2023 Fiscal Year Final Research Report
Development of the combinatorial optimization methods for very large-scale problems based on statistical models
| Project/Area Number |
21K11775
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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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| Review Section |
Basic Section 60020:Mathematical informatics-related
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| Research Institution | Osaka Institute of Technology |
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Principal Investigator |
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| Project Period (FY) |
2021-04-01 – 2024-03-31
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| Keywords | 組合せ最適化 / 統計モデル / 集中化 / 多様化 / 近傍探索 |
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| Outline of Final Research Achievements |
The purpose of this research is to develop a method to efficiently search for solutions to large-scale combinatorial optimization problems. The search method considered here (called metaheuristic) proceeds with the search while selecting solutions probabilistically. Therefore, in order to mathematically consider the solution search efficiency, we conducted an investigation to improve the search efficiency from the viewpoints of probability theory and statistical theory. Next, we constructed a search method based on the results and evaluated it through computer experiments. Furthermore, with an eye to the development of future research, we derived a theoretical formula that should hold true statistically.
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| Free Research Field |
組合せ最適化
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| Academic Significance and Societal Importance of the Research Achievements |
設計、割り当て、スケジューリング等は、組合せ最適化問題に帰着できる場合も多く、大規模な実用上の問題に対しては、原理的に最適解を求めることができない場合も多い。そのような問題に対しては、遺伝的アルゴリズムに代表されるような「進化型計算」と呼ばれる手法が適用されることが多いが、良い解を得るためには非常に多くの計算量を必要とする。本研究で提案する手法では、大規模な問題に対して限られた計算量しか消費できない場合において、従来の手法よりも良い解を求めることができる。
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