Journal of Optimization

Research Article

Introducing Complexity Curtailing Techniques for the Tour Construction Heuristics for the Travelling Salesperson Problem

Table 5


Dataset	Optimal	Farthest insertion heuristic									Fast max difference insertion heuristic
()		()									()
()		Min	% diff.	Max	% diff.	Avg.	% diff.	Stdv	% age	Time	Min	% diff.	Max	% diff.	Avg.	% diff.	Stdv	% age	Time
(a)	(b)	(a)		(b)		(c)		(d)		(e)	(a)		(b)		(c)		(d)		(e)

Burma14	3323	3323	0.00	3442	3.58	3327.83	0.15	21.45	0.65	0.00	3323	0.00	3442	3.58	3326.97	0.12	21.36	0.64	0.00
Ulysses16	6859	6859	0.00	7082	3.25	6900.67	0.61	59.97	0.87	0.00	6859	0.00	7082	3.25	6912.50	0.78	58.89	0.86	0.00
Gr17	2085	2095	0.48	2162	3.69	2102.17	0.82	19.96	0.96	0.00	2085	0.00	2159	3.55	2095.73	0.51	21.58	1.04	0.00
GR21	2707	2707	0.00	2816	4.03	2754.80	1.77	48.57	1.79	0.00	2707	0.00	2707	0.00	2707.00	0.00	0.00	0.00	0.00
Ulysses22	7013	7013	0.00	7592	8.26	7116.03	1.47	131.65	1.88	0.00	7013	0.00	7262	3.55	7088.67	1.08	62.04	0.88	0.00
GR24	1272	1272	0.00	1387	9.04	1322.97	4.01	26.50	2.08	0.00	1272	0.00	1341	5.42	1313.93	3.30	15.82	1.24	0.00
Fri26	937	937	0.00	1021	8.96	957.77	2.22	20.49	2.19	0.00	937	0.00	958	2.24	941.40	0.47	8.00	0.85	0.00
Bayg29	1610	1628	1.12	1746	8.45	1664.53	3.39	28.17	1.75	0.00	1618	0.50	1668	3.60	1631.97	1.36	10.48	0.65	0.00
Bays29	2020	2028	0.40	2083	3.12	2035.80	0.78	12.44	0.62	0.00	2033	0.64	2068	2.38	2038.40	0.91	6.08	0.30	0.00
Dantzig42	699	712	1.86	761	8.87	738.83	5.70	13.07	1.87	0.00	705	0.86	743	6.29	711.63	1.81	8.70	1.25	0.00
Swiss42	1273	1319	3.61	1439	13.04	1371.40	7.73	31.35	2.46	0.00	1273	0.00	1346	5.73	1302.67	2.33	25.60	2.01	0.00
ATT48	10628	10845	2.04	11554	8.71	11205.10	5.43	193.80	1.82	0.00	10653	0.24	11073	4.19	10929.70	2.84	123.93	1.17	0.00
GR48	5046	5099	1.05	5441	7.83	5271.83	4.48	114.17	2.26	0.00	5109	1.25	5295	4.93	5195.73	2.97	61.40	1.22	0.00
HK48	11461	11474	0.11	12513	9.18	11998.70	4.69	316.11	2.76	0.00	11556	0.83	11982	4.55	11611.10	1.31	94.18	0.82	0.00
Eil51	426	437	2.58	462	8.45	450.77	5.81	6.99	1.64	0.00	434	1.88	443	3.99	439.67	3.21	2.33	0.55	0.00
Berlin52	7542	7542	0.00	8677	15.05	8214.50	8.92	316.31	4.19	0.00	7604	0.82	8425	11.71	7948.97	5.40	239.48	3.18	0.00
Brazil58	25395	25664	1.06	27452	8.10	26529.20	4.47	378.63	1.49	0.00	25717	1.27	26546	4.53	26298.90	3.56	196.66	0.77	0.00
ST70	675	696	3.11	736	9.04	710.30	5.23	9.85	1.46	0.00	682	1.04	717	6.22	700.30	3.75	9.18	1.36	0.00
Eil76	538	570	5.95	598	11.15	580.40	7.88	9.64	1.79	0.00	556	3.35	577	7.25	566.20	5.24	5.40	1.00	0.00
PR76	108159	110516	2.18	126235	16.71	115154.00	6.47	4255.54	3.93	0.00	109796	1.51	115392	6.69	111760.00	3.33	1756.05	1.62	0.00
GR96	55209	56854	2.98	63009	14.13	59177.70	7.19	1419.23	2.57	0.00	55738	0.96	59941	8.57	57658.00	4.44	801.67	1.45	0.00
