The non-fixed destination multi depot multiple traveling salesmen problem (MmTSP) in which more than one salesmen depart from several starting cities (depots) and having returned to the one of starting city (depot) that the number of cities in each depot remain the same at the end as it was in the beginning, form tours so that each city is visited with exactly one salesman and the tour lengths stay within certain limits. This problem is of a great complexity and few investigations have been done on it before. In this paper we apply three meta-heuristics algorithms as genetic algorithms (GAs), tabu search (TS) and simulated annealing (SA) for this problem and compare the theoretical properties and computational performance of these algorithms with the optimal answers obtained by solving the problems by Lingo 8. Computational analysis shows that the SA and TS have results very close to optimal solution in medium size and large/very large-sized problems respectively.