Abstract
Packing clusters composed of non-overlapping non-identical convex objects is considered. The packing problem, originally stated in Romanova et al. (Math Probl Eng 2019:Article ID 4136430, 12 pages, 2019), is extended here by introducing balancing (equilibrium) conditions. Packing clusters into a rectangular container is considered. Objects in the cluster are of the same shape and allowed to be continuously translated and rotated subject to maximum distance between clusters. This problem is referred to as a sparse equilibrium packing of clusters and formulated as a nonlinear optimization problem. An algorithmic approach to find a locally optimal solution is developed. Computational results are presented to support efficiency of the method for packing clusters with and without balancing conditions.
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Romanova, T., Pankratov, A., Litvinchev, I., & Marmolejo-Saucedo, J. A. (2020). Optimized packing of object clusters with balancing conditions. In EAI/Springer Innovations in Communication and Computing (pp. 95–108). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-48149-0_8
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