This paper presents a method for optimizing stop-bands in periodic waveguides by combining the wave finite element (WFE) approach with evolutionary optimization algorithms. The WFE method enables efficient dynamic modelling by representing a periodic structure through its unit cell and expressing wave motion in terms of wave amplitudes. This efficiency makes the approach suitable for computationally demanding optimization tasks. Two evolutionary algorithms are employed to optimize the stop-band characteristics over a broad frequency range, enhancing robustness under varying excitation conditions. A numerical example is used to demonstrate the approach and to explore the performance of each evolutionary algorithm. The framework is general and can be extended to more complex periodic systems.