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.