We propose in this paper a new approach to generating interior search directions for multiple objective linear programming (MOLP) problems. The proposed approach is based on using achievement scalarizing functions and aspiration levels to convert a problem with multiple objectives to a problem with a single objective that is amenable for a solution by the interior point affinescaling primal algorithm. The interior solution trajectory takes an interior starting solution and moves it to a nondominated solution on the efficient frontier that corresponds to the optimum of the achievement scalarizing function.