Patterns and pathways of packing circles into a square

Authors:
Chikit Au
Affiliations:
Faculty of Engineering, University of Waikato, Hamilton, New Zealand
Venue:
International Journal of Computer Applications in Technology
Year:
2013

Citing 12
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Abstract

Seeking an improbable, but globally optimum, state is useful in many scientific and engineering endeavours. To handle a larger data size, computational techniques are often employed. Yet, they are bound by the inherent combinatorial complexity. This paper employs the examples of packing a set of circles into a square to verify the existence of the pathways between the global optimisations based on the hypothesis that hopping from one known optimum to an unknown optimum in a global landscape is feasible. Twenty seven proven optimal circle packing configurations are investigated and eleven pathways are identified. These pathways lead to other optimal configurations which conform to the best known results. These pathways are beneficial to obtaining the optimum since it does not require going through the combinatorial many intermediate configuration before reaching the optimum.