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## versión impresa ISSN 1405-5546

### Comp. y Sist. vol.14 no.3 México ene./mar. 2011

Artículos

A Statistical comparative analysis of Simulated Annealing and Variable Neighborhood Search for the Geographic Clustering Problem

Un análisis estadístico comparativo de recocido simulado y búsqueda de vecindad variable para el problema de agregación geográfica

Beatriz Bernábe Loranca1, José E. Espinosa Rosales2, Javier Ramírez Rodríguez3 and María A. Osorio Lama4

1 Facultad de Ciencias de la Computación, Benemérita Universidad Autónoma de Puebla, Puebla, México. Email: beatriz.bernabe@gmail.com

2 Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Puebla, México. Email: espinosa@fcfm.buap.mx

3 Departamento de Sistemas, Universidad Autónoma Metropolitana, Distrito Federal, México. Email: jararo@correo.azc.uam.mx

4 Facultad de Ingeniería Química, Benemérita Universidad Autónoma de Puebla, Puebla, México. Email: mariauxosorio@gmail.com

Article received on October 23, 2009
Accepted on May 06, 2010

Abstract

This paper describes a factorial statistical study that compares the quality of solutions produced by two heuristics: Simulated Annealing (SA) and Variable Neighborhood Search (VNS). These methods are used to solve the Geographic Clustering Problem (GCP), and the quality of the solutions produced for specific times has been compared. With the goal of comparing the quality of the solutions, where both heuristics participate in an impartial evaluation, time has been the only common element considered for VNS and SA. At this point, two factorial experiments were designed and the corresponding parameters for each heuristic were carefully modeled leaving time as the cost function. In instances of 24 objects, the experiments involved the execution of two sets of tests recording the results of the different response times and the associated values of the objective function for each heuristic and instance conditions. The solution to this problem requires a partitioning process where each group is composed of objects that fulfill better the objective: the minimum accumulated distance from the objects to the centroid of each group. The GCP is a combinatorial NP–hard problem (Bação, Lobo and Painho, 2004).

Keywords: Algorithms, Design, Experimentation, Geographic Clustering Problem, Heuristics.

Resumen

Palabras clave: Algoritmos, Diseño, Experimentación, Problema de Agrupamiento Geográfico, Heurísticas.

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