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Memetic algorithms and hyperheuristics applied to a multiobjectivised two-dimensional packing problem

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Abstract

Packing problems are np-hard problems with several practical applications. A variant of a 2d Packing Problem (2dpp) was proposed in the gecco 2008 competition session. In this paper, Memetic Algorithms (mas) and Hyperheuristics are applied to a multiobjectivised version of the 2dpp. Multiobjectivisation is the reformulation of a mono-objective problem into a multi-objective one. The main aim of multiobjectivising the 2dpp is to avoid stagnation in local optima. First generation mas refers to hybrid algorithms that combine a population-based global search with an individual learning process. A novel first generation ma is proposed, and an original multiobjectivisation method is applied to the 2dpp. In addition, with the aim of facilitating the application of such first generation mas from the point of view of the parameter setting, and of enabling their usage in parallel environments, a parallel hyperheuristic is also applied. Particularly, the method applied here is a hybrid approach which combines a parallel island-based model and a hyperheuristic. The main objective of this work is twofold. Firstly, to analyse the advantages and drawbacks of a set of first generation mas. Secondly, to attempt to avoid those drawbacks by applying a parallel hyperheuristic. Moreover, robustness and scalability analyses of the parallel scheme are included. Finally, we should note that our methods improve on the current best-known solutions for the tested instances of the 2dpp.

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  1. http://www.isgec.org/gecco-2008/competitions.html

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Acknowledgments

This work was funded in part by the ec (feder) and the Spanish Ministry of Science and Innovation as part of the ‘Plan Nacional de i+d+i’, with contract number tin2011-25448. The work of Carlos Segura was funded by grant fpu-ap2008-03213. The work of Eduardo Segredo was funded by grant fpu-ap2009-0457 The work was also funded by the hpc-europa2 project (project number: 228398) with the support of the European Commission—Capacities Area—Research Infrastructures. Our research made use of the facilities of hector, the uk’s national high-performance computing service, which is provided by uoe hpcx Ltd at the University of Edinburgh, Cray Inc and nag Ltd, and funded by the Office of Science and Technology through the epsrc’s High End Computing Programme.

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  1. Dpto. Estadística, I. O. y Computación, Universidad de La Laguna, Avda. Astrofísico Francisco Sánchez, s/n, 38271 , La Laguna, Santa Cruz de Tenerife, Spain

    Eduardo Segredo, Carlos Segura & Coromoto León

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  1. Eduardo Segredo
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  2. Carlos Segura
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Correspondence to Eduardo Segredo.

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Segredo, E., Segura, C. & León, C. Memetic algorithms and hyperheuristics applied to a multiobjectivised two-dimensional packing problem. J Glob Optim 58, 769–794 (2014). https://doi.org/10.1007/s10898-013-0088-4

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