Swedish mining company LKAB uses autonoumous vehicles to transport ore at their production areas. The traversal paths of the vehicles are today manually constructed in a CAD program by an engineer. A previously developed physical model of the vehicles suggests that the paths can be improved to allow better traversal times by optimizing their smoothness, i.e. the integral of the derivative curvature squared over the arc-length. This thesis presents an evolutionary algorithm that represents the path as a parametric B-spline and optimizes its smoothness using an evolutionary strategy. The algorithm is evaluated on a few test cases and the results indicate that time savings up to 10-20% are possible for longer paths.