A New Improved Quantum Evolution Algorithm with Local Search Procedure for Capacitated Vehicle Routing Problem

Ligang Cui,Jinlong Zhang,Jie Deng,Lin Wang

doi:10.1155/2013/159495

Abstract

The capacitated vehicle routing problem (CVRP) is the most classical vehicle routing problem (VRP); many solution techniques are proposed to find its better answer. In this paper, a new improved quantum evolution algorithm (IQEA) with a mixed local search procedure is proposed for solving CVRPs. First, an IQEA with a double chain quantum chromosome, new quantum rotation schemes, and self-adaptive quantum Not gate is constructed to initialize and generate feasible solutions. Then, to further strengthen IQEA's searching ability, three local search procedures 1-1 exchange, 1-0 exchange, and 2-OPT, are adopted. Experiments on a small case have been conducted to analyze the sensitivity of main parameters and compare the performances of the IQEA with different local search strategies. Together with results from the testing of CVRP benchmarks, the superiorities of the proposed algorithm over the PSO, SR-1, and SR-2 have been demonstrated. At last, a profound analysis of the experimental results is presented and some suggestions on future researches are given.

Highlights

Vehicle routing problem (VRP) has been presented more than fifty years by Dantzig and Ramser [1], and it is still drawing many researchers’ attention [2, 3]
There are some characters about three local search operators: (1) 1-1 exchange procedure deals with two client vertexes corresponding to two routes, without impacting the sequence of the two routes; (2) 1-0 exchange procedure is to extract one vertex from one route and insert it into another route, while the relative positions of remaining vertexes in two candidate routes are without changes; (3) 2-OPT procedure only arranges the vertexes sequence of one candidate route and has nothing to do with other routes
The capacitated vehicle routing problem (CVRP) has been presented for tens of years, still much attention has been put on it

Summary

Introduction

Vehicle routing problem (VRP) has been presented more than fifty years by Dantzig and Ramser [1], and it is still drawing many researchers’ attention [2, 3]. It is well known that VRP is an NP-hard problem [6]. While CVRP is the most basic problem of VRPs and studying CVRP has a fundamental meaning to learn other advanced problems in this field and develop its solution methodologies [7]. Laporte [8] reviewed the VRP algorithms development from 1959 to 2009; these algorithms were classified as exact algorithm, classical heuristic algorithm, and metaheuristic algorithm. As it was stated in his paper, solving an NP-hard

Methods

Results

Conclusion