Abstract
This document presents a simulation-based method for the polyhedra packing problem (PPP). This problem refers to packing a set of irregular polyhedra (convex and concave) into a cuboid with the objective of minimizing the cuboid’s volume, considering non-overlapping and containment constraints. The PPP has applications in additive manufacturing and packing situations where volume is at a premium. The proposed approach uses Unity® as the simulation environment and considers nine intensification and two diversification movements. The intensification movements induce the items within the cuboid to form packing patterns allowing the cuboid to decrease its size with the help of gravity-like accelerations. On the other hand, the diversification movements are classic transition operators such as removal and filling of pieces and enlargement of the container, which allow searching on different solution neighborhoods. All simulated movements were hybridized with a probabilistic tabu search. The proposed methodology (with and without the hybridization) was compared by benchmarking with all previous works solving the PPP with irregular items. Results show that satisfactory solutions were reached in a short time; even a few published results were improved.
Highlights
Cutting and packing problems (C&PP) have been an object of great interest within the computational geometry and operational research communities (Ma et al, 2018)
AM is known as 3D printing and layer technology (Araújo et al, 2020); it is a set of technologies developed in the late 1980s (Wong and Hernandez, 2012), which allows the production of pieces with specific desired shapes
The problem addressed in this paper is the polyhedra packing problem (PPP) in which a polyhedra set is packed within a cuboid and the objective is to minimize the cuboid’s volume
Summary
Cutting and packing problems (C&PP) have been an object of great interest within the computational geometry and operational research communities (Ma et al, 2018). AM is known as 3D printing and layer technology (Araújo et al, 2020); it is a set of technologies developed in the late 1980s (Wong and Hernandez, 2012), which allows the production of pieces with specific desired shapes This is done by adding material layer-by-layer (Gebhardt and Hotter, 2016) without requiring other physical devices such as molds (Hague et al, 2004). These fixed orientations may not be very suitable when considering irregular shapes in real applications, such as AM Another less common approach is considering the pieces’ free rotation. This study’s problem is packing a polyhedra set (convex and concave) into a minimal volume cuboid, adopting the pieces’ free rotation constraint; this is known as the polyhedra packing problem (PPP) (Romanova et al, 2018), which is an NP-hard problem (Chazelle et al, 1989); the use of approaches alternative to mathematical programming may be appropriate.
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