Question

Question 2 Consider the 5-city travelling salesman problem shown below. The distance between each pair of cities appears on the are connecting ts ds the same in either direction (a) Find a tour by using the nearest-neighbour heuristic starting at city 3. Give the steps and the tour obtained (b) Find a tour by using the cheapest-insertion heuristic starting at city 3. Give the steps and the tour obtained (c) Compare the tours. 13 19 16 4 18 15 23

Answer 1

Nearest meighbeur Start at veater 3. Neighbeuas are R 4,s. op tese the ne So we qet 1个 . Now con "de γ the neighbour Mof the edae 2-4 has least weight t ahe 45 has least weight Hemu l4 13

Nergubours 5 i5 weightSSo and 3 b . inally we will jan the ed ge I- 3 oue -ton as T hsufonewe get 3--4-5-1-3 stance= 14t/3 opbma b Cheapest iotersechin Renisti'c start on 3. Venter dlose to 3 So Consice the Subtour 3--3

To nd ut the imseot vertex to the edge 3- 23+21-14 30 value is at k-4 Minimum

Nouw at edge a-4 =as = RI + 18-13 at 3- 4 a4 35 4 3 23 +18-16 2-3 afe

53 as Minimum value =RR → rep la ce ed 2-3 and in sest vete χ l. 3-1-2-4-3 . at 2- 4 at edgc 34 at edge 3 = 15 t 23-19 = 19

at edge -2 Here replacina the by ve. te χ 5 has -the game effect We i rep lace -2 by S es 1-3 0r 1- le./, ουγ toυγ ts 3-1-5-2-4-3 Optimal distance - Is 21 +13 16

st we obtained th tous 3-2-4-5-1-3. part (b, we obtained the tou 3-1-5--43 Amd we obtained that the op-timal distance is largu wm Seuond case. ie, Optimal distane obtained via Cheapest -intersection heurishic s Mone than that via meas est meigbour heuaistic.