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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Notes
- 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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Zapotecas-Martínez, S., Derbel, B., Liefooghe, A., Aguirre, H.E., Tanaka, K. (2015). Geometric Differential Evolution in MOEA/D: A Preliminary Study. In: Sidorov, G., Galicia-Haro, S. (eds) Advances in Artificial Intelligence and Soft Computing. MICAI 2015. Lecture Notes in Computer Science(), vol 9413. Springer, Cham. https://doi.org/10.1007/978-3-319-27060-9_30
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