On the limited memory BFGS method for large scale optimization
Mathematical Programming: Series A and B
New results in the packing of equal circles in a square
Discrete Mathematics
Packing equal circles in a square: a deterministic global optimization approach
Discrete Applied Mathematics
A New Verified Optimization Technique for the "Packing Circles in a Unit Square" Problems
SIAM Journal on Optimization
New Approaches to Circle Packing in a Square: With Program Codes (Springer Optimization and Its Applications)
Journal of Computational and Applied Mathematics - Special issue: Scientific computing, computer arithmetic, and validated numerics (SCAN 2004)
Efficiently packing unequal disks in a circle
Operations Research Letters
Discrete Applied Mathematics
Patterns and pathways of packing circles into a square
International Journal of Computer Applications in Technology
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This paper considers the problem of finding the densest packings of N(N=1,2,...) equal circles in a square. We propose a physically inspired model to formulate this problem and a new heuristic algorithm to solve this problem. The approach is tested on the instances of N=1,2,...,200. Though many researchers have searched these instances using various methods, we can still find 41 better packings than the best-known ones reported in literature.