This paper describes the use of discrete graphical editing operations to dynamically fit hierarchical structural models to input data. We use the tree adjoining grammar developed by Joshi [l] as a prototypical structural model, and realise the editing process using a genetic algorithm. The novelty of our approach lies firstly in the use of the edit distance between the ordered frontier nodes of a tree and a set of dictionaries of legal labels derived from the input as a cost function. Secondly, we apply genetic algorithms to tree adjoining grammars with the introduction of a new editing operation. We demonstrate the utility of the method on a simple natural language processing problem.