Incorporating emissions models within a multi-objectivevehicle routing problem

The vehicle routing problem with time windows (VRPTW) has previously been investigated as a multi-objective problem. In this paper estimated carbon emissions is added as an objective alongside the number of vehicles required and distance travelled. We term this new problem formulation (E)VRPTW. In order to estimate emissions we require detailed information regarding the nature of the route to be taken. As previous benchmark VRPTW problem instances do not supply such information we generate new problem instances based upon street network data from Open Street Map. Results suggest that by adding emissions as the third objective, in many cases the search may be directed to areas that allow improvement in the distance and vehicles objectives. As emissions and distance are inherently related, we do not search for pareto fronts. Rather we attempt to find solutions that either minimise distance or minimise vehicles used. Adding the third emissions objective is shown to enable a multi-objective EA to find improved solutions in terms of minimal vehicles or minimal distance when compared to the same multi-objective EA using only two objectives.