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Parallelism in divide-and-conquer non-dominated sorting: a theoretical study considering the PRAM-CREW model

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Abstract

Non-dominated sorting is a crucial component of Pareto-based multi- and many-objective evolutionary algorithms. As the number of objectives increases, the execution time of a multi-objective evolutionary algorithm increases, too. Since multi-objective evolutionary algorithms normally have a low data dependency, research-ers have increasingly adopted parallel programming techniques to reduce their execution time. Evidently, it is also desirable to parallelize non-dominated sorting. There are some recent proposals which focus on the parallelization of non-dominated sorting, with a particular emphasis on a very well-known approach called fast non-dominated sorting. In this paper, however, we explore the scope of parallelism in an approach called divide-and-conquer based non-dominated sorting (DCNS), which we recently introduced. This paper explores the parallelism from a theoretical point of view. The parallelization of the DCNS approach has been explored considering the PRAM-CREW (Parallel Random Access Machine, Concurrent Read Exclusive Write) model. The analysis of parallel algorithms is usually carried out under the assumption that an unbounded number of processors are available. So, in our analysis, we have also considered the same assumption. The time and space complexities of the parallel version of the DCNS approach is obtained in different scenarios. The time complexity of the parallel version of the DCNS approach in different scenarios is proved to be \(\mathcal {O}(\log M + N)\). We have also obtained the maximum number of processors which can be required by the parallel version of the DCNS approach. The comparison of the parallel version of the DCNS approach with respect to some other approaches is also performed.

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Notes

  1. https://github.com/Proteek/Best-Order-Sort/.

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Acknowledgements

The second author gratefully acknowledges support from CONACyT Grant No. 2016-01-1920 (Investigación en Fronteras de la Ciencia 2016).

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Authors and Affiliations

  1. Departamento de Computación, CINVESTAV-IPN, 07360, Mexico City, D.F., Mexico

    Sumit Mishra & Carlos A. Coello Coello

  2. Department of Computer Science and Engineering, Indian Institute of Information Technology Guwahati, Guwahati, Assam, 781015, India

    Sumit Mishra

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  1. Sumit Mishra
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  2. Carlos A. Coello Coello
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Correspondence to Sumit Mishra.

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Mishra, S., Coello Coello, C.A. Parallelism in divide-and-conquer non-dominated sorting: a theoretical study considering the PRAM-CREW model. J Heuristics 25, 455–483 (2019). https://doi.org/10.1007/s10732-019-09407-y

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  • DOI: https://doi.org/10.1007/s10732-019-09407-y

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