Optimized packing of arbitrarily oriented cylinders into a cuboid

Abstract This paper addresses the problem of packing arbitrarily oriented circular cylinders into a cuboid of minimal volume. The problem is characterized by nonlinear and nonconvex geometric constraints arising from rotation and distance requirements between objects. An exact analytical model of geometric interactions between cylinders and between cylinders and the container is developed using Φ‐functions and quasi‐Φ‐functions. This formulation enables the representation of packing constraints within a continuous nonlinear programming formulation. To efficiently solve the resulting high‐dimensional optimization problem, a solution approach is proposed that combines a constructive initialization procedure, a decomposition‐based optimization strategy, and an iterative solution scheme. The decomposition approach is based on the use of enclosing spheres to identify potentially interacting objects and reduce the number of active constraints. Numerical experiments demonstrate that the proposed approach is capable of producing dense packing configurations for large‐scale instances.