This paper analyzes the performance of the popular heuristic methods ‘Simulated Annealing (SA)’ and ‘Genetic Algorithm (GA)’  on  the symmetric TSP.  TSP is a well-known combinatorial optimization problem in NP-complete class. NP-completeness of TSP originates many specific approximation algorithms to find optimal or near optimal solutions in a reasonable time. On the other hand, both SA and GA are general purpose heuristic methods that are applicable to almost every kind of problem whose solution lies inside a search space. The performance of SA and GA depends on many factors such as the nature of the problem, design of the algorithm, parameter values, etc. In this paper, a GA and an SA algorithm are given  and their performance with re-spect to several factors is analyzed. The algorithms are tested on some benchmark problems (TSPLIB) which are obtainable via Internet from http://elib.zib.de/pub/mp-testdata/tsp/tsplib/tsp/index.html.