Study of the point scattering uniform algorithms in R⁴⁰space

Abstract

The use of randomness in the spread of points in the R40 space gives doubts about the stability of using these spreads and the stability of global optimization algorithms predictions that are based on these spreads. The uniformity of the following initial points scatter algorithms is analyzed: LPτ sequence, UDC sequence, uniform random spread in R40. The uniformity of the spread was determined by the distance of the points from the centers of the grid cells in two-dimensional coordinate planes of the R40 cube space and by the uniformity of the projections of the points on the coordinate axes in these planes. The authors identified the features of using the points spread algorithms when the number of points is multiple to two and not multiple to two. The UDC sequence is the best initial point spread algorithm in the R40 space by two uniformity factors. LPτ sequence is at the second place and recently used uniform random scatter is at the third place.