On the impact of symmetry-breaking constraints on spatial Branch-and-Bound for circle packing in a square

Authors:
Alberto Costa;Pierre Hansen;Leo Liberti
Affiliations:
LIX, ícole Polytechnique, 91128 Palaiseau, France;LIX, ícole Polytechnique, 91128 Palaiseau, France and GERAD, HEC, 3000 chemin de la Côte-S.te-Catherine, H3T 2A7 Montreal, Canada;LIX, ícole Polytechnique, 91128 Palaiseau, France
Venue:
Discrete Applied Mathematics
Year:
2013

Citing 20
Cited 2

Fixed edge-length graph drawing is NP-hard

Discrete Applied Mathematics
Nonlinear optimization: complexity issues

Nonlinear optimization: complexity issues
Coin graphs, polyhedra, and conformal mapping

Proceedings of the 2nd Slovenian conference on Algebraic and topological methods in graph theory
New results in the packing of equal circles in a square

Discrete Mathematics
Approximation schemes for covering and packing problems in image processing and VLSI

Journal of the ACM (JACM)
DC programming: overview

Journal of Optimization Theory and Applications
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
Packing equal circles in a square: a deterministic global optimization approach

Discrete Applied Mathematics
On the Complexity of Recognizing Intersection and Touching Graphs of Disks

GD '95 Proceedings of the Symposium on Graph Drawing
Approximate algorithms for constrained circular cutting problems

Computers and Operations Research
Generating optimal T-shape cutting patterns for circular blanks

Computers and Operations Research
On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming

Mathematical Programming: Series A and B
Deterministic Global Optimization: Theory, Methods and (NONCONVEX OPTIMIZATION AND ITS APPLICATIONS Volume 37) (Nonconvex Optimization and Its Applications)

Deterministic Global Optimization: Theory, Methods and (NONCONVEX OPTIMIZATION AND ITS APPLICATIONS Volume 37) (Nonconvex Optimization and Its Applications)
New Approaches to Circle Packing in a Square: With Program Codes (Springer Optimization and Its Applications)

New Approaches to Circle Packing in a Square: With Program Codes (Springer Optimization and Its Applications)
Automatic Generation of Symmetry-Breaking Constraints

COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Branching and bounds tighteningtechniques for non-convex MINLP

Optimization Methods & Software - GLOBAL OPTIMIZATION
Solving the problem of packing equal and unequal circles in a circular container

Journal of Global Optimization
Feasibility-based bounds tightening via fixed points

COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
Reformulations in mathematical programming: automatic symmetry detection and exploitation

Mathematical Programming: Series A and B
Greedy vacancy search algorithm for packing equal circles in a square

Operations Research Letters

GloMIQO: Global mixed-integer quadratic optimizer

Journal of Global Optimization
Valid constraints for the Point Packing in a Square problem

Discrete Applied Mathematics

Quantified Score

Hi-index	0.04

Visualization

Abstract

We study the problem of packing equal circles in a square from the mathematical programming point of view. We discuss different formulations, we analyze formulation symmetries, we propose some symmetry breaking constraints and show that not only do they tighten the convex relaxation bound, but they also ease the task of local NLP solution algorithms in finding feasible solutions. We solve the problem by means of a standard spatial Branch-and-Bound implementation, and show that our formulation improvements allow the algorithm to find very good solutions at the root node.