A fast heuristic for a three-dimensional non-convex domain loading problem

Abstract

In this paper we tackle a three-dimensional non-convex domain loading problem. We have to efficiently load identical small boxes into a highly irregular non-convex domain. The boxes to be loaded have a particular shape. If d is the length of the smallest edge of the box, its dimensions are d × nd × md, n ≤ m, with n and m integer values. This loading problem arises from an industrial design problem where it is necessary to obtain good solutions with very low computation time. We propose a fast heuristic based on an approximate representation of the non-convex domain in terms of cubes of dimension d and on the decomposition of the whole problem in several two-dimensional subproblems related to ‘planes’ of height d. The proposed heuristic shows good performances in terms of quality of solution and computation times. The results on several real test cases, coming from the industrial application, are shown

Analysis of irregular three-dimensional packing problems in additive manufacturing: a new taxonomy and dataset

“…A factor that additionally increases their inherent difficulty is the presence of non-overlapping constraints between items and the edges of the container. Further variants of the problem consider other constraints, including weight distribution (Davies and Bischoff 1999), cargo stability (Hemminki, Leipala, and Nevalainen 1998), limited load bearing strength (Bischoff 2006) and packing into a non-rectangular container (Eisenbrand et al 2005;Scheithauer, Stoyan, and Romanova 2005;Boccia et al 2011).…”