Optimization of Packing Irregular Three-Dimensional Objects

Abstract

Introduction. Nowadays the irregular packing problem is becoming more important, since effective space management and optimal arrangement of objects are becoming key factors for ensuring efficiency and saving resources in a wide range of applications, e.g., additive manufacturing, space engineering, material sciences and logistics. It becomes an integral part of strategic development in the fields of production and science. The purpose of the paper. The paper is devoted to construction of a mathematical model and development of an efficient technique for densely filling a container with the maximum number of sets of irregular three-dimensional objects. Results. Irregular objects are approximated with a certain accuracy by non-convex polyhedra, which can be represented by the union of convex polytopes. Non-overlapping and containment constraints are described using quasi-phi-functions and phi-functions. A mathematical model of the packing problem is provided as a mixed-integer nonlinear programming considering given proportions of different types of objects. A solution strategy is proposed to search for local-optimal solutions. To find reasonable feasible packing, a fast algorithm based on a strip approximation of objects is used. A numerical example of the development of a print map of a set of industrial parts with maximum filling of the working chamber of a 3D-printer is given. Conclusions. The results confirm the efficiency of the proposed packing strategy, which is based on an integrated approach that takes into account the geometric features of irregular objects and their completeness. Keywords: packing, irregular objects, set of parts, mathematical modeling, optimization, 3D-printing.