We fit the parameters of a differential equations model describing the production of gap-gene proteins Hunchback and Knirps along the antero-posterior axis of the embryo of Drosophila. As initial data for the differential equations model, we take the antero-posterior distribution of the proteins Bicoid, Hunchback and Tailless at the beginning of cleavage cycle 14. We calibrate and validate the model with experimental data using single- and multi-objective evolutionary optimization techniques. In the multi-objective optimization technique, we compute the associated Pareto fronts. We analyze the cross regulation mechanism between the gap-genes protein pair Hunchback-Knirps and we show that the posterior distribution of Hunchback follow the experimental data if Hunchback is negatively regulated by the Huckebein protein. This approach enables to us predict the posterior localization on the embryo of the protein Huckebein, and to validate with the experimental data the genetic regulatory network responsible for the antero-posterior distribution of the gap-gene protein Hunchback. We discuss the importance of Pareto multi-objective optimization techniques in the calibration and validation of biological models.