A Water Flow-Like Algorithm for the Travelling Salesman Problem

Table 3

Results of the comparison between ACS and WFA-TSP algorithms in small and medium TSP datasets.

Datasets	ACS							WFA-TSP							-value		Improvement %
	Best	Worst	Mean	Std.	Avg. iteration	Avg. time	PDavg	Best	Worst	Mean	Std.	Avg. iteration	Avg. time	PDavg	Time	Solution quality	Accuracy	Time
eil51	427	434	428.80	2.82	5133.5	1.11	0.66	426	427	426.40	0.52	939.5	0.22	0.09	~	0.027	0.56	79.8
eil76	538	555	545.70	6.11	5327.1	2.13	1.43	538	538	538.00	0.00	1638.5	0.55	0.00	0.006	0.003	1.41	74.0
kroA100	21292	22255	21,585.60	311.51	4546.9	2.84	1.43	21282	21282	21,282.00	0.00	1057.7	0.56	0.00	0.001	0.013	1.81	80.2
eil101	638	651	642.30	3.65	5624.2	3.55	2.11	629	638	630.70	2.83	2648.8	1.23	0.27	~	~	1.26	65.2
bier127	118616	121876	119,965.10	1,134.08	5654.2	5.13	1.42	118282	118728	118,451.40	177.62	5616.9	3.56	0.14	0.092	0.003	2.06	30.6
ch130	6184	6447	6,263.00	89.22	6720.3	6.61	2.50	6110	6201	6,133.90	29.29	4892.1	3.45	0.39	0.011	0.004	1.23	47.8
ch150	6556	6756	6,623.50	59.13	7373.7	9.42	1.46	6528	6559	6,542.20	14.22	4204.4	3.53	0.22	~	0.001	2.04	62.5
kroA150	26886	27437	27,122.40	170.31	7217.1	9.33	2.26	26524	26719	26,568.40	58.45	4901.8	4.41	0.17	~	~	1.91	52.7
kroA200	29691	30556	30,011.90	295.79	7299.7	16.06	2.19	29368	29744	29,438.20	114.84	6774.9	9.81	0.24	0.001	~	2.69	38.8
lin318	43119	44089	43,666.10	313.43	8567.7	39.40	3.90	42278	42946	42,490.10	208.54	7695.3	23.18	1.10	~	~	2.06	41.1
rat575	7198	7398	7,293.60	62.71	9712.4	151.50	7.69	6971	7042	7,000.80	21.73	9090.8	79.43	3.36	~	~	4.01	47.5
rat783	9319	9448	9,380.40	35.49	9588.8	287.10	6.52	9126	9256	9,180.20	40.79	9535	147.65	4.25	~	~	2.13	48.5
u1060	257839	259794	258944.30	572.93	9398.3	474.10	15.55	230481	231887	231401.50	478.10	9608.6	317.62	3.26	~	~	10.64	33.0
fl1400	21014	21705	21321.80	254.23	9947.1	879.60	5.94	20365	20523	20449.00	50.46	9095.1	571.01	1.60	~	~	4.09	35.0
d1655	68602	71263	70128.90	1058.69	9952.8	1217.30	12.88	64313	65406	64878.60	344.25	9673.3	746.34	4.43	~	~	7.49	38.6
u1817	70236	71021	70520.00	253.51	9400.9	1324.10	23.28	59713	60839	60155.00	339.21	9607.6	980.08	5.16	~	~	14.70	25.9
d2103	85539	106793	92467.50	8141.66	9880.4	1883.40	14.94	81769	84547	82769.70	883.40	9472.1	1240.28	2.88	~	0.006	10.49	34.1
fl3795	30991	35073	32589.40	1139.27	9951.4	6204.00	13.27	29400	29805	29578.80	135.70	9376	4971.05	2.80	~	~	9.24	19.8
The overall average improvement																	4.4	47.5

Note: minimum (Min), maximum (Max), standard deviation (std.), the percentage deviations of the average with the best-known solution (PD_avg), ~ denotes to 0.000, accuracy % = ((mean_ACS  − mean_WFA-tsp)/mean_ACS) * 100.