TY - CHAP A1 - Tateiwa, Nariaki A1 - Shinano, Yuji A1 - Yamamura, Keiichiro A1 - Yoshida, Akihiro A1 - Kaji, Shizuo A1 - Yasuda, Masaya A1 - Fujisawa, Katsuki T1 - CMAP-LAP: Configurable Massively Parallel Solver for Lattice Problems T2 - HiPC 2021 proceedings N2 - Lattice problems are a class of optimization problems that are notably hard. There are no classical or quantum algorithms known to solve these problems efficiently. Their hardness has made lattices a major cryptographic primitive for post-quantum cryptography. Several different approaches have been used for lattice problems with different computational profiles; some suffer from super-exponential time, and others require exponential space. This motivated us to develop a novel lattice problem solver, CMAP-LAP, based on the clever coordination of different algorithms that run massively in parallel. With our flexible framework, heterogeneous modules run asynchronously in parallel on a large-scale distributed system while exchanging information, which drastically boosts the overall performance. We also implement full checkpoint-and-restart functionality, which is vital to high-dimensional lattice problems. Through numerical experiments with up to 103,680 cores, we evaluated the performance and stability of our system and demonstrated its high capability for future massive-scale experiments. Y1 - 2021 ER - TY - JOUR A1 - Yokoyama, Ryohei A1 - Shinano, Yuji A1 - Wakui, Tetsuya T1 - 時間集約によるエネルギー供給システムの 近似最適設計解の導出および評価 (階層的最適化を援用した近似最適設計) T1 - Derivation and Evaluation of Approximate Optimal Design Solutions of Energy Supply Systems by Time Aggregation (Approximate Optimal Design Using Hierarchical Optimization) JF - 第41回エネルギー・資源学会研究発表会講演論文集 N2 - For the purpose of attaining the highest performance of energy supply systems, it is important to design the systems optimally in consideration of their operational strategies for seasonal and hourly variations in energy demands. An ap- proach to efficiently solve such an optimal design problem with a large number of periods for variations in energy de- mands is to derive an approximate optimal design solution by aggregating periods with a clustering method. However, such an approach does not provide any information on the accuracy for the optimal value of the objective function. The purpose of this paper is to propose a time aggregation approach for deriving suitable aprroximate optimal design solutions and evaluting their values of the objective function accurately. This time aggregation approach is realized by combining a robust optimal design method under uncertain energy demands and a hierarchical approach for solving large scale optimal design problems. A case study is conducted for a cogeneration system with a practical configuration, and it turns out that the proposed approach enables one to evaluate effective upper and lower bounds for the optimal value of the objective function as compared with those obtained by a conventional approach. Y1 - 2022 SP - 144 EP - 148 ER - TY - JOUR A1 - Takeuchi, Kotaro A1 - Yokoyama, Ryohei A1 - Shinano, Yuji A1 - Wakui, Tetsuya T1 - 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 (k-メドイド法に基づく期間クラスタリングの適用) T1 - Optimization of Energy Supply Systems in Consideration of Hierachical Relationship Between Design and Operation (Application of Time-Period Clustering Based on k-Medoids Method) JF - 日本機械学会関西支部第95期定時総会講演会講演論文集 N2 - 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. A hierarchical mixed-integer linear programming method has been proposed to solve such an optimal design problem efficiently. In this paper, a method of reducing model by clustering periods with the k-medoids method is applied to the relaxed optimal design problem at the upper level. Through a case study, it is clarified how the proposed method is effective to enhance the computation efficiency in a large scale optimal design problem. Y1 - 2020 SP - 1 EP - 4 ER - TY - JOUR A1 - Yokoyama, Ryohei A1 - Kamada, Hiroki A1 - Shinano, Yuji A1 - Wakui, Tetsuya T1 - A hierarchical optimization approach to robust design of energy supply systems based on a mixed-integer linear model JF - Energy N2 - In designing energy supply systems, designers should heighten the robustness in performance criteria against the uncertainty in energy demands. In this paper, a robust optimal design method using a hierarchical mixed-integer linear programming (MILP) method is proposed to maximize the robustness of energy supply systems under uncertain energy demands based on a mixed-integer linear model. A robust optimal design problem is formulated as a three-level min-max-min MILP one by expressing uncertain energy demands by intervals, evaluating the robustness in a performance criterion based on the minimax regret criterion, and considering relationships among integer design variables, uncertain energy demands, and integer and continuous operation variables. This problem is solved by evaluating upper and lower bounds for the minimum of the maximum regret of the performance criterion repeatedly outside, and evaluating lower and upper bounds for the maximum regret repeatedly inside. Different types of optimization problems are solved by applying a hierarchical