Unranking combinations using gradient-based optimization

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    1 Citation (Scopus)

    Abstract

    Combinations of m out of n are ubiquitous to model a wide class of combinatorial problems. For an ordered sequence of combinations, the unranking function generates the combination associated to an integer number in the ordered sequence. In this paper, we present a new method for unranking combinations by using a gradient-based optimization approach. Exhaustive experiments within computable allowable limits confirmed the feasibility and efficiency of our proposed approach. Particularly, our algorithmic realization aided by a Graphics Processing Unit (GPU) was able to generate arbitrary combinations within 0.571 seconds and 8 iterations in the worst case scenario, for n up to 1000 and m up to 100. Also, the performance and efficiency to generate combinations are independent of n, being meritorious when n is very large compared to m, or when n is time-varying. Furthermore, the number of required iterations to generate the combinations by the gradient-based optimization decreases with m in average, implying the attractive scalability in terms of m. Our proposed approach offers the building blocks to enable the succinct modeling and the efficient optimization of combinatorial structures.

    Original languageEnglish
    Title of host publicationProceedings - 2018 IEEE 30th International Conference on Tools with Artificial Intelligence, ICTAI 2018
    PublisherIEEE Computer Society
    Pages579-586
    Number of pages8
    Volume2018-November
    ISBN (Electronic)9781538674499
    DOIs
    Publication statusPublished - 2018 Dec 13
    Event30th International Conference on Tools with Artificial Intelligence, ICTAI 2018 - Volos, Greece
    Duration: 2018 Nov 52018 Nov 7

    Other

    Other30th International Conference on Tools with Artificial Intelligence, ICTAI 2018
    CountryGreece
    CityVolos
    Period18/11/518/11/7

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    Keywords

    • Binomial
    • Combinations
    • Combinatorial
    • Combinatorics
    • Gradient based optimization
    • K out of n
    • M our of n
    • Optimization
    • Representation
    • Unranking

    ASJC Scopus subject areas

    • Software
    • Artificial Intelligence
    • Computer Science Applications

    Cite this

    Parque Tenorio, V., & Miyashita, T. (2018). Unranking combinations using gradient-based optimization. In Proceedings - 2018 IEEE 30th International Conference on Tools with Artificial Intelligence, ICTAI 2018 (Vol. 2018-November, pp. 579-586). [8576092] IEEE Computer Society. https://doi.org/10.1109/ICTAI.2018.00094