Question

Consider the following instance of the Travelling Salesman Problem: Highlighted in bold is the following route of length62: A → C → B → E → D → A Using

the 2-opt algorithm, which of the following modifications are valid swaps that can be made to the above route to obtain a shorter route? Remove (A, C'), (B, E)and Add(А, В), (С, Е)- Remove (A, D), (C, B)and Add(С, D), (A, B). Remove (A, C'), (A, D)and add(C, D), (A, A). Remove (A, D), (B,E)and add(А, E), (В, D). Remove (A, D), (B, E)and add(А, В), (D, E).

Fig: 1

Fig: 2

Fig: 3

Fig: 4

Fig: 5

Fig: 6

Fig: 7

Fig: 8

Fig: 9

Fig: 10