@misc{FujiiItoKimetal.2022, author = {Fujii, Koichi and Ito, Naoki and Kim, Sunyoung and Kojima, Masakazu and Shinano, Yuji and Toh, Kim-Chuan}, title = {大規模二次割当問題への挑戦}, journal = {統計数理研究所共同研究リポート 453 最適化:モデリングとアルゴリズム33 2022年3月 「大規模二次割当問題への挑戦」 p.84-p.92}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-86779}, year = {2022}, abstract = {二次割当問題は線形緩和が弱いことが知られ,強化のため多様な緩和手法が考案されているが,その一つである二重非負値計画緩和( DNN 緩和)及びその解法として近年研究が進んでいるニュートン・ブラケット法を紹介し,それらに基づく分枝限定法の実装及び数値実験結果について報告する.}, language = {ja} } @article{ShinanoAchterbergBertholdetal.2013, author = {Shinano, Yuji and Achterberg, Tobias and Berthold, Timo and Heinz, Stefan and Koch, Thorsten and Vigerske, Stefan and Winkler, Michael}, title = {制約整数計画ソルバ SCIP の並列化}, volume = {61}, journal = {統計数理}, number = {1}, pages = {47 -- 78}, year = {2013}, abstract = {制約整数計画(CIP: Constraint Integer Programs)は,制約プログラミング(CP: Constraint Programming),混合整数計画(MIP: Mixed Integer Programming),充足可能性問題(SAT: Satisfability Problem)の研究分野におけるモデリング技術と解法を統合している.その結果,制約整数計画は,広いクラスの最適化問題を扱うことができる.SCIP(Solving Constraint Integer Programs)は,CIP を解くソルバとして実装され,Zuse Institute Berlin(ZIB)の研究者を中心として継続的に拡張が続けられている.本論文では,著者らによって開発された SCIP に対する2 種類の並列化拡張を紹介する.一つは,複数計算ノード間で大規模に並列動作する ParaSCIPである.もう一つは,複数コアと共有メモリを持つ 1 台の計算機上で(スレッド)並列で動作する FiberSCIP である.ParaSCIP は,HLRN II スーパーコンピュータ上で,一つのインスタンスを解くために最大 7,168 コアを利用した動作実績がある.また,統計数理研究所の Fujitsu PRIMERGY RX200S5 上でも,最大 512 コアを利用した動作実績がある.統計数理研究所のFujitsu PRIMERGY RX200S5 上では,これまでに最適解が得られていなかった MIPLIB2010のインスタンスである dg012142 に最適解を与えた.}, language = {ja} } @article{品野2014, author = {品野, 勇治}, title = {最適化研究における数値実験を中心とした アプリケーション駆動研究サイクル}, volume = {59}, journal = {機関誌「オペレーションズ・リサーチ」}, number = {5}, pages = {247 -- 253}, year = {2014}, abstract = {最適化研究におけるアプリケーション駆動研究サイクルを紹介する.アプリケーション駆動研究サイクルは,学術機関での研究と企業における研究成果の利用とのつながりを良くする点では優れている.一方で,ソフトウェア開発・維持に多大な労力を要するため,日本の大学や研究機関における実施には困難さが伴う.ZIBにおいてアプリケーション駆動研究サイクルが,比較的うまく機能している背景を説明する.また,日本においてアプリケーション駆動研究サイクルを活性化するための第一歩として,論文投稿時に,論文中の数値実験に利用した全データ提出の義務化を提案したい.}, language = {ja} } @article{藤澤品野2014, author = {藤澤, 克樹 and 品野, 勇治}, title = {最適化と計算の今後 ―大規模問題をどこまで解決できるのか?―}, volume = {59}, journal = {機関誌「オペレーションズ・リサーチ」}, number = {1}, pages = {11 -- 19}, year = {2014}, abstract = {近年,大規模かつ複雑な最適化問題を高速に解く需要はさまざまな産業界や学術分野において急速に高まりつつある.これからの研究においては最先端理論 (Theory)+超大規模実データ (Practice)+最新計算技術(Computation) の三つを有機的に組み合わせることによって,実用に耐えうる解決策の提示と大規模最適化問題を扱う際の先例となることが求められている.本稿では最適化と計算に関する最新の傾向に触れるとともに,最適化の計算の今後についても考えていきたい.}, language = {ja} } @article{WakayamaYokoyamaShinanoetal.2018, author = {Wakayama, Yuki and Yokoyama, Ryohei and Shinano, Yuji and Wakui, Tetsuya}, title = {エネルギー供給システムの設計および運用の階層的関係を考慮した最適化(時間集約によるモデル縮約とその効果)}, journal = {エネルギー・資源学会第34回エネルギーシステム・経済・環境コンファレンス講演論文集}, pages = {401 -- 404}, year = {2018}, abstract = {A hierarchical mixed-integer linear programming method to solve optimal design problems of energy supply systems efficiently has been proposed. The original problem is solved by dividing it into a relaxed optimal design problem at the upper level and optimal operation problems which are independent of each other at the lower level. In this paper, a method of reducing model by time aggregation is proposed to search design solution candidates efficiently in the relaxed optimal design problem at the upper level. This method is realized only by clustering periods and averaging energy demands for clustered periods, while it guarantees to derive the optimal solution. On one hand, the method may decrease the number of design variables and costraints at the upper level, and thus the computation time at the upper level. On the other hand, it may increase the numbers of generated design solution candidates and solved optimal operation problems, and thus the computation time at both the levels. Though a case study on the optimal design of a cogeneration system, it is clarified how the model reduction is effective to enhance the computation efficiency.