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Authors: Alberto Costa 1 and Ider Tseveendorj 2

Affiliations: 1 École Polytechnique, France ; 2 Université de Versailles Saint Quentin en Yvelines, France

Keyword(s): Symmetry breaking constraints, Packing of equal circles, Reformulation, Narrowing, Nonconvex NLP.

Related Ontology Subjects/Areas/Topics: Artificial Intelligence ; Knowledge Discovery and Information Retrieval ; Knowledge-Based Systems ; Mathematical Modeling ; Methodologies and Technologies ; Operational Research ; Optimization ; Symbolic Systems

Abstract: The Packing Equal Circles in a Square (PECS) problem is a nonconvex nonlinear optimization problem which involves a high degree of symmetry. The Branch-and-Bound algorithms work bad due to the presence of symmetric optima, because the Branch-and-Bound tree becomes large, and the time to reach the leaves (i.e., the optimal solutions) increases. In this paper, we introduce some inequalities which reduce the symmetry of the problem, and we present some numerical results.

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Paper citation in several formats:
Costa, A. and Tseveendorj, I. (2012). SYMMETRY BREAKING CONSTRAINTS FOR THE PROBLEM OF PACKING EQUAL CIRCLES IN A SQUARE. In Proceedings of the 1st International Conference on Operations Research and Enterprise Systems - ICORES, ISBN 978-989-8425-97-3; ISSN 2184-4372, pages 5-10. DOI: 10.5220/0003713100050010

@conference{icores12,
author={Alberto Costa. and Ider Tseveendorj.},
title={SYMMETRY BREAKING CONSTRAINTS FOR THE PROBLEM OF PACKING EQUAL CIRCLES IN A SQUARE},
booktitle={Proceedings of the 1st International Conference on Operations Research and Enterprise Systems - ICORES,},
year={2012},
pages={5-10},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003713100050010},
isbn={978-989-8425-97-3},
issn={2184-4372},
}

TY - CONF

JO - Proceedings of the 1st International Conference on Operations Research and Enterprise Systems - ICORES,
TI - SYMMETRY BREAKING CONSTRAINTS FOR THE PROBLEM OF PACKING EQUAL CIRCLES IN A SQUARE
SN - 978-989-8425-97-3
IS - 2184-4372
AU - Costa, A.
AU - Tseveendorj, I.
PY - 2012
SP - 5
EP - 10
DO - 10.5220/0003713100050010