List-Based Simulated Annealing Algorithm for Traveling Salesman Problem

Table 4

Compare LBSA with GA-PSO-ACO and MSA-IBS on 35 benchmark instances from TSPLIB.

Instance	OPT	GA-PSO-ACO			MSA-IBS			LBSA
		Best	Mean	PEav	Best	Mean	PE	Best	Mean	PEav
Att48	33522	33524	33662	0.42	33522	33554.64	0.10	33522	33536.6	0.04
Eil51	426	426	431.84	1.37	426	426.48	0.11	426	426.5	0.12
Berlin52	7542	7544.37	7544.37	0.03	7542	7542	0	7542	7542	0
St70	675	679.60	694.60	2.90	675	677.16	0.32	675	675.55	0.08
Eil76	538	545.39	550.16	2.26	538	538.2	0.04	538	538	0
Pr76	108159	109206	110023	1.72	108159	108288	0.12	108159	108268.3	0.10
Rat99	1211	1218	1275	5.28	1211	1211.04	0.00	1211	1211.1	0.01
Rad100	7910	7936	8039	1.63	7910	7914.56	0.06	7910	7914.7	0.06
KroD100	21294	21394	21484	0.89	21294	21340.64	0.22	21294	21314.2	0.09
Eil101	629	633.07	637.93	1.42	629	629.6	0.10	629	629	0
Lin105	14379	14397	14521	0.99	14379	14380.48	0.01	14379	14379	0
Pr107	44303	44316	44589	0.65	44303	44379.88	0.17	44303	44392.25	0.20
Pr124	59030	59051	60157	1.91	59030	59032.88	0.00	59030	59031.8	0.00
Bier127	118282	118476	120301	1.71	118282	118334.6	0.04	118282	118351.2	0.06
Ch130	6110	6121.15	6203.47	1.53	6110	6121.96	0.20	6110	6127.95	0.29
Pr144	58537	58595	58662	0.21	58537	58549.72	0.02	58537	58570.15	0.06
KroA150	26524	26676	26803	1.05	26524	26538.2	0.05	26524	26542.6	0.07
Pr152	73682	73861	73989	0.42	73682	73727.96	0.06	73682	73688.8	0.01
U159	42080	42395	42506	1.01	42080	42182.32	0.24	42080	42198.85	0.28
Rat195	2323	2341	2362	1.68	2328	2334.2	0.48	2328	2331	0.34
RroA200	29368	29731	31015	5.61	29368	29422.64	0.19	29368	29405.35	0.13
Gil262	2378	2399	2439	2.57	2379	2383.56	0.23	2379	2382.45	0.19
Pr299	48191	48662	48763	1.19	48192	48263.08	0.15	48191	48250	0.12
Lin318	42029	42633	42771	1.77	42076	42292.04	0.63	42070	42264.35	0.56
Rd400	15281	15464	15503	1.45	15324	15377.56	0.63	15311	15373.75	0.61
Pcb442	50778	51414	51494	1.41	50879	51050.12	0.54	50832	51041.7	0.52
Rat575	6773	6912	6952	2.64	6819	6854.64	1.21	6829	6847.95	1.11
U724	41910	42657	42713	1.92	42150	42302.12	0.94	42205	42357.8	1.07
Rat783	8806	9030	9126	3.63	8897	8918.28	1.28	8887	8913.25	1.22
Pr1002	259045	265987	266774	2.98	261463	262211.7	1.22	261490	262202.5	1.22
D1291	50801	52378	52443	3.23	51098	51340.84	1.06	51032	51358.7	1.10
D1655	62128	64401	65241	5.01	62784	63011.96	1.42	62779	62994.65	1.39
Nl4461	182566	18933	192574	5.48	185377	185631.1	1.68	185290	185501.7	1.61
Brd14051	469385	490432	503560	7.28	478040	478618.8	1.97	477226	477612.7	1.75
Pla33810	66048945	70299195	72420147	9.65	67868250	68038833.1	3.01	67754877	67848535.1	2.72
Average				2.43			0.53			0.49