Joint Routing and Charging Problem of Multiple Electric Vehicles: A Fast Optimization Algorithm

Abstract

Logistics has gained great attentions with the prosperous development of e-commerce, which is often seen as the classic optimal vehicle routing problem. Meanwhile, electric vehicle (EV) has been widely used in logistic fleet to curb the emission of green house gases in recent years. Thus, solving the optimization problem of joint routing and charging of multiple EVs is in a urgent need, whose objective function includes charging time, charging cost, EVs travel time, usage fees of EV and revenue from serving customers. This joint problem is formulated as a mixed integer programming (MIP) problem, which, however, is NP-hard due to integer restrictions and bilinear terms from the coupling between routing and charging decisions. The main contribution of this paper lies at proposing an efficient two-stage algorithm that can decompose the original MIP problem into two linear programming (LP) problems, by exploiting the exactness of LP relaxation and eliminating the coupled term. This algorithm can achieve a nearoptimal solution in polynomial time. In addition, another variant algorithm is proposed based on the two-stage one, to further improve the quality of solution. Compared with the state-of-theart algorithm, extensive simulations are implemented to validate the effectiveness of the proposed algorithm. Index Terms-Electric vehicle, routing problem, mixed integer programming, linear programming NOMENCLATURE Given Parameters KThe set of EVs RThe set of transportation request nodes M i Revenue from serving requests when i ∈ R c v EVs' usage cost d ij Travel distance from node i to j where i, j ∈ V e ij Energy consumption traveling from node i to node j, e ij = d ij , where is the energy consumption rate g i Charging time per unit power(1 kWh) at node i, i ∈ V

An electric vehicle routing model with charging stations consideration for sustainable logistics

“…Initially, exact algorithms were used to solve the electric vehicle routing problem, which can find the optimal solution, including algorithms such as Branch and Price (Bahrami et al, 2020;Lee, 2021), Branch and Price and Cut and Mixed Integer Programming (Yao et al, 2022a;. For example, used the Branch and Price and Cut to solve the electric vehicle routing problem with charging stations, while Yao et al (2022a) explored the joint distribution routing problem for electric vehicles by Mixed Integer Programming. Usually, exact algorithms are suitable for solving small-scale optimization problems.…”

“…Initially, exact algorithms were used to solve the electric vehicle routing problem, which can find the optimal solution, including algorithms such as Branch and Price (Bahrami et al ., 2020; Lee, 2021), Branch and Price and Cut (Duman et al ., 2022; Lam et al ., 2022) and Mixed Integer Programming (Yao et al ., 2022a; Zhou et al ., 2021). For example, Lam et al .…”

“…For example, Lam et al . (2022) used the Branch and Price and Cut to solve the electric vehicle routing problem with charging stations, while Yao et al . (2022a) explored the joint distribution routing problem for electric vehicles by Mixed Integer Programming.…”

Optimal Design of Modular Electrical Infrastructure for Large-Scale Electric Bus Depots

“…Their contribution was to design a battery storage system, that can mitigate the peak demands to reduce the electricity bills. In [15] a case study for solving an optimization problem of routing and charging electric vehicles is presented. The authors decomposed the MIP problem into two linear programming problems.…”

Joint Routing and Charging Problem of Electric Vehicles With Incentive-Aware Customers Considering Spatio-Temporal Charging Prices

“…Due to the local zero-carbon emissions of EVs, the EVRP has recently drawn great attention from the academic community [2], [11], [15], [16], [17], [18]. In order to cope with the computational complexity stemming from the routing and charging problem of EVs, which is essentially a mixed-integer nonlinear programming problem, we proposed a computational-efficient method based on convex optimization [15].…”