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.