A Randomized Variable Neighborhood Search Algorithm for solving the Capacitated Vehicle Routing Problem

With the rapid development of market economy and the evolution of modern technology, logistics industry has also achieved great development. In logistics distribution, the optimization of distribution path plays a vital role in improving service quality, reducing logistics costs and improving economic benefits for enterprises. Because of the low efficiency of the single heuristic algorithm in solving Capacitated Vehicle Routing Problem (CVRP), this paper proposes a new hybrid algorithm. This hybrid algorithm uses the greedy algorithm to get initial solution, and takes random variable neighborhood search(VNS) as the local search method, and combined with the Metropolis acceptance criteria. The proposed algorithm tests many instances which are widely used and compares with the other heuristic algorithm. In particular, it is capable of finding the optimal solution for all tested instances and it is much faster than the well-known Lin-Kernighan-Helsgaun (LKH) algorithm in terms of computational speed.

I. Introduction

The Capacitated Vehicle Routing Problem (CVRP) was originally proposed by Dantzig and Ramser in 1959 [1] and it is an version of the Traveling Salesman Problem(TSP), and its purpose is to find a set of optimal tours for a fleet of homogenous vehicles with a given capacity limit, where each vehicle deviates from the depot and visits several customers, and finally returns to the depot. Fig 1 gives an illustrating example of the CVRP with 3 vehicles and 13 customers.