Charging station location problem for maximizing the space-time-electricity accessibility: A Lagrangian relaxation-based decomposition scheme

The driving range of electric vehicles limits the accessibility of their users. Charging infrastructures such as charging stations are essential to improve the accessibility of electric vehicles. Existing charging station location studies neglected accessibility-based indicators in their optimization models. For the charging station location problem, this paper proposes a novel objective function that maximizes the space-time-electricity accessibility of electric vehicles. Then we formulate an integer-programming model in the space-time-electricity network. A Lagrangian relaxation-based decomposition scheme is developed to solve this problem. The constraints that couple flow with location variables are dualized to the objective function, resulting in a set of independent routing subproblems and a knapsack subproblem. At each iteration, a primal heuristic utilizes the result of the intermediate knapsack subproblem to generate a feasible solution and Lagrangian multipliers are updated by the subgradient optimization method. The numerical experiments are conducted on three networks, showing that the proposed method achieves good integrality gaps.