Towards an evolved lower bound for the most circular partition of a square

Abstract

We examine the problem of partitioning a square into convex polygons which are as circular as possible. Circular means that the polygon's aspect ratio is supposed to be near 1. The aspect ration of a convex polygon denotes the ratio of the diameters of the smallest circumscribing circle to the largest inscribed disk. This problem has been solved for the equilateral triangle as well as for regular k-gon with k > 4. In the case of a square, the optimal solution is still an open problem. We are planning to find a solution which is ldquogood enoughrdquo with the help of evolutionary algorithms.