A fast algorithm for particle simulations
Journal of Computational Physics
Computer simulation using particles
Computer simulation using particles
Computational structure of the N-body problem
SIAM Journal on Scientific and Statistical Computing
New results in the packing of equal circles in a square
Discrete Mathematics
Algorithm 813: SPG—Software for Convex-Constrained Optimization
ACM Transactions on Mathematical Software (TOMS)
Nonmonotone Spectral Projected Gradient Methods on Convex Sets
SIAM Journal on Optimization
Large-Scale Active-Set Box-Constrained Optimization Method with Spectral Projected Gradients
Computational Optimization and Applications
Packing equal circles in a square: a deterministic global optimization approach
Discrete Applied Mathematics
An {\it bf O(N)} Algorithm for Three-Dimensional N-body Simulations
An {\'it bf O(N)} Algorithm for Three-Dimensional N-body Simulations
Reformulation descent applied to circle packing problems
Computers and Operations Research
Numerical Comparison of Augmented Lagrangian Algorithms for Nonconvex Problems
Computational Optimization and Applications
Orthogonal packing of rectangular items within arbitrary convex regions by nonlinear optimization
Computers and Operations Research
Augmented Lagrangian methods under the constant positive linear dependence constraint qualification
Mathematical Programming: Series A and B
Computational Optimization and Applications
A beam search algorithm for the circular packing problem
Computers and Operations Research
Cutting circles and polygons from area-minimizing rectangles
Journal of Global Optimization
A unified approach for physically-based simulations and haptic rendering
Proceedings of the 2009 ACM SIGGRAPH Symposium on Video Games
Computers and Operations Research
Solving the problem of packing equal and unequal circles in a circular container
Journal of Global Optimization
Orthogonal packing of identical rectangles within isotropic convex regions
Computers and Industrial Engineering
A heuristic approach for packing identical rectangles in convex regions
Computers and Operations Research
An augmented beam search-based algorithm for the circular open dimension problem
Computers and Industrial Engineering
Packing congruent hyperspheres into a hypersphere
Journal of Global Optimization
Packing unit spheres into the smallest sphere using VNS and NLP
Computers and Operations Research
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Given a fixed set of identical or different-sized circular items, the problem we deal with consists on finding the smallest object within which the items can be packed. Circular, triangular, squared, rectangular and also strip objects are considered. Moreover, 2D and 3D problems are treated. Twice-differentiable models for all these problems are presented. A strategy to reduce the complexity of evaluating the models is employed and, as a consequence, instances with a large number of items can be considered. Numerical experiments show the flexibility and reliability of the new unified approach.