C++ Neural Networks and Fuzzy Logic: Preface

•

Tour 1. 1 − 2 − 3 − 4 − 1 In this tour city 2 is visited first, followed by city 3, from where the

salesperson goes to city 4, and then returns to city 1. For city 2, the corresponding ordered array is (1,

0, 0, 0), because city 2 is the first in this permutation of cities. Then x

21

 = 1, x

22

 = 0, x

23

 = 0, x

24

 = 0.

Also (0, 1, 0, 0), (0, 0, 1, 0), and (0, 0, 0, 1) correspond to cities 3, 4, and 1, respectively. The total

distance of the tour is d

12

 + d

23

 + d

34

 + d

41

= 10 + 6 + 9 + 7 = 32.

•

Tour 2. 1 − 3 − 4 − 2 − 1

•

Tour 3. 1 − 4 − 2 − 3 − 1

There seems to be some discrepancy here. If there is one, we need an explanation. The discrepancy is that we

can find many more tours that should be valid because no city is visited more than once. You may say they are

distinct from the three previously listed. Some of these additional tours are: