Show me the steps to solve Content and structure

An European Tourist Trip

You are planning a trip for your next holidays. You have already identified $9$ cities $($Paris$,$ Madrid, Lisbon, Barcelona, Amsterdam, Roma, Milan, Brussels and Berlin$)$ that you want to visit, represented by the nodes of the graph in the Figure below. The edges represent the possible flight connections between cities with the numbers being the time required to go from one city to the other. You are interested in minimizing the total time spent flying so your goal is to find the order in which you must visit all cities $($for example, Paris, then Roma, then Madrid, etc.$).$ An important input to solve the problem is that you have a round flight ticket from home to Paris, which means that your European tour must start and finish in Paris $($that is$,$ Paris must be the first city to visit and the sequence must finish in Paris$).$Thanks to your university cursus, you know that there are some decision$-$aid tools based on mathematical programming that can help you solve the problem. However, knowing that obtaining the optimal route using mathematical programming can be computationally expensive, you are more interested in finding a good route using a heuristic procedure. It is also expected to describe in detail the procedure employed to find the solution and to discuss the impact of this heuristic solution on the sequencing of cities to be visited.