In this talk, first of all some previous results will be presented, indicating that the evolutionary algorithms may be constructed to perform similar to the dynamic programming for a wide class of optimization problems. After that, some ideas from (Woeginger, 2000) will be displayed in order to define the class of DP-benevolent problems, where the dynamic programming implies existence of an FPTAS. The two approaches will be combined to show that if an NP optimization problem is DP-benevolent, then there exists an evolutionary algorithm which gives a fully polynomial randomized approximation scheme for the problem.