Rat99	1211	1257	3.80	1382	14.12	1313.20	8.44	32.08	2.65	0.00	1244	2.73	1296	7.02	1272.03	5.04	12.63	1.04	0.00
KroA100	21282	22026	3.50	23487	10.36	22608.10	6.23	392.16	1.84	0.00	21478	0.92	22599	6.19	21628.70	1.63	217.73	1.02	0.00
KroB100	22141	22693	2.49	24518	10.74	23508.10	6.17	396.25	1.79	0.00	22211	0.32	23405	5.71	22949.90	3.65	282.76	1.28	0.00
KroC100	20749	21105	1.72	22599	8.92	21853.70	5.32	375.72	1.81	0.00	20749	0.00	21838	5.25	21045.70	1.43	225.82	1.09	0.00
KroD100	21294	21745	2.12	23374	9.77	22528.60	5.80	376.69	1.77	0.00	21403	0.51	22708	6.64	21880.20	2.75	286.35	1.34	0.00
KroE100	22068	22514	2.02	24147	9.42	23229.20	5.26	484.60	2.20	0.00	22179	0.50	23195	5.11	22749.20	3.09	300.23	1.36	0.00
RD100	7910	8255	4.36	8936	12.97	8619.23	8.97	167.00	2.11	0.00	7965	0.70	8380	5.94	8158.47	3.14	111.72	1.41	0.00
Eil101	629	660	4.93	701	11.45	679.60	8.04	10.61	1.69	0.00	648	3.02	683	8.59	664.60	5.66	7.90	1.26	0.00
Lin105	14379	14863	3.37	16088	11.89	15435.30	7.35	309.15	2.15	0.00	14402	0.16	15179	5.56	14708.30	2.29	182.60	1.27	0.00
PR107	44303	45030	1.64	45933	3.68	45450.50	2.59	245.78	0.55	0.00	44489	0.42	45420	2.52	44925.80	1.41	216.48	0.49	0.00
GR120	6942	7162	3.17	7817	12.60	7462.97	7.50	162.80	2.35	0.00	7164	3.20	7494	7.95	7323.47	5.50	79.69	1.15	0.00
PR124	59030	60305	2.16	65845	11.54	62875.70	6.51	1339.81	2.27	0.00	59767	1.25	62202	5.37	60323.20	2.19	625.42	1.06	0.00
Bier127	118282	123796	4.66	130733	10.53	126795.00	7.20	1891.57	1.60	0.00	121130	2.41	131232	10.95	123455.00	4.37	1996.69	1.69	0.00
CH130	6110	6335	3.68	6884	12.67	6556.80	7.31	139.36	2.28	0.00	6328	3.57	6686	9.43	6441.50	5.43	78.33	1.28	0.00
PR136	96772	102573	5.99	107287	10.87	105143.00	8.65	1129.12	1.17	0.00	99960	3.29	104166	7.64	102520.00	5.94	975.59	1.01	0.00
GR137	69853	73391	5.06	81011	15.97	76135.90	8.99	1606.32	2.30	0.00	71773	2.75	74864	7.17	72760.50	4.16	785.68	1.12	0.00
PR144	58537	59336	1.36	64705	10.54	62041.30	5.99	1383.72	2.36	0.00	59005	0.80	63056	7.72	59680.10	1.95	807.68	1.38	0.00
CH150	6528	6864	5.15	7479	14.57	7094.67	8.68	148.20	2.27	0.00	6733	3.14	7103	8.81	6901.07	5.71	97.47	1.49	0.00
kroA150	26524	27407	3.33	29394	10.82	28514.90	7.51	544.26	2.05	0.00	27066	2.04	28285	6.64	27593.20	4.03	284.44	1.07	0.00
kroB150	26130	27337	4.62	28912	10.65	27859.30	6.62	375.99	1.44	0.00	26322	0.73	27868	6.65	27049.60	3.52	392.87	1.50	0.00
PR152	73682	74827	1.55	77967	5.82	76401.20	3.69	808.26	1.10	0.00	74029	0.47	76257	3.49	74715.40	1.40	615.89	0.84	0.00
U159	42080	44506	5.77	49335	17.24	46856.30	11.35	1195.20	2.84	0.00	43367	3.06	45621	8.41	44070.50	4.73	527.23	1.25	0.00
SI175	21407	21751	1.61	22193	3.67	21911.90	2.36	119.10	0.56	0.00	21527	0.56	21883	2.22	21707.30	1.40	112.23	0.52	0.00
