Mathematical model and solution algorithm for packing problem of convex polyhedra

Abstract

We investigate the problem of packing convex polyhedra into a container (rectangular, spherical, or cylindrical) of minimal size, allowing for continuous rotations and translations of the polyhedra. To construct a mathematical model of the problem, we utilize radical-free quasi-phi-functions and phi-functions, formulating it as a nonlinear programming (NLP) problem. Additionally, we propose an efficient solution algorithm aimed at reducing problem dimensionality and computational costs. Computational results from several experiments are presented.