Romanova, T, Bennell, J orcid.org/0000-0002-5338-2247, Stoyan, Y et al. (1 more author) (2018) Packing of concave polyhedra with continuous rotations using nonlinear optimisation. European Journal of Operational Research, 268 (1). pp. 37-53. ISSN 0377-2217
Abstract
We study the problem of packing a given collection of arbitrary, in general concave, polyhedra into a cuboid of minimal volume. Continuous rotations and translations of polyhedra are allowed. In addition, minimal allowable distances between polyhedra are taken into account. We derive an exact mathematical model using adjusted radical free quasi phi-functions for concave polyhedra to describe non-overlapping and distance constraints. The model is a nonlinear programming formulation. We develop an efficient solution algorithm, which employs a fast starting point algorithm and a new compaction procedure. The procedure reduces our problem to a sequence of nonlinear programming subproblems of considerably smaller dimension and a smaller number of nonlinear inequalities. The benefit of this approach is borne out by the computational results, which include a comparison with previously published instances and new instances.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 Elsevier B.V. This is an author produced version of a paper published in The European Journal of Operational Research. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Packing; Concave polyhedra; Continuous rotations; Mathematical modelling; Nonlinear optimisation |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Business (Leeds) > Faculty Office (LUBS) (Leeds) > Deans Office and Facilities (LUBS) (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 04 Dec 2018 11:57 |
Last Modified: | 31 Jan 2020 01:38 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.ejor.2018.01.025 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:139289 |