A Statistical Comparison of Objective Functions for the Vehicle Routing Problem with Route Balancing

The Vehicle Routing Problem with Route Balancing (VRPRB) is a bi-objective version of the original Vehicle Routing Problem (VRP) in which, besides minimizing the total distance traveled by the vehicles involved, the balance among route loads is also pursued. Different objective functions (OFs) to achieve balanced route configurations have been proposed in the literature, however to the best of the authors' knowledge there is still no consensus on which OF is the most suitable one for addressing, through metaheuristics, this challenging multi-objective optimization problem. This paper inquires into the effectiveness of seven different OFs for the VRPRB. Their influence on the performance of a basic single-solution-based evolutionary algorithm is analyzed by comparing the quality of the Pareto-approximations produced for a set of well-known benchmark instances. The obtained results indicate that studying alternative evaluation schemes for the VRPRB represents a highly valuable direction for future research which merits more attention.