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Model building and algorithms via integer programming for discrete nonconvex optimization

Research Project

Project/Area Number 17K01246
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Social systems engineering/Safety system
Research InstitutionTokyo University of Agriculture and Technology

Principal Investigator

Miyashiro Ryuhei  東京農工大学, 工学(系)研究科(研究院), 准教授 (50376860)

Project Period (FY) 2017-04-01 – 2020-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2019: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2017: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
KeywordsOR / 整数計画法 / 数理計画法 / アルゴリズム / 最適化 / 数理計画
Outline of Final Research Achievements

Mathematical optimization problems are not only theoretically but also practically important. These problems contain a class of nonconvex discrete optimization problems. Such problems are difficult to solve exactly because of their nonlinear and discrete nature. However, recent progress on machine learning requests us to solve these problems exactly.
In this research, we developed a model building method and algorithms via integer programming (integer optimization) for a class of nonconvex discrete optimization problems. The proposed method allows us to solve feature selection problems in statistics and machine learning faster than existing methods. In addition, the quality of the obtained solutions is better than those obtained by the previous methods, for example, L1-regularization.

Academic Significance and Societal Importance of the Research Achievements

社会的に解きたい問題には,複数のものからいくつかのものを選択する際に,最もよい選び方を決めたいという形式のものが多い.ただしこの種の問題は,現在の解き方では高性能なコンピュータを用いても計算に多大な時間がかかるものが大部分である.本研究では,そのような問題のうち特定の形式の問題について,より高速に解くための方法を開発した.研究成果を応用することにより,例えば機械学習という分野で扱われる「特徴選択」と呼ばれるような問題がより高速に解けるようになることが期待できる.

Report

(4 results)
  • 2019 Annual Research Report   Final Research Report ( PDF )
  • 2018 Research-status Report
  • 2017 Research-status Report
  • Research Products

    (24 results)

All 2020 2019 2018 2017

All Journal Article (9 results) (of which Peer Reviewed: 7 results,  Open Access: 7 results) Presentation (15 results) (of which Int'l Joint Research: 7 results,  Invited: 1 results)

  • [Journal Article] Best subset selection via cross-validation criterion2020

    • Author(s)
      Takano Yuichi, Miyashiro Ryuhei
    • Journal Title

      TOP

      Volume: - Issue: 2 Pages: 475-488

    • DOI

      10.1007/s11750-020-00538-1

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Feature Subset Selection for Ordered Logit Model via Tangent-Plane-Based Approximation2019

    • Author(s)
      Mizuho Naganuma, Yuichi Takano, and Ryuhei Miyashiro
    • Journal Title

      IEICE Transactions on Information and Systems

      Volume: E102.D Issue: 5 Pages: 1046-1053

    • DOI

      10.1587/transinf.2018EDP7188

    • NAID

      130007641148

    • ISSN
      0916-8532, 1745-1361
    • Year and Date
      2019-05-01
    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Steepest-edge rule and its number of simplex iterations for a nondegenerate LP2019

    • Author(s)
      田野昌也、宮代隆平、北原知就
    • Journal Title

      Operations Research Letters

      Volume: 47 Issue: 3 Pages: 151-156

    • DOI

      10.1016/j.orl.2019.02.003

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Feature subset selection for the multinomial logit model via mixed-integer optimization2019

    • Author(s)
      Shunsuke Kamiya, Ryuhei Miyashiro, Yuichi Takano
    • Journal Title

      Proceedings of Machine Learning Research

      Volume: 89 Pages: 1254-1263

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Mixed integer quadratic optimization formulations for eliminating multicollinearity based on variance inflation factor2019

    • Author(s)
      R. Tamura, K. Kobayashi, Y. Takano, R. Miyashiro, K. Nakata, T. Matsui
    • Journal Title

      Journal of Global Optimization

      Volume: 73 Issue: 2 Pages: 431-446

    • DOI

      10.1007/s10898-018-0713-3

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] A layered network formulation for the safe walking route design problem2018

    • Author(s)
      K. Tanaka, R. Miyashiro, Y. Miyamoto
    • Journal Title

      Journal of Advanced Mechanical Design, Systems, and Manufacturing

      Volume: 12 Issue: 3 Pages: JAMDSM0065-JAMDSM0065

    • DOI

      10.1299/jamdsm.2018jamdsm0065

    • NAID

      130007401937

    • ISSN
      1881-3054
    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] 混合整数二次錐計画法による情報量規準最小化手法の高速化2018

    • Author(s)
      神谷俊介,高野祐一,宮代隆平
    • Journal Title

      数理解析研究所講究録

      Volume: 2069 Pages: 42-49

    • Related Report
      2018 Research-status Report
    • Open Access
  • [Journal Article] 多重共線性を考慮した回帰式の変数選択問題の定式化2018

