Placement of two- and three-dimensional irregular shapes for inertia moment and balance

We present a heuristic for the problem of placing irregular shapes in two or three dimensions within a container, such that the placement of the shapes is optimized for balance and inertia moment and no two shapes overlap. The heuristic is based on a technique that iteratively removes overlap, which has previously proven successful for bin-packing problems with rectangular objects and strip-packing problems with irregular shapes. We extend this method and demonstrate its ability to optimize an objective function related to the individual position of each shape. The approach iteratively reduces an augmented objective function, which is the sum of balance, inertia moment and overlap and uses the metaheuristic Guided Local Search.