Unranking combinations using gradient-based optimization

Victor Parque*, Tomoyuki Miyashita

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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
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

Publication series

NameProceedings - International Conference on Tools with Artificial Intelligence, ICTAI
Volume2018-November
ISSN (Print)1082-3409

Other

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

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

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