Although the double-double (DD) laminates proposed by Tsai provide a promising option for achieving better structural performance with lower manufacturing and maintenance costs, the buckling performance of perforated DD laminates still remains clear. In this study, optimal ply angles, rotation angles, and the corresponding maximum buckling loads are determined for DD laminates with various cutouts, which are used for comparisons to evaluate the effects of cutout size and shape on the buckling behaviour of perforated DD laminates. Apart from conventional circular and elliptical cutouts, the use of a combined-shape cutout for DD laminates is also investigated. As a large number of optimisations are required to obtain the maximum buckling loads for different cases in this study, an efficient optimisation method for perforated DD laminates is proposed based on an artificial neural network (ANN) and a genetic algorithm (GA). Unlike conventional quadaxial (QUAD) laminates, the repetition of a four-ply sublaminate in DD laminates makes their layup to be represented by only two ply angles; hence, the application of ANN models for predicting the buckling behaviour of various perforated DD laminates is studied in this paper. The superior performance of the ANN models is demonstrated by comparisons with other machine learning models. Instead of using the time-consuming FEA, the developed ANN model is utilised within a GA to obtain the maximum buckling load of perforated DD laminates. Compared to the circular cutout, the use of elliptical and combined-shape cutouts leads to more noticeable changes in the optimal ply angles as the cutout size increases. Based on the obtained results, the use of the combined-shape cutout is recommended for DD laminates.