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Packing of concave polyhedra with continuous rotations using nonlinear optimisation

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.
0377-2217
37-53
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.
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), 37-53. (doi:10.1016/j.ejor.2018.01.025).

Record type: Article

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.

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EJOR_Concave polyhedra (002) - Accepted Manuscript
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Accepted/In Press date: 11 January 2018
e-pub ahead of print date: 31 January 2018
Published date: 1 July 2018

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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: 07 Oct 2020 04:47

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