Two-Level Weight Optimization of Composite Laminates Using Integer Programming

TR Number



Journal Title

Journal ISSN

Volume Title


American Institute of Aeronautics and Astronautics


Optimization of composite laminates requires the satisfaction of constraints where the design ply thicknesses and orientations can only take discrete values prescribed by the manufacturers. Heuristics such as particle swarm or genetic algorithms are inefficient in such cases because they provide suboptimal solutions when the number of design variables is large. They also are computationally expensive in handling the combinatorial nature of the problem. In contrast, with the help of binary decision variables, mixed integer programming can be adopted to optimize such laminates efficiently. This paper presents an approach to reformulate lamination parameters and failure constraints as functions of binary decision variables. The buckling load maximization for a simply supported laminated plate is initially demonstrated using integer linear programming. Next, the laminate weight is minimized by varying the number of plies for a given external bi-axial compressive load and subjected to buckling and material failure constraints. A variation of laminate weight minimization is demonstrated by fixing the number of plies and assuming discrete changes in ply thicknesses. This is achieved using a sequential two-level optimization for laminates having uniform ply thickness. Finally, a scalability study is performed to evaluate the performance of mixed integer programming for different problem sizes. It is demonstrated that all three formulations with integer programming achieve significant performance gain and robustness over standard heuristic solvers.