Global Optimization on Funneling Landscapes
Journal of Global Optimization
Approximate algorithms for constrained circular cutting problems
Computers and Operations Research
New heuristics for packing unequal circles into a circular container
Computers and Operations Research
New Approaches to Circle Packing in a Square: With Program Codes (Springer Optimization and Its Applications)
Note on: an improved algorithm for the packing of unequal circles within a larger containing circle
Computers and Industrial Engineering
A Population-based Approach for Hard Global Optimization Problems based on Dissimilarity Measures
Mathematical Programming: Series A and B
PERM for solving circle packing problem
Computers and Operations Research
Adaptive and restarting techniques-based algorithms for circular packing problems
Computational Optimization and Applications
Variable space search for graph coloring
Discrete Applied Mathematics
A beam search algorithm for the circular packing problem
Computers and Operations Research
Discrete Applied Mathematics
An Effective Hybrid Algorithm for the Circles and Spheres Packing Problems
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
Computers and Industrial Engineering
Computers and Operations Research
Formulation space search for circle packing problems
SLS'07 Proceedings of the 2007 international conference on Engineering stochastic local search algorithms: designing, implementing and analyzing effective heuristics
Solving the problem of packing equal and unequal circles in a circular container
Journal of Global Optimization
Efficiently packing circles into a larger containing circle
HPCA'09 Proceedings of the Second international conference on High Performance Computing and Applications
Efficiently packing unequal disks in a circle
Operations Research Letters
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In this paper we present a heuristic algorithm for the problem of packing unequal circles in a fixed size container such as the unit circle, the unit square or a rectangle. We view the problem as being one of scaling the radii of the unequal circles so that they can all be packed into the container. Our algorithm is composed of an optimisation phase and an improvement phase. The optimisation phase is based on the formulation space search method whilst the improvement phase creates a perturbation of the current solution by swapping two circles. The instances considered in this work can be categorised into two: instances with large variations in radii and instances with small variations in radii. We consider six different containers: circle, square, rectangle, right-angled isosceles triangle, semicircle and circular quadrant. Computational results show improvements over previous work in the literature.