MILP method developed for ordinary optimal design problems without and with its modifications. In a case study, the proposed approach is applied to the robust optimal design of a cogeneration system. Through the study, its validity and effectiveness are ascertained, and some features of the obtained robust designs are clarified. Y1 - 2021 U6 - https://doi.org/https://doi.org/10.1016/j.energy.2021.120343 VL - 229 ER - TY - JOUR A1 - Yokoyama, Ryohei A1 - Takeuchi, Kotaro A1 - Shinano, Yuji A1 - Wakui, Tetsuya T1 - Effect of model reduction by time aggregation in multiobjective optimal design of energy supply systems by a hierarchical MILP method JF - Energy N2 - The mixed-integer linear programming (MILP) method has been applied widely to optimal design of energy supply systems. A hierarchical MILP method has been proposed to solve such optimal design problems efficiently. In addition, a method of reducing model by time aggregation has been proposed to search design candidates accurately and efficiently at the upper level. In this paper, the hierarchical MILP method and model reduction by time aggregation are applied to the multiobjective optimal design. The methods of clustering periods by the order of time series, by the k-medoids method, and based on an operational strategy are applied for the model reduction. As a case study, the multiobjective optimal design of a gas turbine cogeneration system is investigated by adopting the annual total cost and primary energy consumption as the objective functions, and the clustering methods are compared with one another in terms of the computation efficiency. It turns out that the model reduction by any clustering method is effective to enhance the computation efficiency when importance is given to minimizing the first objective function, but that the model reduction only by the k-medoids method is effective very limitedly when importance is given to minimizing the second objective function. Y1 - 2021 U6 - https://doi.org/https://doi.org/10.1016/j.energy.2021.120505 VL - 228 ER - TY - GEN A1 - Tateiwa, Nariaki A1 - Shinano, Yuji A1 - Yamamura, Keiichiro A1 - Yoshida, Akihiro A1 - Kaji, Shizuo A1 - Yasuda, Masaya A1 - Fujisawa, Katsuki T1 - CMAP-LAP: Configurable Massively Parallel Solver for Lattice Problems N2 - Lattice problems are a class of optimization problems that are notably hard. There are no classical or quantum algorithms known to solve these problems efficiently. Their hardness has made lattices a major cryptographic primitive for post-quantum cryptography. Several different approaches have been used for lattice problems with different computational profiles; some suffer from super-exponential time, and others require exponential space. This motivated us to develop a novel lattice problem solver, CMAP-LAP, based on the clever coordination of different algorithms that run massively in parallel. With our flexible framework, heterogeneous modules run asynchronously in parallel on a large-scale distributed system while exchanging information, which drastically boosts the overall performance. We also implement full checkpoint-and-restart functionality, which is vital to high-dimensional lattice problems. Through numerical experiments with up to 103,680 cores, we evaluated the performance and stability of our system and demonstrated its high capability for future massive-scale experiments. T3 - ZIB-Report - 21-16 KW - Discrete optimization KW - Lattice problem KW - Lattice-based cryptography KW - Shortest vector problem KW - Parallel algorithms KW - Ubiquity Generator Framework Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82802 SN - 1438-0064 N1 - Revised version is accepted to HiPC 2021 ER - TY - JOUR A1 - Yokoyama, Ryohei A1 - Hiramatsu, Yuto A1 - Shinano, Yuji A1 - Wakui, Tetsuya T1 - Evaluation of robustness in multiple performance criteria for designing energy supply systems based on a mixed-integer linear model JF - The 35th International Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact of Energy Systems (ECOS 2022) N2 - In designing energy supply systems, it is important to consider the uncertainty in energy demands, evaluate the robustness in some performance criteria, and heighten the robustness. A robust optimal design method has been previously proposed to maximize the robustness in a single performance criterion against the uncertainty in energy demands based on a mixed-integer linear model. In this paper, as a preliminary step toward multiobjective robust optimal design, a method of evaluating robustness in multiple performance criteria against the uncertainty in energy demands is proposed based on a mixed-integer linear model. The problems of evaluating the robustness in the performance criteria are formulated as bilevel mixed-integer linear programming (MILP) ones. They are solved by evaluating lower and upper bounds for the maximum regrets in the performance criteria alternately and repeatedly with the aid of a solution method based on reformulation and decomposition. In addition, for the purpose of applying the proposed method to practical problems, a hierarchical MILP method is used to efficiently solve some MILP problems in the solution process. Through a case