A hybrid approach of simulation and metaheuristic for the polyhedra packing problem

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.

A Universal Formation Mechanism of Hollow Multi‐Shelled Structures Dominated by Concentration Waves

“…As mentioned above, when considering h as a variable, the reaction of the precursor needs to be taken into account, including the polymerization rate of metal clusters, crystal growth rate, grain size, etc., which are difficult to reflect in the current mathematical model. As an alternative, the relationships between particle size and the shell structure could be given with the aid of a simulation software package (Supporting note 4 and Supporting data 2) [25] . The R tr is obtained from the mathematical model and preset in the program.…”

“…As an alternative, the relationships between particle size and the shell structure could be given with the aid of a simulation software package (Supporting note 4 and Supporting data 2). [25] The R tr is obtained from the mathematical model and preset in the program. The simulations are conducted under the assumptions that particles will connect when a collision occurs and that all particles are of the same size.…”