Rat195	2323	2503	7.75	2686	15.63	2585.10	11.28	42.01	1.81	0.00	2487	7.06	2588	11.41	2525.47	8.72	25.35	1.09	0.00
d198	15780	16277	3.15	17207	9.04	16696.60	5.81	311.97	1.98	0.00	16015	1.49	16621	5.33	16214.40	2.75	161.35	1.02	0.00
KroA200	29368	30533	3.97	32481	10.60	31225.90	6.33	448.47	1.53	0.00	30258	3.03	31662	7.81	31002.70	5.57	372.36	1.27	0.00
KroB200	29437	31227	6.08	33304	13.14	32006.80	8.73	427.13	1.45	0.00	30387	3.23	31877	8.29	30987.90	5.27	438.01	1.49	0.00
GR202	40160	42038	4.68	45263	12.71	43423.10	8.13	725.72	1.81	0.00	40889	1.82	43698	8.81	41942.20	4.44	646.74	1.61	0.00
TS225	126643	134365	6.10	143384	13.22	139859.00	10.44	2128.75	1.68	0.00	135470	6.97	138995	9.75	136429.00	7.73	1115.29	0.88	0.00
TSP225	3916	4182	6.79	4501	14.94	4292.40	9.61	78.76	2.01	0.00	4118	5.16	4292	9.60	4187.50	6.93	45.32	1.16	0.00
PR226	80369	81020	0.81	84593	5.26	82441.70	2.58	848.57	1.06	0.00	81598	1.53	83216	3.54	82492.30	2.64	296.77	0.37	0.00
GR229	134602	142714	6.03	154567	14.83	147270.00	9.41	3066.84	2.28	0.00	138704	3.05	145318	7.96	141429.00	5.07	1740.97	1.29	0.00
Gil262	2378	2507	5.42	2683	12.83	2597.10	9.21	42.29	1.78	0.00	2448	2.94	2548	7.15	2514.13	5.72	24.39	1.03	0.00
PR264	49135	53814	9.52	55504	12.96	54821.70	11.57	425.79	0.87	0.00	53021	7.91	55170	12.28	54211.90	10.33	508.62	1.04	0.00
A280	2579	2847	10.39	3043	17.99	2931.93	13.68	50.88	1.97	0.00	2691	4.34	2861	10.93	2792.60	8.28	44.26	1.72	0.00
PR299	48191	51625	7.13	56160	16.54	53082.40	10.15	985.20	2.04	0.00	48763	1.19	52054	8.02	50174.00	4.11	747.97	1.55	0.00
Lin318	42029	44730	6.43	46981	11.78	45840.00	9.07	575.64	1.37	0.00	43516	3.54	45306	7.80	44471.20	5.81	506.01	1.20	0.00
Linhp318	41345	44730	8.19	46981	13.63	45840.00	10.87	575.64	1.39	0.00	43516	5.25	45306	9.58	44471.20	7.56	506.01	1.22	0.00
RD400	15281	16441	7.59	17139	12.16	16724.50	9.45	164.65	1.08	0.00	15876	3.89	16431	7.53	16132.40	5.57	128.14	0.84	0.00
FL417	11861	12201	2.87	13147	10.84	12657.10	6.71	245.19	2.07	0.00	12061	1.69	12214	2.98	12171.80	2.62	32.24	0.27	0.00
GR431	171414	181584	5.93	200082	16.72	191434.00	11.68	5458.44	3.18	0.00	177362	3.47	183560	7.09	180437.00	5.26	1412.80	0.82	0.00
PR439	107217	116581	8.73	124415	16.04	120425.00	12.32	2176.87	2.03	0.00	110900	3.44	117753	9.83	114517.00	6.81	1734.12	1.62	0.00
PCB442	50778	55660	9.61	59032	16.26	57419.30	13.08	736.18	1.45	0.00	54452	7.24	56840	11.94	55421.30	9.14	550.44	1.08	0.00
D493	35002	37545	7.27	39044	11.55	38212.00	9.17	440.14	1.26	0.00	36402	4.00	37732	7.80	36984.00	5.66	294.40	0.84	0.00
ATT532	27686	29670	7.17	31101	12.33	30257.50	9.29	360.98	1.30	0.00	28797	4.01	29796	7.62	29293.20	5.81	242.24	0.87	0.00
