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Table 4: Comparisons between the results for asymmetric
instances in the TSPLIB of the techniques Hard WTA
(HWTA) and Soft WTA (SWTA).
TSP
name
Optimal
solution
Average error (%)
HWTA SWTA HWTA2 SWTA2
br17 39 0.7 0
0
0
0
ftv33 1286 0.7 0
0
0
0
ftv35 1473 0.5 3.12
0.61
3.12
0.61
ftv38 1530 0.9 3.73
2.94
3.01
2.94
pr43 5620 0.7 0.29
0.20
0.05
0
ftv44 1613 0.25 2.60
2.23
2.60
2.23
ftv47 1776 0.9 3.83
5.29
3.83
2.82
ry48p 14422 0.5 5.59
2.85
1.24
0.76
ft53 6905 0.5 2.65
3.72
2.65
2.49
ftv55 1608 0.7 11.19
2.11
6.03
1.87
ftv64 1839 0.9 2.50
1.41
2.50
1.41
ft70 38673 0.7 1.74
4.10
1.74
4.10
ftv70 1950 0.5 8.77
1.70
8.56
1.70
kro124p 36230 0.7 7.66
7.27
7.66
4.36
ftv170 2755 0.25 12.16
10.56
12.16
10.56
rbg323 1326 0.7 16.14
3.02
16.14
0.23
rbg358 1163 0.7 12.73
5.76
8.17
4.73
rbg403 2465 0.9 4.71
3.53
4.71
0.65
rbg443 2720 0.9 8.05
2.98
2.17
0.85
4 CONCLUSIONS
This paper presents a modification to the application
of the 'Winner Takes All' technique in Wang’s
Recurrent Neural Network to solve the Traveling
Salesman Problem. This technique is called Soft
'Winner Takes All', because the winner neuron
receives only part of the activation of the other
competing neurons.
The results were compared with the Hard
'Winner Takes All' variation, Self-Organizing Maps
and insertion heuristics and removal of arcs,
showing improvement in most of the tested
symmetric and asymmetric problems from the
TSPLIB.
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