	142063	271591	63667	31727	60579	131923	34854	31727	61139	133314	34801
pr226	75797	169009	297280	76223	91773	243451	454610	114227	34845	101101	248381	73633	34845	100943	250000	71767
pr264	42743	101884	188189	46735	57515	149315	278195	69900	16339	46435	114410	32724	16524	46883	117359	33250
pr299	33418	78941	144137	38053	42242	113477	208744	53805	14293	51391	114725	36170	14344	51988	118493	36699
pr76	37970	61320	102253	20609	38692	77148	135311	30936	37971	48125	82033	13526	37971	48825	83361	14041
rat195	1032	2319.6	4174	1040.4	1271	3201	6023	1518	604.2	1595.2	3553	990.7	605	1593.6	3354.1	984.7
rat99	466	838.9	1491	299.2	503	1069.9	2007	442	432.4	625.3	1215.9	230.8	432.9	625.8	1120.4	227.1
rd400	9050	23770	43172	12268	12312	33286	62312	17169	2970	16509	39917	13220	2903	16603	39024	13265
st70	209	368	624	120.3	221	448.8	817	178.6	206.4	275.81	481.14	86.41	207.4	276.8	492.14	88.51
tsp225	1971	4479	7780	2066	2521	6188	10987	2891	998	3068	6843	2045	998	3130	7060	2091
Average	15970	34284	61388	14944	19258	47185	87984	21728	9797	21823	47810	13037	9805	21885	47857	12940