This work deals with a new method that determines the optimal arrangements of overhead power line conductors by an optimization method called Differential evolution. During the optimization procedure the root mean square values of the electric field strength and the magnetic field density on the border of the overhead power line right of way are used as the main criteria. Both, electric and magnetic fields, are evaluated with methods, where the impact of conductor sagging is considered. The position of the each power line conductor is determined in an optimization process. In the given case, the aim of optimization is to find such arrangement of conductors where the values of the electric and magnetic fields on the border of the overhead power line right of way are under the prescribed limits, whereas the tower height is as low as possible.