Modeling and Solving a Composite Structure Design Problem with Constraint Programming (Short Paper)

Composite structures are composed of plies (layers) of carbon fibers. For each ply, one must decide its orientation from the set of possible angles: -45°, 0°, 45°, and 90°. The stack of plies must follow strict constraints on the chosen orientations to achieve mechanical properties of the composite, such as sufficient buckling load. The design problem becomes more complex when determining the stack of plies for a complete surface material, that does not require the same number of plies in every region of the surface. Not only must the orientations be selected in each region, but it is also necessary to decide which plies are discontinued between adjacent regions. Thanks to its declarative nature, Constraint Programming (CP) offers an elegant modeling of the constraints, making it easy for designers to activate or deactivate them as needed. We propose a CP model, implemented in MiniZinc. The performance of this model on synthetic yet realistic instances when solved by different exact solvers, including Mixed Integer Programming (MIP) solvers, demonstrates the superiority of CP over MIP on our MiniZinc model, and over a commercial solution implemented by an industrial partner. It opens up the adoption of CP as an efficient building block of Computer-Aided Design tools for composite structures. By making the model and instances publicly available, we also hope to facilitate the inclusion of this problem in CP solver competitions and stimulate further research in this area.