An Empirical Investigation of Four Well-Known Polynomial-Size VRP Formulations

TL;DR

This paper conducts a comprehensive computational comparison of four polynomial-size CVRP formulations, evaluating their performance with various inequalities and a granulation scheme across 121 instances.

Contribution

It provides an extensive empirical analysis of different CVRP formulations and introduces a topology-driven granulation scheme to improve solution efficiency.

Findings

Formulations vary in bounding performance and efficiency.

Adding valid inequalities improves solution bounds.

Granulation scheme reduces computational complexity.

Abstract

This study presents an in-depth computational analysis of four well-known Capacitated Vehicle Routing Problem (CVRP) formulations with polynomial number of subtour elimination constraints: a node-based formulation and three arc-based (single, two- and multi-commodity flow) formulations. For each formulation, several valid inequalities (VIs) are added for the purpose of tightening the formulation. Moreover, a simple topology-driven granulation scheme is proposed to reduce the number of a certain type of VIs. The lower and upper bounding performance and the solution efficiency of the formulations and respective VI configurations are benchmarked with state-of-the-art commercial optimization software. The extensive computational analysis embraces 121 instances with up to 100 customer nodes. We believe that our findings could be useful for practitioners as well as researchers developing algorithms for the CVRP.