Surrogate models are an essential engineering tool and their popularity has increased recently due to the high computational cost of evaluating real-world simulations. However, most of these functions are described by mixed variables (continuous and categorical), which makes it harder to create accurate interpolation functions. This work builds a surrogate model from a given mixed data set, in order to quickly and accurately calculate the mechanical performance of hybrid discontinuous composites. Then, in order to find the optimal hybridization, three different approaches are performed: mono-objective, targeted and multi-objective. Starting from a virtual database provided by the industrial partner, the mixed categorical optimization process is performed by coupling a multi-armed bandit strategy with a continuous Bayesian optimization solver. The efficiency of the proposed approach is tested and two main results are achieved. The obtained surrogate models are shown to be sufficiently accurate, having an R² score grater than 90% in average. Our proposed optimization process is also able to identify correctly the optimal fibres with respect to the desirable targets.