C++ Neural Networks and Fuzzy Logic: Preface

C++ Neural Networks and Fuzzy Logic

by Valluru B. Rao

MTBooks, IDG Books Worldwide, Inc.

ISBN: 1558515526   Pub Date: 06/01/95

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Output from a Sample Program Run

The program, as mentioned, is created for the Kohonen approach to the traveling salesperson problem for five

cities. There is no user input from the keyboard. All parameter values are given to the program with

appropriate statements in the function main. A scale factor of 0.05 is given to apply to the gain parameter,

which is given as 1. Initially, the distance of each neuron weight vector from an input vector is set at 1000, to

facilitate finding the closest for the first time. The cities with coordinates (7,3), (4,6), (14,13), (0,12), (5,10)

are specified for input vectors.

The tour found is not the one in natural order, namely 0 ’ 1 ’ 2 ’ 3 ’ 4 ’ 0, with a distance of 43.16. The tour

found has the order 0 ’ 3 ’ 1 ’ 4 ’ 2 ’ 0, which covers a distance of 44.43, which is slightly higher, as shown in

Figure 15.2. The best tour, 0 ’ 2 ’ 4 ’ 3 ’ 1 ’ 0 has a total distance of 38.54.

Figure 15.2

  City placement and tour found for TSP.

Table 15.2 gives for the five−city example, the 12 (5!/10) distinct tour distances and corresponding

representative tours. These are not generated by the program, but by enumeration and calculation by hand.

This table is provided here for you to see the different solutions for this five−city example of the traveling

salesperson problem.

Table 15.2 Distances and Representative Tours for Five−City Example