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Mathematical Problems in Engineering
Volume 2012, Article ID 954249, 14 pages
Research Article

A Hybrid Approach Using an Artificial Bee Algorithm with Mixed Integer Programming Applied to a Large-Scale Capacitated Facility Location Problem

1Escuela de Ingeniería Informática, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362807, Chile
2Department of Engineering Science, University of Auckland, Auckland 1020, New Zealand
3Instituto de Estadística, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362807, Chile
4CIMFAV Facultad de Ingeniería, Universidad de Valparaíso, Valparaíso 2362735, Chile
5Universidad Autónoma de Chile, Santiago 7500138, Chile
6Departamento de Computación e Informática, Universidad de Playa Ancha, Valparaíso 33449, Chile
7Escuela de Ingeniería Industrial, Universidad Diego Portales, Santiago 8370109, Chile

Received 6 September 2012; Revised 12 November 2012; Accepted 14 November 2012

Academic Editor: Rui Mu

Copyright © 2012 Guillermo Cabrera G. et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present a hybridization of two different approaches applied to the well-known Capacitated Facility Location Problem (CFLP). The Artificial Bee algorithm (BA) is used to select a promising subset of locations (warehouses) which are solely included in the Mixed Integer Programming (MIP) model. Next, the algorithm solves the subproblem by considering the entire set of customers. The hybrid implementation allows us to bypass certain inherited weaknesses of each algorithm, which means that we are able to find an optimal solution in an acceptable computational time. In this paper we demonstrate that BA can be significantly improved by use of the MIP algorithm. At the same time, our hybrid implementation allows the MIP algorithm to reach the optimal solution in a considerably shorter time than is needed to solve the model using the entire dataset directly within the model. Our hybrid approach outperforms the results obtained by each technique separately. It is able to find the optimal solution in a shorter time than each technique on its own, and the results are highly competitive with the state-of-the-art in large-scale optimization. Furthermore, according to our results, combining the BA with a mathematical programming approach appears to be an interesting research area in combinatorial optimization.