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 (PDavg), ~ denotes to 0.000, accuracy % = ((meanACS − meanWFA-tsp)/meanACS) * 100.