Optimization of the aircraft panel assembly constructed by skin and stringers is investigated. For the design of panel assembly of the aircraft structure, it is necessary to determine the best shape of the stringer which accomplishes lowest weight under the condition of no instability. A panel assembly can fail in a variety of instability modes under compression. Overall modes of flexure or torsion can occur and these can interact in a combined flexural/torsion mode. Flexure and torsion can occur symmetrically or anti-symmetrically. Local instabilities can also occur. The local instabilities considered in this paper are buckling of the free and attached flanges, the stiffener web and the inter-rivet buckling. A program is developed to find out critical load for each instability mode at the specific stringer shape. Based on the developed program, optimization is performed to find optimum stringer shape. The developed instability analysis program is not adequate for sensitivity analysis, therefore RSM (Response Surface Method) is utilized instead to model weight and instability constraints. Since the problem has many local minimum, Genetic algorithm is utilized to find global optimum.