Packaging optimization using the dynamic vector fields method

Summary In this paper, a novel packaging optimization method for convex objects is presented. This method solves the packaging optimization problem through dynamic simulation of object positions and rotations over time. Object positions and orientations are determined by dynamic vector fields, which accelerate objects according to optimization objectives or physical effects between objects or their environment. Using these vector fields, any number of objectives or effects can be accounted for, and this scalability allows the method to potentially be employed to solve a wide variety of engineering packaging optimization problems. The current implementation, as presented in this paper, represents the foundation of the method that future improvements will build upon and is currently limited to the analysis of convex objects. Three basic vector fields are presented to solve packing density maximization problems: the first maximizes packing density, the second prevents collisions between objects, and the third optimally orients objects relative to each other. Collisions between objects are relaxed in this method, allowing objects to pass through each other, which provides the potential for reduced initial condition dependence and has shown promising results thus far. Several test problems are presented and solved, demonstrating the method and its ability to generate optimal solutions.