One of the problems that have been solved by DNA computing - as a kind of bio-computing techniques - is traveler salesman problem (TSP) which is a typical optimization problem. Previously proposed DNA computing methods for solving TSP suppose that all intercity costs are the same, so the minimization of the traveling cost has not been considered. On the other hand the earlier algorithms have some bugs that may fail in experimental environments. In this paper we have modified the previous algorithm to minimize the traveling cost in solving TSP. Also we have debugged the algorithms for an exact operation in experimental environments