Median line location problem with positive and negative weights and Euclidean norm

Let n existing facilities be given in the plane. The classical version of the median line location problem asks to find a line L in the plane, so that the sum of the weighted distances from L to all existing facilities is minimized. We consider the semi-obnoxious case, where every point has either a positive or a negative weight. In this paper, we discuss some properties of semi-obnoxious median line location problem with Euclidean norm and propose a particle swarm optimization algorithm for this problem.