The Time-dependent Electric Vehicle Routing Problem: Model and solution

Abstract

We study a new problem named the Time-dependent Electric Vehicle Routing Problem (TDEVRP) which involves routing a fleet of electric vehicles to serve a set of customers and determining the vehicle’s speed and departure time at each arc of the routes with the purpose of minimizing a cost function. We propose an integer linear programming (ILP) model to formulate the TDEVRP and show that the state-of-the-art commercial optimizer (CPLEX) can only solve instances of very limited sizes (with no more than 15 customers). We thus propose an iterated variable neighbourhood search (IVNS) algorithm to find near-optimal solutions for larger instances. The key ingredients of IVNS include a fast evaluation method that allows local search moves to be evaluated in constant time O(1), a variable neighbourhood descent (VND) procedure to optimize the node sequences, and a departure time and speed optimization procedure(DSOP) to optimize the speed and departure time on each arc of the routes. The proposed algorithm demonstrates excellent performances on a set of newly created instances. In particular, it can achieve optimal or near-optimal solutions for all small-size instances (with no more than 15 customers) and is robust for large-size instances where the gap between the average and the best solution value is consistently lower than 2.38%. Additional experimental results on 40 benchmark instances of the closely related Time-Dependent Pollution Routing Problem indicate that the proposed IVNS algorithm also performs very well and even discovers 39 new best-known solutions (improved upper bounds).