Ensuring the correctness of model transformations is a critical concern in Model-Driven Engineering, as it directly conditions the reliability of the software development activities that depend on them. To validate the correctness of model transformation processes, it is necessary to have a representative and diverse set of input testing models. However, manually constructing such a set is costly and error-prone. In this work, we propose a multi-start constructive procedure for the automatic generation of test model sets. The method starts by building a trivial feasible model and then constructs new ones by applying different operators. By identifying the feasible region of the search space, the method is able to efficiently generate feasible models. The proposed method is evaluated in comparison to the state of the art on three families of instances of varying complexity, considering both unconstrained and constrained settings. Results show that the constructive procedure effectively constructs feasible high-quality models in low computing times, even for instances for which the state-the-art method is not able to find feasible solutions at all within the time limit.