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INFORMATICA, 2012, Vol. 23, No. 4, 601-620
© Institute of Mathematics and Informatics,

ISSN 0868-4952

Multimodal Evolutionary Algorithm for Multidimensional Scaling with City-Block Distances

Juana López REDONDO, Pilar Martínez ORTIGOSA, Julius ZILINSKAS

Department of Computer Architecture and Technology, University of Granada Periodista Daniel Saucedo Aranda, s/n. 18071 Granada, Spain Department of Informatics, University of Almería Campus de Excelencia Internacional Agroalimentario (ceiA3), Spain Vilnius University Institute of Mathematics and Informatics Akademijos 4, LT-08663 Vilnius, Lithuania E-mail: jlredondo@atc.ugr.es, ortigosa@ual.es, julius.zilinskas@mii.vu.lt

Abstract

Multidimensional scaling with city-block distances is considered in this paper. The technique requires optimization of an objective function which has many local minima and can be non-differentiable at minimum points. This study is aimed at developing a fast and effective global optimization algorithm spanning the whole search domain and providing good solutions. A multimodal evolutionary algorithm is used for global optimization to prevent stagnation at bad local optima. Piecewise quadratic structure of the least squares objective function with city-block distances has been exploited for local improvement. The proposed algorithm has been compared with other algorithms described in literature. Through a comprehensive computational study, it is shown that the proposed algorithm provides the best results. The algorithm with fine-tuned parameters finds the global minimum with a high probability.

Keywords:

multidimensional scaling
city-block distances
evolutionary algorithms
multimodal algorithms

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