It is usually said that genetic algorithm should be used when nothing else works. In practice, genetic algorithm are very often used for large sized global optimization problems, but are not very efficient for local optimization problems. The Nelder-Mead simplex algorithm has some common characteristics with genetic algorithm, but it can only find a local optimum close to the starting point. In this article, a combined Nelder-Mead Simplex and Genetic algorithm is introduced and tested on classical test functions on which both genetic algorithm or local optimization techniques are not efficient when separately used.