study on a cogeneration system, the robustness in the annual total cost and primary energy consumption is evaluated and its trade-off relationship is clarified. As a result, it turns out how the values of these performance criteria are close to the optimal ones in relation to the uncertainty in energy demands. This work will be an important step toward developing a multiobjective robust optimal design method. Y1 - 2022 SP - 1937 EP - 1948 ER - TY - JOUR A1 - Yokoyama, Ryohei A1 - Shinano, Yuji A1 - Wakui, Tetsuya T1 - Day and time aggregations for optimal design of energy supply systems with storage units by a hierarchical MILP method JF - PROCEEDINGS OF ECOS 2022 - THE 35 TH INTERNATIONAL CONFERENCE ON EFFICIENCY, COST, OPTIMIZATION, SIMULATION AND ENVIRONMENTAL IMPACT OF ENERGY SYSTEMS N2 - Mixed-integer linear programming (MILP) methods have been applied widely to optimal design of energy supply systems. A hierarchical MILP method has been proposed to solve such optimal design problems efficiently. In addition, some strategies have been proposed to enhance the computation efficiency furthermore. As one of the strategies, a method of reducing model by time aggregation has been proposed to search design candidates efficiently in the relaxed optimal design problem at the upper level. In this paper, the hierarchical MILP method with the strategies is extendedly applied to the optimal design of energy supply systems with storage units. Especially, the method of reducing model is extended by aggregating both representative days and sampling times separately in consideration of the characteristics of energy storage units. A case study is conducted on the optimal design of a cogeneration system with a thermal storage tank. Through the study, it turns out the hierarchical MILP method is effective to derive the optimal solutions in short computation times. It also turns out that the model reduction with day and time aggregations is effective to shorten the computation times furthermore when the number of candidates for equipment capacities is relatively small. Y1 - 2022 SP - 1891 EP - 1902 ER - TY - JOUR A1 - Yokoyama, Ryohei A1 - Shinano, Yuji A1 - Wakui, Tetsuya T1 - Day and time aggregations for optimal design of energy supply systems with storage units by a hierarchical MILP method JF - The 35th International Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact of Energy Systems (ECOS 2022) N2 - Mixed-integer linear programming (MILP) methods have been applied widely to optimal design of energy supply systems. A hierarchical MILP method has been proposed to solve such optimal design problems efficiently. In addition, some strategies have been proposed to enhance the computation efficiency furthermore. As one of the strategies, a method of reducing model by time aggregation has been proposed to search design candidates efficiently in the relaxed optimal design problem at the upper level. In this paper, the hierarchical MILP method with the strategies is extendedly applied to the optimal design of energy supply systems with storage units. Especially, the method of reducing model is extended by aggregating both representative days and sampling times separately in consideration of the characteristics of energy storage units. A case study is conducted on the optimal design of a cogeneration system with a thermal storage tank. Through the study, it turns out the hierarchical MILP method is effective to derive the optimal solutions in short computation times. It also turns out that the model reduction with day and time aggregations is effec- tive to shorten the computation times furthermore when the number of candidates for equipment capacities is relatively small. Y1 - 2022 SP - 1891 EP - 1902 ER - TY - GEN A1 - Fujii, Koichi A1 - Kim, Sunyoung A1 - Kojima, Masakazu A1 - Mittelmann, Hans D. A1 - Shinano, Yuji T1 - An Exceptionally Difficult Binary Quadratic Optimization Problem with Symmetry: a Challenge for The Largest Unsolved QAP Instance Tai256c N2 - Tai256c is the largest unsolved quadratic assignment problem (QAP) instance in QAPLIB. It is known that QAP tai256c can be converted into a 256 dimensional binary quadratic optimization problem (BQOP) with a single cardinality constraint which requires the sum of the binary variables to be 92. As the BQOP is much simpler than the original QAP, the conversion increases the possibility to solve the QAP. Solving exactly the BQOP, however, is still very difficult. Indeed, a 1.48% gap remains between the best known upper bound (UB) and lower bound (LB) of the unknown optimal value. This paper shows that the BQOP admits a nontrivial symmetry, a property that makes the BQOP very hard to solve. The symmetry induces equivalent subproblems in branch and bound (BB) methods. To effectively improve the LB, we propose an efficient BB method that incorporates a doubly nonnegative relaxation, the standard orbit branching and a technique to prune equivalent subproblems. With this BB method, a new LB with 1.25% gap is successfully obtained, and computing an LB with 1.0% gap is shown to be still quite difficult. T3 - ZIB-Report - 23-27 Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-93072 SN - 1438-0064 ER -