Solving the Continuous <Emphasis Type="Italic">p</Emphasis>-Dispersion Problem Using Non-linear Programming

The problem of locating p maximally dispersed points in a convex space is considered. This problem is formulated as a non-linear programming problem. It is shown that this problem, in a square, is equivalent to the problem of packing the square with p equal circles of largest possible radius. Computational experience with the non-linear programming formulation of the dispersion problem is reported. Four of the solutions found are superior to the best known solutions in the literature for the corresponding circle-packing problem.