Mathematical modeling with graph structures for a conflict resolution and its application to a labeling issue of processed food

• Project/Area Number: 19K04880
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 25010:Social systems engineering-related
• Research Institution: Kyoto Institute of Technology
• Principal Investigator: Karuno Yoshiyuki 京都工芸繊維大学, 機械工学系, 教授 (80252542)
• Project Period (FY): 2019-04-01 – 2023-03-31
• Project Status: Completed (Fiscal Year 2022)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2021: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2020: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2019: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 数理モデリング / グラフ構造 / アルゴリズム設計

Outline of Research at the Start

本研究では，適切な食品表示案の提示が可能になるように，有向二部グラフを用いた競合解消数理モデルの計算の困難性を解明する．しかしながら，基礎となる反転グラフのモデル自体，その計算の困難性については未解明の事項が多く，早急な完全解決が望みがたい．ここでは，帰着の構成に基づくアルゴリズム設計という基本方針に従って，保存される近似性能に留意しつつ，設定クラス毎の計算の困難性を明らかにする計画である．

Outline of Final Research Achievements

For the switching graph problem on directed bipartite structure as a conflict resolution model, a polynomial time procedure is designed to convert a given digraph into an equivalent undirected graph. Utilizing an optimization criterion on the equivalent undirected graph, an integer programming formulation is presented. For an extended version of the switching graph problem with budget constraints, an exact approach based on the integer program is also proposed. The two-step transformation makes it possible to obtain an optimal solution for a larger size instance of the conflict resolution model than the size of a known benchmark.

Academic Significance and Societal Importance of the Research Achievements

反転グラフ問題はグラフ構造を用いた競合解消モデルの一つであるが，その数学的構造や計算の困難性には未解明の事項が多く残されていた．先行研究で厳密解法について具体的に言及されることがなかったのも，そのためと考えられる．研究成果の学術的は，帰着の技法を用いて，その競合解消モデルの数学的構造の一面を明らかにしたこと，また，その数学的構造を用いて厳密解を求めるための計算手法を具体的に提示したことである．この競合解消モデルは，食品表示における健康被害防止の課題と関係する可能性があり，理論に裏打ちされた計算手法の実現は，将来的には社会的意義にも繋がると考えられる．

Research Products

• [Journal Article] An improved performance of greedy heuristic solutions for a bi-criteria mixture packaging problem of two types of items with bounded weights (2020)
  • Author(s): Yoshiyuki Karuno, Oki Nakahama
  • Journal Title: Journal of Advanced Mechanical Design, Systems, and Manufacturing Volume: 14 Issue: 5 Pages: JAMDSM0066-JAMDSM0066
  • DOI: 10.1299/jamdsm.2020jamdsm0066
  • NAID: 130007867992
  • ISSN: 1881-3054
  • Peer Reviewed / Open Access
• [Presentation] An integer programming formulation of collecting weighted items in directed bipartite graphs with a budget constraint (2023)
  • Author(s): Yoshiyuki Karuno, Akihiro Tomozawa, Kazuki Tsuji
  • Organizer: The 11th International Conference on Industrial Application Engineering 2023
  • Int'l Joint Research
• [Presentation] 有向二部グラフにおける反転コストを考慮した重み付きアイテム収集問題に対するIPソルバーの適用 (2023)
  • Author(s): 軽野義行，友澤明宏，辻和樹
  • Organizer: 日本機械学会生産システム部門研究発表講演会2023
• [Presentation] 辞書式二目的最適化問題の定式化例とアルゴリズム (2020)
  • Author(s): 軽野義行
  • Organizer: 2020年度日本OR学会中部支部シンポジウム
  • Invited
• [Presentation] An application of integer programming solvers to an item collecting problem in directed bipartite graphs (2020)
  • Author(s): Yoshiyuki Karuno and Seiya Yoshikawa
  • Organizer: The 8th IIAE International Conference on Industrial Application Engineering 2020
  • Int'l Joint Research