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 language | English |
|---|---|
| Title of host publication | Proceedings - 2018 IEEE 30th International Conference on Tools with Artificial Intelligence, ICTAI 2018 |
| Publisher | IEEE Computer Society |
| Pages | 579-586 |
| Number of pages | 8 |
| Volume | 2018-November |
| ISBN (Electronic) | 9781538674499 |
| DOIs | |
| Publication status | Published - 2018 Dec 13 |
| Event | 30th International Conference on Tools with Artificial Intelligence, ICTAI 2018 - Volos, Greece Duration: 2018 Nov 5 → 2018 Nov 7 |
Other
| Other | 30th International Conference on Tools with Artificial Intelligence, ICTAI 2018 |
|---|---|
| Country | Greece |
| City | Volos |
| Period | 18/11/5 → 18/11/7 |
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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
Unranking combinations using gradient-based optimization. / Parque Tenorio, Victor; Miyashita, Tomoyuki.
Proceedings - 2018 IEEE 30th International Conference on Tools with Artificial Intelligence, ICTAI 2018. Vol. 2018-November IEEE Computer Society, 2018. p. 579-586 8576092.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Unranking combinations using gradient-based optimization
AU - Parque Tenorio, Victor
AU - Miyashita, Tomoyuki
PY - 2018/12/13
Y1 - 2018/12/13
N2 - 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.
AB - 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.
KW - Binomial
KW - Combinations
KW - Combinatorial
KW - Combinatorics
KW - Gradient based optimization
KW - K out of n
KW - M our of n
KW - Optimization
KW - Representation
KW - Unranking
UR - http://www.scopus.com/inward/record.url?scp=85060821842&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85060821842&partnerID=8YFLogxK
U2 - 10.1109/ICTAI.2018.00094
DO - 10.1109/ICTAI.2018.00094
M3 - Conference contribution
AN - SCOPUS:85060821842
VL - 2018-November
SP - 579
EP - 586
BT - Proceedings - 2018 IEEE 30th International Conference on Tools with Artificial Intelligence, ICTAI 2018
PB - IEEE Computer Society
ER -