    • Author(s)
      田村隆太,小林健,高野祐一,宮代隆平,中田和秀,松井知己
    • Journal Title

      オペレーションズ・リサーチ

      Volume: 63 Pages: 128-133

    • Related Report
      2017 Research-status Report
    • Open Access
  • [Journal Article] BEST SUBSET SELECTION FOR ELIMINATING MULTICOLLINEARITY2017

    • Author(s)
      R. Tamura, K. Kobayashi, Y. Takano, R. Miyashiro, K. Nakata, T. Matsui
    • Journal Title

      Journal of the Operations Research Society of Japan

      Volume: 60 Issue: 3 Pages: 321-336

    • DOI

      10.15807/jorsj.60.321

    • NAID

      130005874223

    • ISSN
      0453-4514, 2188-8299
    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Presentation] Feature subset selection for the multinomial logit model via mixed-integer optimization2019

    • Author(s)
      Shunsuke Kamiya, Ryuhei Miyashiro, Yuichi Takano
    • Organizer
      The 22nd International Conference on Artificial Intelligence and Statistics
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Best subset selection via cross-validation criterion2019

    • Author(s)
      Yuichi Takano, Ryuhei Miyashiro
    • Organizer
      International Conference on Nonlinear Analysis and Convex Analysis--International Conference on Optimization: Techniques and Applications
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 整数最適化アプローチへの入門2019

    • Author(s)
      宮代隆平
    • Organizer
      電子情報通信学会2019年総合大会
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] 交差確認規準による回帰式の最良変数選択2019

    • Author(s)
      高野祐一,宮代隆平
    • Organizer
      日本オペレーションズ・リサーチ学会 2019年春季研究発表会
    • Related Report
      2018 Research-status Report
  • [Presentation] On the number of simplex iterations of the steepest-edge for a nondegenerate LP2018

    • Author(s)
      M. Tano, R. Miyashiro, T. Kitahara
    • Organizer
      The 23rd International Symposium on Mathematical Programming
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] Recent advances in mixed-integer optimization approaches to feature subset selection2018

    • Author(s)
      Y. Takano, R. Miyashiro
    • Organizer
      INFORMS Annual Meeting 2018
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] 外部近似法による多項ロジットモデルの最良部分集合選択2018

    • Author(s)
      神谷俊介,宮代隆平,高野祐一
    • Organizer
      最適化とその応用:未来を担う若手研究者の集い2018
    • Related Report
      2018 Research-status Report
  • [Presentation] 退化していない線形計画問題におけるsteepest-edge規則の反復回数2018

    • Author(s)
      田野昌也,宮代隆平,北原知就
    • Organizer
      最適化とその応用:未来を担う若手研究者の集い2018
    • Related Report
      2018 Research-status Report
  • [Presentation] 数理最適化法による順序ロジットモデルの変数選択2018

    • Author(s)
      永沼瑞穂,高野祐一,宮代隆平
    • Organizer
      最適化とその応用:未来を担う若手研究者の集い2018
    • Related Report
      2018 Research-status Report
  • [Presentation] 多項ロジットモデルの最良部分集合選択2018

    • Author(s)
      神谷俊介,宮代隆平,高野祐一
    • Organizer
      日本オペレーションズ・リサーチ学会60周年記念事業 本部SSOR2018
    • Related Report
      2018 Research-status Report
  • [Presentation] Mixed-integer quadratic optimization formulations for eliminating multicollinearity based on variance inflation factor2017

    • Author(s)
      R. Tamura, K. Kobayashi, Y. Takano, R. Miyashiro, K. Nakata, T. Matsui
    • Organizer
      INFORMS 2017
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] Solution Methods of Safe Walking Route Design Problem2017

    • Author(s)
      Y. Miyamoto, R. Miyashiro, K. Tanaka
    • Organizer
      INFORMS 2017
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] Relaxation of tree assumption in safe walking route design problem2017

    • Author(s)
      K. Tanaka, R. Miyashiro, Y. Miyamoto
    • Organizer
      International Symposium on Scheduling 2017
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] 特徴選択に対する整数計画アプローチ2017

    • Author(s)
      宮代隆平
    • Organizer
      日本オペレーションズ・リサーチ学会「離散アルゴリズムの応用と理論」研究部会
    • Related Report
      2017 Research-status Report
  • [Presentation] 混合整数二次錐計画法を用いた情報量規準最小化手法の高速化2017

    • Author(s)
      神谷俊介,高野祐一,宮代隆平
    • Organizer
      京都大学数理解析研究所研究集会「数理最適化の発展:モデル化とアルゴリズム」
    • Related Report
      2017 Research-status Report

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Published: 2017-04-28   Modified: 2021-02-19  

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