Examples of Genetic Algorithms Usage in Geometry and Algorithmic Design

Abstract

In this paper, the authors test genetic algorithms as geometric and design issues’ solvers to explain and explore the possibilities of this computing technique in design and research. The tests and explanations are based on three classical geometry problems of the Ancient Greece and on a pattern distribution algorithm, created by the authors and inspired by the definition of Lebesgue covering dimension. The basic tools for research are: Rhinoceros, the Grasshopper plug-in and the Galapagos tool. The tests prove that, as a result based on computing techniques, genetic algorithms can be used to find solutions without the implementation of analytic methods. This advantage of evolutionary computing can be very useful in case of complex issues, where implementation of analytic methods reveals itself difficult or even impossible.