One of the core technologies in lightweight structures is the optimal design of laminated composite stiffened panels. The increasing tailoring potential of new materials added to the simultaneous optimization of various design regions, leading to design spaces that are vast and non-convex. In order to find an optimal design using limited information, this paper proposes a workflow consisting of design of experiments, metamodeling and optimization phases. A machine learning strategy based on support vector machine (SVM) is used for data classification and interpolation. The combination of mass minimization and buckling evaluation under combined load is handled by a multi-objective formulation. The choice of a deterministic algorithm for the optimization cycle accelerates the convergence towards an optimal design. The analysis of the Pareto frontier illustrates the compromise between conflicting objectives. As a result, a balance is found between the exploration of new design regions and the optimal design refinement. Numerical experiments evaluating the design of a representative upper skin wing panel are used to show the viability of the proposed methodology.