For the symmetric TSP problem with the distance matrix given in Table $2($where the

entry i$,$ j represents the distance from city i to city j$)$ find the optimum tour using

hill climbing, with a $2-$change neighborhood $($i$.$e$.$ swap $2$ non$-$adjacent edges$),$ starting

at tour $132451.$ Show all steps.

City $1$ City $2$ City $3$ City $4$ City $5$

City $1$ $8131817$

City $28$ $266$

City $3132$ $1416$

City $418614$ $16$

City $51761616$

Table $2$: Distance matrix for Problem $2.$

$2$