For TSP there are well known heuristic and approximation solutions which run in low-polynomial time, like Christofides / 2-OPT and so on.
I need a practical, fast algorithm, ideally sub-quadratic complexity, to solve the minimum weighted set cover problem (which is NP hard). It solves subproblems in a genetic algorithm so needs to be fast rather than optimal. Are there any standard algorithms used to solve this?