This paper introduces a 2D and 3D positioning system which uses a single transmitter and multiple receivers (i.e. beacon-based system). This system uses Differences in Time Of Flights (DTOF) of ultrasonic waves. A novel and robust solution for error sensitivity problem for DTOF equations is introduced. This solution is based on finding the optimal location of the receivers using genetic algorithms. The optimal location enables the system to have acceptable positioning accuracy of 5 cm (96.7%) in 3D space using low cost hardware that has low accuracy in ranging estimations. They also solve singularity condition for DTOF equations for all transmitters' locations in the entire workspace.