List-Based Simulated Annealing Algorithm for Traveling Salesman Problem

Table 5

Compare LBSA with ASA-GS and MSA-IBS on 40 benchmark instances from TSPLIB.

Number	Instance	OPT	ASA-GS			MSA-IBS			LBSA
			Mean	PEav	Time	Mean	PEav	Time	Mean	PEav	Time
1	Ch150	6528	6539.8	0.16	10.91	6529	0.02	0.86	6529.8	0.03	1.29
2	Kroa150	26524	26538.6	0.05	10.9	26524	0	0.82	26524	0	0.98
3	Krob150	26130	26178.1	0.18	10.9	26135	0.02	1.51	26137	0.03	1.65
4	Pr152	73682	73694.7	0.01	10.85	73682	0	0.84	73682	0	0.87
5	U159	42080	42398.9	0.75	11.49	42080	0	0.79	42080	0	0.91
6	Rat195	2323	2348.05	1.07	14.37	2330.2	0.31	1.86	2328	0.22	1.93
7	D198	15780	15845.4	0.41	14.6	15780	0	1.39	15780	0	1.53
8	Kroa200	29368	29438.4	0.23	14.26	29378	0.03	1.74	29373.8	0.02	1.67
9	Krob200	29437	29513.1	0.25	14.24	29439.8	0.01	1.95	29442.2	0.02	2.1
10	Ts225	126643	126646	0.00	16.05	126643	0	1.3	126643	0	1.54
11	Pr226	80369	80687.4	0.39	16.7	80369	0	1.93	80369.8	0.00	2.16
12	Gil262	2378	2398.61	0.86	19.43	2378.8	0.03	2.39	2379.2	0.05	2.72
13	Pr264	49135	49138.9	0.00	19.09	49135	0	1.43	49135	0	1.49
14	Pr299	48191	48326.4	0.28	21.94	48226.4	0.07	2.67	48221.2	0.06	2.93
15	Lin318	42029	42383.7	0.84	23.35	42184.4	0.37	2.4	42195.6	0.40	2.58
16	Rd400	15281	15429.8	0.97	30.4	15347.2	0.43	3.2	15350.4	0.45	3.46
17	Fl417	11861	12043.8	1.54	32.02	11875.6	0.12	3.72	11867.8	0.06	4.01
18	Pr439	107217	110226	2.80	34.92	107407.2	0.18	3.6	107465.2	0.23	3.95
19	Pcb442	50778	51269.2	0.96	35.75	50970	0.38	3.68	50877	0.19	4.31
20	U574	36905	37369.8	1.25	48.47	37155.8	0.68	5.21	37164.6	0.70	6.13
21	Rat575	6773	6904.82	1.94	52.1	6839.8	0.99	5.27	6837.4	0.95	5.99
22	U724	41910	42470.4	1.33	66.83	42212.2	0.72	8.11	42252	0.82	8.34
23	Rat783	8806	8982.19	2.00	78.9	8893.4	0.99	8.99	8888.2	0.93	8.9
24	Pr1002	259045	264274	2.01	164.42	261481.8	0.94	12.71	261805.2	1.07	12.96
25	Pcb1173	56892	57820.5	1.63	193.08	57561.6	1.18	8.9	57431.8	0.95	9.61
26	D1291	50801	52252.3	2.85	214.64	51343.8	1.07	10.59	51198.8	0.78	11.77
27	Rl1323	270199	273444	1.20	210.16	271818.4	0.6	11.53	271714.4	0.56	12.64
28	Fl1400	20127	20782.2	3.25	232.02	20374.8	1.23	17.72	20249.4	0.61	15.43
29	D1655	62128	64155.9	3.26	281.88	62893	1.23	16.18	63001.4	1.41	16.45
30	Vm1748	336556	343911	2.18	276.98	339617.8	0.91	19.7	339710.8	0.94	19.05
31	U2319	234256	236744	1.06	410.97	235236	0.42	17.02	235975	0.73	18.94
32	Pcb3038	137694	141242	2.57	554.28	139706.2	1.46	27.64	139635.2	1.41	29.05
33	Fnl4461	182566	187409	2.65	830.9	185535.4	1.63	30.43	185509.4	1.61	29.67
34	Rl5934	556045	575437	3.48	1043.95	566166.8	1.82	50.76	566053	1.80	52.5
35	Pla7397	23260728	24166453	3.89	1245.22	2.38E+07	2.48	100.69	2.38E+07	2.24	89.61
36	Usa13509	19982859	20811106	4.14	2016.05	2.04E+07	2.06	365.12	2.04E+07	1.89	326.76
37	Brd14051	469385	486197	3.58	2080.5	478609.6	1.97	375.28	478010	1.84	369.86
38	D18512	645238	669445	3.75	2593.97	658149.2	2.00	654.85	657457.2	1.89	629.14
39	Pla33810	66048945	69533166	5.27	4199.88	68075607	3.07	1959.68	68029226.4	3.00	1998.19
40	Pla85900	142382641	156083025	9.63	8855.13	146495515.6	2.89	7596.18	145526542.6	2.21	7586.6
Average				1.87	650.31		0.81	283.52		0.75	282.49