The Travelling Salesman Problem $($TSP$)$ is$,$ again, a classic NP$-$hard problem in optimization, and

is commonly stated as: "Given a list of cities and the distances between each pair of cities, what is the shortest

possible route that visits each city?"

Consider the problem represented as a sequence of cities, $1..$n$.$ Note that a valid representation for TSP must

consist of a permutation of the elements $\{1,$dots,$n\}$ so that each element appears once and only once in the string

$($i$.$e$.$ no city is visited twice and no cities are skipped$).$ For simplicity, suppose that the TSP "tour" can begin

and end in any city.

Describe an effective solution to TSP $($as described above$)$ using a genetic algorithm. Please be sure that you

address the details for each of the essential components in a GA; be specific about how you will apply the GA

operations to adhere to the aforementioned "valid representation."