Packing of concave polyhedra with continuous rotations using nonlinear optimisation
Packing of concave polyhedra with continuous rotations using nonlinear optimisation
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.
37-53
Romanova, T.
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Bennell, Julia
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Stoyan, Y.
cdfc8474-9402-44a0-b856-09d5e2f5dc57
Pankratov, A.
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1 July 2018
Romanova, T.
fc983dc2-e442-41b5-824a-d61e2574e693
Bennell, Julia
38d924bc-c870-4641-9448-1ac8dd663a30
Stoyan, Y.
cdfc8474-9402-44a0-b856-09d5e2f5dc57
Pankratov, A.
d327ed99-ef96-4be0-935e-98daaf1c122e
Romanova, T., Bennell, Julia, Stoyan, Y. and Pankratov, A.
(2018)
Packing of concave polyhedra with continuous rotations using nonlinear optimisation.
European Journal of Operational Research, 268 (1), .
(doi:10.1016/j.ejor.2018.01.025).
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.
Text
EJOR_Concave polyhedra (002)
- Accepted Manuscript
More information
Accepted/In Press date: 11 January 2018
e-pub ahead of print date: 31 January 2018
Published date: 1 July 2018
Identifiers
Local EPrints ID: 418130
URI: http://eprints.soton.ac.uk/id/eprint/418130
ISSN: 0377-2217
PURE UUID: ae81df5c-c5b6-4726-a90b-1a9fd3c2af28
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Date deposited: 22 Feb 2018 17:30
Last modified: 16 Mar 2024 06:14
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Contributors
Author:
T. Romanova
Author:
Julia Bennell
Author:
Y. Stoyan
Author:
A. Pankratov
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