Flexible optical network (FON) architectures are considered a very promising solution where spectrum resources are allocated within flexible frequency grids. Routing and spectrum allocation (RSA) in FON is known to be an NP-complete problem. So far, this problem has been optimally solved for small instances by the application of integer linear programming and has been sub-optimally solved for more realistic instances by heuristic strategies. In this paper, we introduce the application of differential evolution (DE) to the RSA problem in flexible optical networks. Comparative studies show that in many cases DE outperforms many other well-known evolutionary computational approaches. Furthermore, the method typically requires few control parameters. An illustrative example is presented showing the effectiveness and efficiency of the proposed algorithm. Different heuristics and the DE-RSA algorithm are compared. To the best of our knowledge, our work is the first application of a DE algorithm to the RSA problem.