A study on the effect of the asymmetry on real capacitated vehicle routing problems

Matrices with distances between pairs of locations are essential for solving vehicle routing problems like the Capacitated Vehicle Routing Problem (CVRP), Traveling Salesman Problem (TSP) and others. This work deals with the complex reality of transportation networks and asymmetry. Through a series of comprehensive and thorough computational and statistical experiments we study the effect that many factors like asymmetry, geographical location of the depot and clients, demand, territory and maximum vehicle capacity have in the solution of $CVRP$ instances. We examine both classical heuristics as well as current state-of-the-art metaheuristics and show that these methods are seriously affected by the studied factors from a solution time and quality of solutions perspective. We systematically compare the solutions obtained in the symmetric scenario with those obtained in the real asymmetric case at a quantitative as well as a qualitative level, with the objective of carefully measuring and understanding the differences between both cases.