The most common heuristics to solve the TSP problem (in particular the Kernighan–Lin heuristic) require to work on a randomly generated tour and to improve the solution starting from that. However, the only way I came up with to do that is to generate a random permutation of the vertices and to check if it is a solution or not.
For large instances of the problem (for example 1000 vertices) this process can take a while. Is there another smart way to generate a random tour for TSP problem faster?? Note that I'm looking for a tour, no matter the cost, and not an optimal solution.
Thanks in advance