# Conway Crossover to Create Hyperdimensional Point Packings, with
Applications

### Daniel Ashlock and Steffen Graether

Submitted to CEC 2016

Point packings in the unit square are placements of *n* points
in the unit square that maximize the minimum distance between any two
of the points. Such packings are surrogates for the 2D-stock cutting
problem. In this study we examine a unique representation for the
point packing problem and extend the problem to higher dimensions and
more complex shapes. The representation uses the Conway operator, a
*k*-ary variation operator based on the lexicode algorithm.
Three application of point packings are demonstrated. A parameter
study for the Conway operator based algorithm is performed
demonstrating that large populations are uniformly desirable but that
the part of the operator that corresponds to mutation has a strongly
problem dependent value for good performance. The three applications
demonstrated are selecting well-space RGB color palettes,
initialization of populations in an evolutionary optimizer, and fast
clustering of codon usage data. Color palettes of different size are
presented. The optimization application is found to gain substantial
performance by using point packings as initializers. The
bioinformatics application demonstrates significantly non-random
clustering of a family of intrinsically disordered proteins known as
dehydrins.