}, language = {ja} } @article{TaniguchiYokoyamaShinanoetal.2015, author = {Taniguchi, Shusuke and Yokoyama, Ryohei and Shinano, Yuji and Ohkura, Masashi and Wakui, Tetsuya}, title = {エネルギー供給システムの設計および運用の階層的関係を考慮した最適化(多目的最適化におけるK-ベスト解の探索)}, journal = {エネルギー・資源学会第31回エネルギーシステム・経済・環境コンファレンス講演論文集}, pages = {267 -- 272}, year = {2015}, abstract = {A mixed-integer linear programming method utilizing the hierarchical relationship between design and operation variables proposed to solve the optimal design problem of energy supply systems efficiently is extended to search K-best solutions in multiobjective optimization: At the upper level, the optimal values of design variables are searched by the branch and bound method with operation variables relaxed to continuous ones; At the lower level, the values of operation variables are optimized independently at the respective periods set for variations in energy demands by the branch and bound method with the values of design variables given tentatively during the search at the upper level. A weighting method is employed for multiobjective optimization, and a weighted sum of the annual total cost and primary energy consumption is adopted as the objective function to be minimized. A practical case study on the optimal design of a cogeneration system is conducted. The validity and effectiveness of the proposed method are clarified, and the trade-off relationship between the annual total cost and primary energy consumption is confirmed.}, language = {ja} } @article{TakeuchiYokoyamaShinanoetal.2019, author = {Takeuchi, Kotaro and Yokoyama, Ryohei and Shinano, Yuji and Wakui, Tetsuya}, title = {エネルギー供給システムの 設計と運用の階層的関係を考慮した最適化 (運用を考慮した期間クラスタリングによるモデル縮約)}, journal = {エネルギー・資源学会第35回エネルギーシステム・経済・環境コンファレンス講演論文集}, pages = {169 -- 174}, year = {2019}, abstract = {To attain the highest performance of energy supply systems, it is necessary to determine design specifications optimally in consideration of operational strategies corresponding to seasonal and hourly variations in energy demands. Mixed-integer linear programming (MILP) methods have been applied widely to such multi-period optimal design problems. A hierarchical MILP method has been proposed to solve the problems very efficiently. In addition, by utilizing features of the hierarchical MILP method, a method of reducing model by clustering periods has also been proposed to search design solution candidates efficiently in the relaxed optimal design problem at the upper level. In this paper, by utilizing features of the hierarchical MILP method, a method of clustering periods is proposed based on the optimal operational strategies of energy supply systems obtained by solving the relaxed optimal design problem. As a case study, the method is applied to the optimal design of a gas turbine cogeneration system, and it is clarified that the method is effective to enhance the computation efficiency in comparison with a conventional method of clustering periods regularly.