The Electric Vehicle Routing Problem with Nonlinear Charging Functions

TL;DR

This paper introduces exact and heuristic algorithms for the electric vehicle routing problem with nonlinear charging functions, capturing realistic EV features and solving benchmark instances efficiently.

Contribution

It presents a novel branch-and-price-and-cut algorithm and a tabu search heuristic for the E-VRP-NL, addressing nonlinear charging and complex operational constraints.

Findings

Exact algorithm solves instances with up to 40 customers.

Heuristic outperforms existing methods in solution quality.

Algorithms are validated on benchmark instances from the literature.

Abstract

This paper outlines an exact and a heuristic algorithm for the electric vehicle routing problem with a nonlinear charging function (E-VRP-NL) introduced by Montoya et al. (2017). The E-VRP-NL captures several realistic features of electric vehicles including the battery limited driving range and nonlinear charging process at the charging stations. We formulate this problem as a set-partitioning and solve it using a column generation based algorithm. The resulting pricing problem of the column generation is a complicated problem as, next to the usual operational constraints e.g. time windows and vehicle capacity, electric vehicle related features are also considered. In particular, the nonlinear nature of the battery charging process requires the incorporation of a set of sophisticated recursive functions in the pricing algorithm. We show how these recursive functions allow for the simultaneous evaluation of the routing and charging decisions. Moreover, we illustrate how they can efficiently be embedded in the pricing algorithm. The column generation algorithm is integrated in a branch and bound algorithm and cutting planes are added resulting in a branch-and-price-and-cut algorithm for the E-VRP-NL. Next to the exact algorithm, we also develop a tabu search based heuristic to solve the problem quickly. To prove the efficiency of the proposed algorithms, their performance is tested on benchmark instances from the literature. Our exact algorithm can optimally solve instances with up to 40 customers, including several instances previously unsolved to optimality. The tabu search heuristic proves to be superior to state-of-the-art heuristics in the literature both on solution quality and computation times.