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 semiobnoxious 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.