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Solving circle packing problems by global optimization: numerical results and industrial applications. (English) Zbl 1156.90013
Summary: A (general) circle packing is an optimized arrangement of $N$ arbitrary sized circles inside a container (e.g., a rectangle or a circle) such that no two circles overlap. In this paper, we present several circle packing problems, review their industrial applications, and some exact and heuristic strategies for their solution. We also present illustrative numerical results using ‘generic’ global optimization software packages. Our work highlights the relevance of global optimization in solving circle packing problems, and points towards the necessary advancements in both theory and numerical practice.
##### MSC:
 90C26 Nonconvex programming, global optimization 90B85 Continuous location
##### Software:
Global Optimization Toolbox For Maple; MathOptimizer