2023 Fiscal Year Final Research Report
Practical algorithms for packing problems and related problems with packing constraints
| Project/Area Number |
17K00038
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Mathematical informatics
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| Research Institution | Chuo University |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2024-03-31
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| Keywords | 数理情報 / アルゴリズム / 数理工学 / 組合せ最適化 / 配置問題 |
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| Outline of Final Research Achievements |
The packing problem is a combinatorial optimization problem in which several objects with 2D or 3D shapes are placed in a given region so that they do not overlap each other. Although this problem has many real-world applications, experts agree that it is very difficult to solve the problem with general-purpose mathematical optimization solvers (e.g., general-purpose solvers for mixed integer programming problems) and that it is necessary to design dedicated algorithms.
In this research project, we studied the design of new algorithms for packing problems and the use of existing algorithms for basic packing problems to packing problems with different objectives and constraints, and optimization problems with packing constraints such as delivery planning and scheduling.
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| Free Research Field |
数理情報学
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| Academic Significance and Societal Importance of the Research Achievements |
実社会に現れる問題の多くが組合せ最適化問題として定式化されることが知られている。汎用的な解法（汎用数理最適化ソルバーなど）によって課題の解決ができる場合は良いが，そうでない場合も多い．本研究において，汎用解法での解決が難しい配置問題に対する専用解法を開発したことで，この問題に対する良質の解を現実的な時間で得られるようになった．また，そのような専用アルゴリズムやその考え方を他の課題でも利用できることを示し，専用アルゴリズムの活用できる範囲を拡げられる可能性を示した．
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