A Hybrid Bat Algorithm with Path Relinking for Capacitated Vehicle Routing Problem

Yongquan Zhou,Hongqing Zheng,Jian Xie

doi:10.1155/2013/392789

Yongquan Zhou, Hongqing Zheng + Show 1 more

Open Access

https://doi.org/10.1155/2013/392789

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Abstract

The capacitated vehicle routing problem (CVRP) is an NP-hard problem with wide engineering and theoretical background. In this paper, a hybrid bat algorithm with path relinking (HBA-PR) is proposed to solve CVRP. The HBA-PR is constructed based on the framework of continuous bat algorithm; the greedy randomized adaptive search procedure (GRASP) and path relinking are effectively integrated into bat algorithm. Moreover, in order to further improve the performance, the random subsequences and single-point local search are operated with certain loudness (probability). In order to verify the validity of the method in this paper, and it's efficiency and with other existing methods, several classical CVRP instances from three classes of CVRP benchmarks are selected to tested. Experimental results and comparisons show that the HBA-PR is effective for CVRP.

Highlights

The vehicle routing problem (VRP) is a classical combinatorial optimization problem that was proposed in the late 1950s, and it is still a research hotspot in the field of Operations Research
We propose a hybrid bat algorithm (HBA-PR) to solve capacitated vehicle routing problem
We propose in this work, to incorporate greedy randomized adaptive search procedure, path-relinking strategies, subsequence, and single-point local search to the bat algorithm by defining distinct ways to solve capacitated vehicle routing problem

Summary

Introduction

The vehicle routing problem (VRP) is a classical combinatorial optimization problem that was proposed in the late 1950s, and it is still a research hotspot in the field of Operations Research. The capacitated vehicle routing problem (CVRP) is introduced by Dantzig and Ramser in 1959 [1], which designs a set of customer demands that have to be served with a fleet of vehicles from a depot or central node, each vehicle has the uniform capacity, and each customer has a certain demand that must be satisfied at minimal cost. These costs usually represent distances, traveling times, number of vehicles employed, or a combination of these factors. We propose a hybrid bat algorithm (HBA-PR) to solve capacitated vehicle routing problem.

Problem Descriptions and Bat Algorithm

Hybrid Bat Algorithm with Path Relinking for CVRP

Numerical Simulation Results and Comparisons

BKS 661 742 669 831 569 375 839 521 212 216 216 741

Conclusions