Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682212120210201The semi-obnoxious minisum circle location problem with Euclidean norm669678486910.22075/ijnaa.2021.4869ENMehranehGholamiFaculty of Mathematical Sciences, Shahrood University of Technology, University Blvd., Shahrood, IranJafarFathaliFaculty of Mathematical Sciences, Shahrood University of Technology, University Blvd., Shahrood, Iran0000-0003-1397-8529Journal Article20210215The 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.https://ijnaa.semnan.ac.ir/article_4869_42ebf726b5dc93e5d0a99ef7b8525b66.pdf