C++ Neural Networks and Fuzzy Logic: Preface

Table 15.1 Energy Levels for Six of the Valid Tours

Tour #Non−Zero x’sValue for the Last TermEnergy LevelComment

1x

14

, x

21

, x

32

, x

43

32321 − 2 − 3 − 4 − 1 tour

2x

14

, x

23

, x

31

, x

42

45451 − 3 − 4 − 2 − 1 tour

3x

14

, x

22

, x

33

, x

41

39391 − 4 − 2 − 3 − 1 tour

4x

14

, x

21

, x

33

, x

42

45451 − 2 − 4 − 3 − 1 tour

5x

13

, x

21

, x

34

, x

42

39393 − 2 − 4 − 1 − 3 tour

6x

11

, x

24

, x

33

, x

42

32322 − 1 − 4 − 3 − 2 tour

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 IDG Books Worldwide, Inc.

C++ Neural Networks and Fuzzy Logic:Preface

Example of a Traveling Salesperson Problem for Hand Calculation

340

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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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Neural Network for Traveling Salesperson Problem

Hopfield and Tank used a neural network to solve a traveling salesperson problem. The solution you get may

not be optimal in certain instances. But by and large you may get a solution close to an optimal solution. One

cannot find for the traveling salesperson problem a consistently efficient method of solution, as it has been

proved to belong to a set of problems called NP−complete problems. NP−complete problems have the

distinction that there is no known algorithm that is efficient and practical, and there is little likelihood that

such an algorithm will be developed in the future. This is a caveat to keep in mind when using a neural

network to solve a traveling salesperson problem.