Abstarct: In this thesis we first present an introduction to basic concepts of location problem. Then we consider the line location problem in the plane and its properties by using different norms. Also we express line location in three dimensions space. Different cases of this problem is investigated and considered the proposed algorithms for this problem. Also we introduce semi-obnoxious line location and using particle swarm optimization (pso) for solving this problem. We obtain some properties of semi-obnoxious line location problem and offer an algorithm to locate the semi-obnoxious median line in the plane. We obtain the computational results and we show this algorithm can be used as an efficient algorithm for this problem.