The semi-obnoxious minisum circle location problem with Euclidean norm

The objective of the classical version of the minisum circle location problem is finding a circle C in the plane such that the sum of the weighted distances from the circumference of C to a set of given points is minimized, where every point has a positive weight. In this paper, we investigate the semi-obnoxious case, where every existing facility has either a positive or negative weight. The distances are measured by the Euclidean norm. Therefore, the problem has a nonlinear objective function and global nonlinear optimization methods are required to solve this problem. Some properties of the semi-obnoxious minisum circle location problem with Euclidean norm are discussed. Then a cuckoo optimization algorithm is presented for finding the solution of this problem.