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Signs-Based vs. Symbolic Models Read chapter Read first chapter

2015 | OriginalPaper | Chapter

Geometric Differential Evolution in MOEA/D: A Preliminary Study

Authors : Saúl Zapotecas-Martínez, Bilel Derbel, Arnaud Liefooghe, Hernán E. Aguirre, Kiyoshi Tanaka

Published in: Advances in Artificial Intelligence and Soft Computing

Publisher: Springer International Publishing

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Abstract

The multi-objective evolutionary algorithm based on decomposition (MOEA/D) is an aggregation-based algorithm which has became successful for solving multi-objective optimization problems (MOPs). So far, for the continuous domain, the most successful variants of MOEA/D are based on differential evolution (DE) operators. However, no investigations on the application of DE-like operators within MOEA/D exist in the context of combinatorial optimization. This is precisely the focus of the work reported in this paper. More particularly, we study the incorporation of geometric differential evolution (gDE), the discrete generalization of DE, into the MOEA/D framework. We conduct preliminary experiments in order to study the effectiveness of gDE when coupled with MOEA/D. Our results indicate that the proposed approach is able to outperform the standard version of MOEA/D, when solving a combinatorial optimization problem having between two and four objective functions.

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Footnotes
1
Note, however, that in the minimization case \(d_1 = \frac{||(\varvec{F}(\varvec{x}) -\varvec{z}^{\star } )^\intercal \mathbf {\lambda }||}{||\mathbf {\lambda }||}\), \(d_2 = \left| \left| (\mathbf {F}(\mathbf {x}) - \right. \right. \) \(\left. \left. \mathbf {z}^{\star }) - d_1\frac{\mathbf {\lambda }}{||\mathbf {\lambda }||}\right| \right| \) and the reference point is such that \(\forall i\in \{1,\ldots ,M\},\forall \mathbf {x}\in X, z^\star <f_i(\mathbf {x})\).
 
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Metadata
Title
Geometric Differential Evolution in MOEA/D: A Preliminary Study
Authors
Saúl Zapotecas-Martínez
Bilel Derbel
Arnaud Liefooghe
Hernán E. Aguirre
Kiyoshi Tanaka
Copyright Year
2015
Book
Advances in Artificial Intelligence and Soft Computing

Print ISBN: 978-3-319-27059-3

Electronic ISBN: 978-3-319-27060-9

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-27060-9_30

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