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Generalized Circle Packings: Model Formulations and Numerical Results

Frank J. Kampas
Organization: WAM Systems, Inc.
János D. Pintér
Organization: Pintér Consulting Service Inc.
URL: http://www.pinterconsulting.com

2004 International Mathematica Symposium
Conference location

Banff, Canada

In this paper, we introduce a new class of packing models. Our objective is to find the minimal size circle that contains various non-overlapping circle configurations that comprise, in principle, arbitrary sized circles. Our Mathematica application package MathOptimizer Professional is used to solve model instances: numerical results are reported up to 20-circle configurations. The criteria used reflect certain preferences related to the circle configuration sought. Obviously, this problem can be directly generalized to the case of optimized arbitrary dimensional spherical arrangements.

We present several model formulations and then solve corresponding instances applying global optimization techniques. The objective of global optimization (GO) is to find the best solution of nonlinear decision models that – possibly or probably – have a multitude of global and local optima. Even the 'standard' uniform circle packing models lead to GO problems.

*Applied Mathematics > Optimization
*Wolfram Technology > Application Packages > Applications from Independent Developers > MathOptimizer Professional

circle packing, optimization, global optimization, global optima, local optima
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