A Multi-Objective approach to the Electric Vehicle Routing Problem

The electric vehicle routing problem (EVRP) has garnered great interest from researchers and industrialists in an attempt to move from fuel-based vehicles to healthier and more efficient electric vehicles (EVs). While it seems that the EVRP should not be much different from traditional vehicle routing problems (VRPs), challenges like limited cruising time, long charging times, and limited availability of charging facilities for electric vehicles makes all the difference. Previous works target logistics and delivery-related solutions wherein a homogeneous fleet of commercial EVs have to return to the initial point after making multiple stops. On the opposing front, we solve a personal electric vehicle routing problem and provide an optimal route for a single vehicle in a long origin-destination (OD) trip. We perform multi-objective optimization - minimizing the total trip time and the cumulative cost of charging. In addition, we incorporate external and real-life elements like traffic at charging stations, detour distances for reaching a charging station, and variable costs of electricity at different charging stations into the problem formulation. In particular, we define a multi-objective mixed integer non-linear programming (MINLP) problem and obtain a feasible solution using the $\epsilon$-constraint algorithm. We further implement meta-heuristic techniques such as Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) to obtain the most optimal route and hence, the objective values. The experiment is carried out for multiple self-generated data instances and the results are thereby compared.