The polyhedral norm approach to the problem of locating obnoxious routes

In this paper we deal with the problem of locating a linear obnoxious route on the plane when polyhedral norms are used to measure distances. These kind of routes are potentially dangerous for the facilities (population centers, installations, …), so a maximization of the minimum weighted distance from the facilities is used as objective function. Moreover, to prevent the effect of disasters motivated by accidents, a polygon has been associated to each facility which represents a security area around its position. We propose an algorithm for solving these problems and two refinements for improving its convergence.