Solving the Capacitated Vehicle Routing Problem using a new Genetic Algorithm

Abstract

The Capacitated Vehicle Routing Problem (CVRP) [1, 2, 3] is an extension to the Vehicle Routing Problem (VRP), a well-known NP-hard optimization problem. In our CVRP, we are given a depot, the number of vehicles and their capacity, as well as a set of customers and their demands, both the depot and the set of customers lie in the Euclidean space. The goal is to find for each vehicle an optimal route (tour) starting and finishing at the depot, such that all customers are served exactly once.\nIn this study, we investigate the effectiveness of using a Genetic Algorithm (GA) [4] approach to solve the CVRP by treating the entire solution as a chromosome and individual routes as genes. Our approach uses a unique framework for the mutation operation which is a combination of three different algorithms, namely the reallocation mutation, the exchange mutation, and the reposition mutation. In the past, these mutation algorithms were only executed exclusively depending on the case. The combination of all these three approaches allows diversity in the chromosome population, thus allowing exploration of the search space without prematurely converging into a local minima.\nFor our experiments, we implemented our GA from scratch and relied on the benchmark CVRP datasets for the comparison. Our comparison with the best-known previous solutions for these datasets shows that in some cases our GA outperforms or is close to them.