Ali535	202339	216002	6.75	238252	17.75	227611.00	12.49	6102.76	3.02	0.01	210768	4.17	221967	9.70	216135.00	6.82	2858.38	1.41	0.01
SI535	48450	49496	2.16	50025	3.25	49816.20	2.82	148.87	0.31	0.00	49020	1.18	49346	1.85	49167.90	1.48	83.64	0.17	0.00
PA561	2763	3061	10.79	3204	15.96	3118.40	12.86	29.61	1.07	0.01	3007	8.83	3141	13.68	3092.17	11.91	33.81	1.22	0.01
U574	36905	40097	8.65	42081	14.03	40969.00	11.01	370.18	1.00	0.01	38752	5.00	39928	8.19	39252.00	6.36	346.62	0.94	0.01
Rat575	6773	7374	8.87	7594	12.12	7508.17	10.85	53.59	0.79	0.01	7191	6.17	7444	9.91	7300.83	7.79	58.16	0.86	0.01
P654	34643	35659	2.93	41131	18.73	37016.60	6.85	1376.23	3.97	0.01	35334	1.99	36176	4.43	35971.10	3.83	207.24	0.60	0.01
D657	48912	52482	7.30	55079	12.61	53826.00	10.05	650.07	1.33	0.01	51459	5.21	53624	9.63	52371.20	7.07	430.21	0.88	0.01
GR666	294358	324349	10.19	341937	16.16	332601.00	12.99	4859.02	1.65	0.01	311264	5.74	328227	11.51	317068.00	7.72	3965.46	1.35	0.01
U724	41910	45425	8.39	47487	13.31	46237.80	10.33	470.09	1.12	0.01	44499	6.18	45481	8.52	44946.70	7.25	277.31	0.66	0.01
Rat783	8806	9607	9.10	9959	13.09	9809.83	11.40	70.02	0.80	0.01	9419	6.96	9665	9.75	9532.33	8.25	62.85	0.71	0.01
DSJ1000	18659688	2.04E + 07	9.33	2.12E + 07	13.46	20705300.00	10.96	199033.00	1.07	0.03	1.97E + 07	5.63	2.02E + 07	8.51	19916900.00	6.74	138698.00	0.74	0.02
DSJ1000_Ceil	18660188	2.04E + 07	9.33	2.12E + 07	13.46	20705900.00	10.96	199248.00	1.07	0.03	1.97E + 07	5.63	2.02E + 07	8.51	19914600.00	6.72	136854.00	0.73	0.02
Pr1002	259045	279938	8.07	290550	12.16	285664.00	10.28	2895.93	1.12	0.03	270964	4.60	280759	8.38	276781.00	6.85	2215.42	0.86	0.02
Si1032	92650	98444	6.25	99088	6.95	98819.50	6.66	154.80	0.17	0.03	95552	3.13	96430	4.08	96050.60	3.67	196.73	0.21	0.02
U1060	224094	245679	9.63	254238	13.45	248951.00	11.09	2035.57	0.91	0.03	235078	4.90	241873	7.93	238367.00	6.37	1861.23	0.83	0.02
Vm1084	239297	262043	9.51	274616	14.76	267609.00	11.83	2850.55	1.19	0.03	253819	6.07	262898	9.86	256516.00	7.20	1871.48	0.78	0.02
Pcb1173	56892	64918	14.11	66795	17.41	65640.20	15.38	442.92	0.78	0.04	62530	9.91	64149	12.76	63103.30	10.92	358.86	0.63	0.02
D1291	50801	60221	18.54	63234	24.47	61956.00	21.96	614.26	1.21	0.05	57501	13.19	59945	18.00	58810.80	15.77	641.59	1.26	0.03
RL1304	252948	292602	15.68	308095	21.80	301514.00	19.20	3688.25	1.46	0.05	279047	10.32	291228	15.13	285207.00	12.75	3363.99	1.33	0.03
RL1323	270199	312400	15.62	328087	21.42	320036.00	18.44	4117.85	1.52	0.05	297661	10.16	307528	13.82	302587.00	11.99	2445.58	0.91	0.03
NRW1379	56638	62208	9.83	63899	12.82	62863.50	10.99	420.18	0.74	0.06	60170	6.24	61393	8.40	60785.70	7.32	279.13	0.49	0.03
FL1400	20127	20949	4.08	21909	8.85	21338.30	6.02	273.56	1.36	0.06	20516	1.93	21201	5.34	20786.70	3.28	213.61	1.06	0.03
