A multi-sphere scheme for 2D and 3D packing problems

Authors:
Takashi Imamichi;Hiroshi Nagamochi
Affiliations:
Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, Japan;Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, Japan
Venue:
SLS'07 Proceedings of the 2007 international conference on Engineering stochastic local search algorithms: designing, implementing and analyzing effective heuristics
Year:
2007

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Abstract

In this paper, we deal with a packing problem that asks to place a given set of objects such as non-convex polytopes compactly in R2 and R3, where we treat translation, rotation and deformation as possible motions of each object. We propose a multi-sphere scheme that approximates each object with a set of spheres to find a compact layout of the original objects. We focus on the case that all objects are rigid, and develop an efficient local search algorithm based on a nonlinear program formulation.