Recently, there has been renewed interest in improving the logit-based route choice model because of the importance of the route choice model in intelligent transportation systems applications, particularly the applications of advanced traveler information systems. The paired combinatorial logit (PCL) model and its equivalent mathematical programming formulation for the route choice problem have been studied. An algorithm based on the partial linearization method is presented for solving the PCL stochastic user equilibrium problem. Detailed examples are provided to explain how this hierarchical logit model resolves the overlapping problem through the similarity index while still accounting for both congestion and stochastic effects in the mathematical programming formulation.