SYMMETRY BREAKING CONSTRAINTS FOR THE PROBLEM OF PACKING EQUAL CIRCLES IN A SQUARE

Alberto Costa, Ider Tseveendorj

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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in Harvard Style

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 - Volume 1: ICORES, ISBN 978-989-8425-97-3, pages 5-10. DOI: 10.5220/0003713100050010


in Bibtex Style

@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 - Volume 1: ICORES,},
year={2012},
pages={5-10},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003713100050010},
isbn={978-989-8425-97-3},
}


in EndNote Style

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