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

TL;DR

This paper introduces a fast, two-stage optimization algorithm for the complex joint routing and charging problem of multiple electric vehicles, enabling near-optimal solutions in polynomial time.

Contribution

It proposes an efficient two-stage algorithm that decomposes a complex MIP problem into two LP problems, improving solution speed and quality for EV routing and charging.

Findings

Achieves near-optimal solutions in polynomial time.

Decomposes MIP into LP problems for efficiency.

Further improves solution quality with a variant algorithm.

Abstract

Logistics has gained great attentions with the prosperous development of 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. 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.