Study of the entire solution set and preference solutions in set-valued programming

2023 Fiscal Year Final Research Report

• Project/Area Number: 19K03637
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 12040:Applied mathematics and statistics-related
• Research Institution: Shimane University
• Principal Investigator: Kuroiwa Daishi 島根大学, 学術研究院理工学系, 教授 (40284020)
• Project Period (FY): 2019-04-01 – 2024-03-31
• Keywords: 集合値最適化 / 重み付け法 / 大域的評価法

Outline of Final Research Achievements

Set-valued programming problem is a problem to find a set from a family of sets. In this study, we research about preferred solutions for the decision maker. We obtained results about kinds of the weighting method and the global criterion method for set optimization. By using these methods, "hidden" solutions can be found from the previous scalarization methods. These results are not only generalizations of multi-objective optimization problems, but also as a new approach to related fields of various optimization theories such as game theory and mathematical economics.

Free Research Field

集合値最適化

Academic Significance and Societal Importance of the Research Achievements

多目的最適化の拡張であり、実社会において頻繁に現れる問題の解を、意思決定者の好みで解を用意に見つけることが出来る。