Structural plate elements in composite structures are typically fabricated by stacking orthotropic layers, each of which is composed of reinforcing fibers and matrix materials. In this work, three optimum design approaches are compared to clarify the advantages and disadvantages for optimizing the buckling performance of laminated composite plates. The first approach is developed recently by the authors, where the buckling load is maximized with respect to the lamination parameters by a gradient method and then the optimum lay-up design is determined by minimizing the errors between the optimum parameters and parameters for all possible discrete lay-ups. The second approach is the layerwise optimization (LO) approach where the fiber orientation angle in each layer is optimized step-by-step by repeating one dimensional search. The third one is a direct application of a simple genetic algorithm (SGA). In numerical examples, three sets of results are compared to discuss on the methodology for buckling optimization.