Is there a way to find very rough minimum and maximum estimates for the travelling salesman problem? The estimates only need to be within the roughly same magnitude, but it's important that the minimum estimate is lower (or equal) to the actual distance and that the maximum estimate is higher (or equal) to the actual distance.
EDIT: Metric TSP unfortunately does not apply. To add some context: I'm searching for non-dominated fronts (pareto fronts) for a Multiobjective TSP, e.g. optimizing for multiple variables like travel time and distance. I'm using NSGA-II which requires an upper and lower bound for each objective function, which translates into rough estimates for single-objective TSP, with the constraint that the upper estimate has to be higher than the real max distance and vice versa.