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Metaheuristics for the template design problem: encoding, symmetry and hybridisation

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Abstract

The template design problem (TDP) is a hard combinatorial problem with a high number of symmetries which makes solving it more complicated. A number of techniques have been proposed in the literature to optimise its resolution, ranging from complete methods to stochastic ones. However, although metaheuristics are considered efficient methods that can find enough-quality solutions at a reasonable computational cost, these techniques have not proven to be truly efficient enough to deal with this problem. This paper explores and analyses a wide range of metaheuristics to tackle the problem with the aim of assessing their suitability for finding template designs. We tackle the problem using a wide set of metaheuristics whose implementation is guided by a number of issues such as problem formulation, solution encoding, the symmetrical nature of the problem, and distinct forms of hybridisation. For the TDP, we also propose a slot-based alternative problem formulation (distinct to other slot-based proposals), which represents another option other than the classical variation-based formulation of the problem. An empirical analysis, assessing the performance of all the metaheuristics (i.e., basic, integrative and collaborative algorithms working on different search spaces and with/without symmetry breaking) shows that some of our proposals can be considered the state-of-the-art when they are applied to specific problem instances.

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Notes

  1. To this end, individuals, whose genotypic distance (in a Hamming sense) to individuals in the receiving population is maximal, are selected.

  2. In order to favour transparent research, and encourage comparison with other research, both the data employed in the work presented here and the source code of the algorithms generated from it have been deposited in a public repository: https://github.com/drrueda/TDP (August 2019).

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Acknowledgements

This work is partially funded by Ministerio Español de Economía y Competitividad (Projects TIN2014-56494-C4-1-P, UMA::EPHEMECH—https://ephemech.wordpress.com/ and TIN2017-85727-C4-1-P, UMA::DeepBio–https://deepbio.wordpress.com/) and Universidad de Málaga.

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Correspondence to Antonio J. Fernández-Leiva.

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Rodríguez Rueda, D., Cotta, C. & Fernández-Leiva, A.J. Metaheuristics for the template design problem: encoding, symmetry and hybridisation. J Intell Manuf 32, 559–578 (2021). https://doi.org/10.1007/s10845-020-01587-w

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