A spatial branch-and-bound algorithm for some unconstrained single-facility location problems

Abstract: "A globally convergent spatial branch-and-bound algorithm is given here which is shown to be useful on several unconstrained single-facility location problems. These include the min-sum, min-max, and max-min problems with cost functions that are continuous and non-decreasing in distance. For the special case of the min-sum problem with Euclidean metric and power cost functions, a quadratic lower-bounding function is developed that results in a convergence rate superior to that of using a simple lower bounding function from the Big Square-Small Square algorithm of Hansen et al."