The generalized lambda distribution, λ,λ,λ,λ(GLD ) 1 432 is a four-parameter family that has been used for fitting distributions to a wide variety of data sets. Minimization through traditional calculus-based methods has been implemented with relative success, but due to computational and theoretical shortcomings of those methods, the moment space has been limited. This paper solve those troubles by using Genetic Algorithms (search algorithms based on the mechanics of natural selection and natural genetics) applied to the methods of moments. Examples of better solutions than the ones find out with traditional calculusbased methods are included.