  Graph matching is one of the most important problems in graph theory and
combinatorial optimization, with many applications in various domains. Although
meta-heuristic algorithms have had good performance on many NP-Hard and
NP-Complete problems, for this problem there are not reported superior
solutions by these algorithms. The reason of this inefficiency has not been
investigated yet. In this paper we show that simulated annealing as an
stochastic optimization method is unlikely to be even close to the optimal
solution for this problem. In addition to theoretical discussion, the
experimental results also verified our idea; for example, in two sample graphs,
the probability of reaching to a solution with more than three correct matches
is about $0.02$ in simulated annealing.
