Domain Approximation Method for Solving Multifacility Location Problems on a Sphere

This paper considers the problem of optimally locating new facilities on a sphere among existing facilities so that the sum of all weighted geodesic distance pairs is minimized. A method involving an iterative solution is presented. The procedure involves the approximation of the domain of objective function, which in the limit approaches to that of the original objective function. Computational experience with the procedure is described.