Mathematical program with equilibrium constraints approach with genetic algorithm for joint optimization of charging station location and discrete transport network design

This paper focuses on the joint optimization of the charging station location problem (CSLP) and discrete network design problem (DNDP) in a transportation network. We present a variational inequality (VI) formulation to describe the user equilibrium (UE) state of gasoline vehicles (GVs) and electric vehicles (EVs). Based on the mixed-UE model, a mathematical program with equilibrium constraints (MPEC) model is formulated for integrating the decisions of deploying EV charging stations (EVCSs) and adding new links to minimize the total travel cost (TTC) of all vehicles. A modified genetic algorithm is developed to tackle the MPEC model with an adaptive path generation procedure to address the mixed-UE model. Finally, we conduct numerical experiments to identify the efficacy of the proposed models and algorithms. Specifically, we propose a two-step optimization model and explore a performance comparison between the joint and two-step optimization approaches, while the joint optimization exhibits superiority in minimizing the TTC.