}, language = {ja} } @article{KamadaYokoyamaShinanoetal.2019, author = {Kamada, Hiroki and Yokoyama, Ryohei and Shinano, Yuji and Wakui, Tetsuya}, title = {混合整数線形モデルによる エネルギー供給システムのロバスト最適設計 (階層的最適化手法の適用)}, journal = {エネルギー・資源学会第35回エネルギーシステム・経済・環境コンファレンス講演論文集}, pages = {163 -- 168}, year = {2019}, abstract = {A robust optimal design method of energy supply systems under uncertain energy demands has been proposed using a mixed- integer linear model for constituent equipment. A robust optimal design problem has been formulated as a three-level min-max- min optimization one by expressing uncertain energy demands by intervals, evaluating the robustness in a performance criterion based on the minimax regret criterion, and considering hierarchical relationships among design variables, uncertain energy demands, and operation variables. However, this method takes a long computation time, and thus it can be applied only to small-scale problems. In this paper, mixed-integer linear programming method in consideration of the hierarchical relationship between design and operation variables is applied to parts of the robust optimal design method which take long computation times to solve problems efficiently. In a case study, this revised method is applied to the robust optimal design of a cogeneration system with a simple configuration, and the validity and effectiveness of the method are ascertained.}, language = {ja} } @article{YokoyamaShinanoTaniguchietal.2014, author = {Yokoyama, Ryohei and Shinano, Yuji and Taniguchi, Syusuke and Ohkura, Masashi and Wakui, Tetsuya}, title = {エネルギー供給システムの設計および運用の階層的関係を考慮した最適化(手法の提案)}, journal = {第33回エネルギー・資源学会研究発表会講演論文要旨集・講演論文集}, pages = {183 -- 188}, year = {2014}, abstract = {A mixed-integer linear programming (MILP) method utilizing the hierarchical relationship between design and op- eration variables is proposed to solve the optimal design problem of energy supply systems efficiently: At the upper level, the optimal values of design variables are searched by the branch and bound method; At the lower level, the values of operation variables are optimized by the branch and bound method under the values of design variables given tentatively during the search at the upper level; Lower bounds for the optimal value of the objective function are evaluated, and are utilized for the bounding operations at both the levels. This method is implemented into open and commercial MILP solvers. Illustrative and practical case studies on the optimal design of cogeneration systems are conducted, and the validity and effectiveness of the proposed method are clarified.}, language = {ja} } @article{YokoyamaShinanoTaniguchietal.2014, author = {Yokoyama, Ryohei and Shinano, Yuji and Taniguchi, Syusuke and Ohkura, Masashi and Wakui, Tetsuya}, title = {エネルギー供給システムの設計および運用階層的関係を考慮した最適化(K-ベスト解の探索)}, journal = {日本機械学会第11回最適化シンポジウム2014講演論文集}, pages = {1 -- 4}, year = {2014}, abstract = {A mixed-integer linear programming methodutilizing the hierarchical relationship between design and operation variables proposed ot solve the optimal design problem of energy supply systems efficiently is extended ot search K-best solutions: At the upper level, the optimal values ofdesign variables are searched with operation variables relaxed to continuous ones; At the lower level, the values of operation variables are optimized with the values of design variables given tentatively; The obtained solution is used to renew K-best incumbent solutions, and the upper bound for the value of the objective function for K-best solutions is replaced correspondingly. A practical case study is conducted, and the validity and effectiveness of the proposed method are clarified.}, language = {ja} }