In (a) and (b), assuming a 2-exchange transformation operator, connect solutions A and B, which are TSP tours in path representation, to their possible neighbors among tours C, D, E, F, G
(a) A: 1 2 3 4 5 6 7
C: 1 3 5 7 2 4 6
D: 1 2 5 4 3 6 7
E: 2 3 1 7 5 4 6
F: 4 1 7 5 3 2 6
G: 1 2 3 7 6 5 4
(b) B: 1 3 2 7 5 4 6
C: 1 3 5 7 2 4 6
D: 1 2 5 4 3 6 7
E: 2 3 1 7 5 4 6
F: 4 1 7 5 3 2 6
G: 1 2 3 7 6 5 4
I have no clue what this is asking me to do.
Definitions (inferred from the problem text, maybe you discussed this in class too)
TSP tour in path representation:
An ordered sequence of the digits 1 thru 7, each digit cited once and only once.
Each digit represents a city visited by the Traveling Salesperson.
For example D: 1 2 5 4 3 6 7, indicates that Salesperson starts in city 1, goes to city2,
then city 5... and ends in city 7.
It is probably useful at this point to introduce the concept of a 'stop' and to label these with lowercase letters, a trhu g. (no relation at all with the uppercase letters used to identify various paths in the problem).
In the D path, the a stop is city 1, the c stop is city 5 etc.
a 2-exchange transformation operator
An operation which transforms a TSP path by exchanging exactly two cities (or, more precisely, by swapping the city for two of the stops).
A 2-exchange Transformation operation can therefore be understood as an operation which takes three arguments: a Path X, two stop indexes m,n, and returns the path X' where the cities at m and n have been swaped.
If we call this operation Swp(), we can write
Swp(A, c, e) = 1 2 5 4 3 6 7
The assignment (Your mission, would you accept it ;-) )
connect solutions A and B, which are TSP tours in path representation, to their possible neighbors among tours C, D, E, F, G
I'm guessing the requirement it is to identify among C,D, E F and G (upper case i.e. the Paths) which are "neighbor" paths of A (or of B), i.e. which of these can be derived from A (or from B) with a single Swp() operation (and probably to provide the said operation parameters).
By extension one may interpret the assignment as one where one needs to find a (not the as there may be several) list of Swp() operations needed to go from A to another path, in a minimal number of steps.