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Cliques for Multi-Term Linearization of 0–1 Multilinear Program for Boolean Logical Pattern Generation

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Optimization of Complex Systems: Theory, Models, Algorithms and Applications (WCGO 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 991))

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Abstract

0–1 multilinear program (MP) holds a unifying theory to Boolean logical pattern generation. For a tighter polyhedral relaxation of MP, this note exploits cliques in the graph representation of data under analysis to generate valid inequalities for MP that subsume all previous results and, collectively, provide a much stronger relaxation of MP. A preliminary numerical study demonstrates strength and practical benefits of the new results.

\({}^{1}\)This work was supported by National Natural Science Foundation of China (Grant Number: 61806095.)

\({}^{2}\)Corresponding author. This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant Number: 2017R1D1A1A02018729.)

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Authors and Affiliations

  1. Department of Computer Science and Technology, School of Computer Science and Engineering, Nanjing University of Science and Technology, 200 Xiaolingwei, Xuanwu District, Nanjing, 210094, Jiangsu, People’s Republic of China

    Kedong Yan

  2. School of Industrial Management Engineering, Korea University, 145 Anam-Ro, Seongbuk-Gu, Seoul, 02841, Republic of Korea

    Hong Seo Ryoo

Authors
  1. Kedong Yan
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  2. Hong Seo Ryoo
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Corresponding author

Correspondence to Hong Seo Ryoo .

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Editors and Affiliations

  1. Computer science and Applications Department, LGIPM, University of Lorraine, Metz Cedex 03, France

    Hoai An Le Thi

  2. Computer Science and Applications Department, LGIPM, University of Lorraine, Metz Cedex 03, France

    Hoai Minh Le

  3. Laboratory of Mathematics, National Institute for Applied Sciences (INSA)-Rouen Normadie, Saint-Étienne-du-Rouvray Cedex, France

    Tao Pham Dinh

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Yan, K., Ryoo, H.S. (2020). Cliques for Multi-Term Linearization of 0–1 Multilinear Program for Boolean Logical Pattern Generation. In: Le Thi, H., Le, H., Pham Dinh, T. (eds) Optimization of Complex Systems: Theory, Models, Algorithms and Applications. WCGO 2019. Advances in Intelligent Systems and Computing, vol 991. Springer, Cham. https://doi.org/10.1007/978-3-030-21803-4_38

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