U1432	152970	168810	10.35	174677	14.19	171655.00	12.21	1166.59	0.76	0.06	165373	8.11	169884	11.06	167195.00	9.30	1092.88	0.71	0.03
FL1577	22249	25155	13.06	27824	25.06	26228.30	17.89	514.47	2.31	0.07	24030	8.00	25892	16.37	24835.70	11.63	445.83	2.00	0.04
D1655	62128	71507	15.10	73675	18.59	72508.90	16.71	530.78	0.85	0.08	68217	9.80	70258	13.09	69165.90	11.33	447.10	0.72	0.04
VM1748	336556	371239	10.31	381960	13.49	376862.00	11.98	3094.47	0.92	0.10	355083	5.50	364325	8.25	359501.00	6.82	2503.97	0.74	0.05
U1817	57201	67612	18.20	69628	21.73	68406.70	19.59	596.43	1.04	0.10	63383	10.81	65642	14.76	64709.40	13.13	519.68	0.91	0.05
RL1889	316536	365077	15.34	376387	18.91	371580.00	17.39	3230.94	1.02	0.12	348074	9.96	359023	13.42	352505.00	11.36	2975.08	0.94	0.06
D2103	80450	98109	21.95	100527	24.96	99264.90	23.39	657.60	0.82	0.14	93544	16.28	95910	19.22	94908.90	17.97	527.46	0.66	0.07
U2152	64253	75721	17.85	77597	20.77	76732.50	19.42	527.56	0.82	0.15	72492	12.82	74131	15.37	73311.70	14.10	430.31	0.67	0.07
U2319	234256	247881	5.82	251176	7.22	250028.00	6.73	715.57	0.31	0.17	245939	4.99	248584	6.12	247465.00	5.64	687.33	0.29	0.09
Pr2392	378032	428627	13.38	438782	16.07	432695.00	14.46	2243.77	0.59	0.19	406210	7.45	417522	10.45	411749.00	8.92	2681.97	0.71	0.09
Pcb3038	137694	156708	13.81	159518	15.85	158069.00	14.80	586.58	0.43	0.32	151346	9.91	153766	11.67	152435.00	10.71	603.48	0.44	0.15
FL3795	28772	33124	15.13	35354	22.88	34331.30	19.32	542.79	1.89	0.49	31317	8.85	33137	15.17	32407.00	12.63	585.13	2.03	0.24
FNL4461	182566	202328	10.82	204937	12.25	203925.00	11.70	601.55	0.33	0.74	196918	7.86	198936	8.97	197617.00	8.24	495.01	0.27	0.32
RL5915	565530	683054	20.78	697158	23.28	690217.00	22.05	3493.67	0.62	1.39	648152	14.61	662852	17.21	656416.00	16.07	3429.91	0.61	0.56
RL5934	556045	660399	18.77	681665	22.59	672930.00	21.02	4608.88	0.83	1.40	630512	13.39	649307	16.77	641010.00	15.28	3805.45	0.68	0.56
pla7397	23260728	26066700	12.06	26640000	14.53	26382900.00	13.42	143431.00	0.62	2.32	25178800	8.25	25559100	9.88	25383600.00	9.13	87578.50	0.38	0.86
rl11849	923288	1093120	18.39	1108780	20.09	1102520.00	19.41	3886.70	0.42	10.11	1046110	13.30	1060200	14.83	1054670.00	14.23	3259.40	0.35	2.23
usa13509	19982859	22318200	11.69	22561500	12.90	22442600.00	12.31	59189.90	0.30	15.01	21566100	7.92	21768200	8.93	21673900.00	8.46	50429.90	0.25	2.88
brd14051	469385	522027	11.22	527320	12.34	524714.00	11.79	1160.75	0.25	16.43	506838	7.98	510569	8.77	508872.00	8.41	910.74	0.19	3.12
d15112	1573084	1750830	11.30	1762650	12.05	1756490.00	11.66	2965.69	0.19	19.11	1698080	7.95	1707830	8.57	1704060.00	8.33	2482.61	0.16	3.61

			6.84		12.89		9.51		1.52	0.64		4.30		8.27		6.02		0.99	0.14