A path-planning algorithm for automated road vehicles on multi-lane motorways is derived from the opportune formulation of an optimal control problem. In this framework, the objective function to be minimized contains appropriate respective terms to reflect: the goals of the vehicle advancement; passenger comfort; prevailing traffic rules (e.g., overtaking only from left); and the avoidance of obstacles (other moving vehicles) and of the vehicle departing from the road. Each term is coupled with a weighting factor that reflects its comparative importance. For the numerical solution of the optimal control problem, a very efficient feasible direction algorithm is used. To avoid local minima, a simplified dynamic programming algorithm is also conceived to deliver the initial guess trajectory for the optimal control algorithm. With low computation times, the approach is readily executable within a model-predictive control frame. The performance of the proposed algorithm is illustrated using two typical driving scenarios.