Globally Optimized Spherical Point Arrangements: Model Variants and Illustrative Results

The “well-balanced” distribution of points over the surface of a sphere is of significant interest in various fields of science. The quality of point configurations is typically expressed by criterion functions that have many local optima. A general global optimization framework is suggested to solve such problems. To illustrate the viability of this approach, the model development and solver system LGO is applied to four different model versions. Numerical results – including the visual representation of criterion functions in these models – are presented. The global optimization approach can be tailored to specific problem settings, and it is also applicable to a large variety of other model forms.