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

## TL;DR

This paper evaluates seven different objective functions for the Vehicle Routing Problem with Route Balancing, analyzing their impact on solution quality using an evolutionary algorithm and benchmark instances.

## Contribution

It provides a comparative analysis of objective functions for VRPRB, highlighting the importance of evaluation schemes in multiobjective optimization.

## Key findings

- Different OFs significantly influence Pareto solution quality.
- Some OFs outperform others in balancing routes effectively.
- Studying alternative evaluation schemes is valuable for future research.

## Abstract

The Vehicle Routing Problem with Route Balancing (VRPRB) is a biobjective 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 multiobjective 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.