A particle swarm optimization method for semi-obnoxious line location problem with rectilinear norm

- We consider the semi-obnoxious line location problem with L1 norm.
- A swarm algorithm is proposed to tackle the given problem.
- Some useful properties are presented in the case that the sum of weighs is positive.

Location theory is one of the useful and interesting fields of operations research and has many applications in the real life. In the most of location problems the goal is finding location of one or more facilities according to a given criteria to serve clients. In this paper we consider the line location problem with l1 norms where the clients have either positive or negative weight. In the line location problem we want to find a line L in the plane, so that the sum of weighted distances from L to all existing facilities is minimized. In this paper we discuss some properties of the problem. We show the algorithm of line location with positive weight can't be applied to the positive and negative case. So we propose a particle swarm optimization (PSO) to solve this problem and compare it with a genetic algorithm. Comparing results of these methods with those obtained by the algorithm of positive case, show that PSO is an efficient method for solving line location problem.