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Optimal clustering of a pair of irregular objects

Optimal clustering of a pair of irregular objects
Optimal clustering of a pair of irregular objects
Cutting and packing problems arise in many fields of applications and theory. When dealing with irregular objects, an important subproblem is the identification of the optimal clustering of two objects. Within this paper we consider a container (rectangle, circle, convex polygon) of variable sizes and two irregular objects bounded by circular arcs and/or line segments, that can be continuously translated and rotated. In addition minimal allowable distances between objects and between each object and the frontier of a container, may be imposed. The objects should be arranged within a container such that a given objective will reach its minimal value. We consider a polynomial function as the objective, which depends on the variable parameters associated with the objects and the container. The paper presents a universal mathematical model and a solution strategy which are based on the concept of phi-functions and provide new benchmark instances of finding the containing region that has either minimal area, perimeter or homothetic coefficient of a given container, as well as finding the convex polygonal hull (or its approximation) of a pair of objects.
minimum containment, irregular shapes, cutting and packing, mathematical modeling, optimisation
0925-5001
497-524
Bennell, J.
38d924bc-c870-4641-9448-1ac8dd663a30
Scheithauer, G.
20048fd2-0af4-4c61-9aff-87c6e6aa8ff0
Stoyan, Y.
cdfc8474-9402-44a0-b856-09d5e2f5dc57
Romanova, T.
fc983dc2-e442-41b5-824a-d61e2574e693
Pankratov, A.
d327ed99-ef96-4be0-935e-98daaf1c122e
Bennell, J.
38d924bc-c870-4641-9448-1ac8dd663a30
Scheithauer, G.
20048fd2-0af4-4c61-9aff-87c6e6aa8ff0
Stoyan, Y.
cdfc8474-9402-44a0-b856-09d5e2f5dc57
Romanova, T.
fc983dc2-e442-41b5-824a-d61e2574e693
Pankratov, A.
d327ed99-ef96-4be0-935e-98daaf1c122e

Bennell, J., Scheithauer, G., Stoyan, Y., Romanova, T. and Pankratov, A. (2015) Optimal clustering of a pair of irregular objects. Journal of Global Optimization, 61 (3), 497-524. (doi:10.1007/s10898-014-0192-0).

Record type: Article

Abstract

Cutting and packing problems arise in many fields of applications and theory. When dealing with irregular objects, an important subproblem is the identification of the optimal clustering of two objects. Within this paper we consider a container (rectangle, circle, convex polygon) of variable sizes and two irregular objects bounded by circular arcs and/or line segments, that can be continuously translated and rotated. In addition minimal allowable distances between objects and between each object and the frontier of a container, may be imposed. The objects should be arranged within a container such that a given objective will reach its minimal value. We consider a polynomial function as the objective, which depends on the variable parameters associated with the objects and the container. The paper presents a universal mathematical model and a solution strategy which are based on the concept of phi-functions and provide new benchmark instances of finding the containing region that has either minimal area, perimeter or homothetic coefficient of a given container, as well as finding the convex polygonal hull (or its approximation) of a pair of objects.

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JGO_optimal clusters_final.pdf - Accepted Manuscript
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More information

Accepted/In Press date: 15 April 2014
e-pub ahead of print date: 30 April 2014
Published date: March 2015
Keywords: minimum containment, irregular shapes, cutting and packing, mathematical modeling, optimisation
Organisations: Centre of Excellence in Decision, Analytics & Risk Research

Identifiers

Local EPrints ID: 390813
URI: https://eprints.soton.ac.uk/id/eprint/390813
ISSN: 0925-5001
PURE UUID: d55cd58a-a8cf-40a1-9ae1-41198a964b89

Catalogue record

Date deposited: 13 Apr 2016 14:47
Last modified: 19 Jul 2019 20:11

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