It's well known that to find a hamilton cycle is NPC, while TSP is NPH.
But it seems that for majority of graphs (density of edge > 0.1, order > 100) there is a fast algorithm to find different hamilton cycles if the graph is hamilton graph. For example, g = graphs.RandomGNP(1300,0.1), it takes 31453 seconds to find 100000 different solutions by SageMath.
Thus there is a possibility to get a solution of TSP within reasonable time.
In order to know the level of possibility, could you provide some TSP examples (answer is known but not let me know in advance) from real world?