@misc{YokoyamaShinanoTaniguchietal.2014, author = {Yokoyama, Ryohei and Shinano, Yuji and Taniguchi, Syusuke and Ohkura, Masashi and Wakui, Tetsuya}, title = {Optimization of energy supply systems by MILP branch and bound method in consideration of hierarchical relationship between design and operation}, issn = {1438-0064}, doi = {10.1016/j.enconman.2014.12.020}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-49413}, year = {2014}, abstract = {To attain the highest performance of energy supply systems, it is necessary to rationally determine types, capacities, and numbers of equipment in consideration of their operational strategies corresponding to seasonal and hourly variations in energy demands. In the combinatorial optimization method based on the mixed-integer linear programming (MILP), integer variables are used to express the selection, numbers, and on/off status of operation of equipment, and the number of these variables increases with those of equipment and periods for variations in energy demands, and affects the computation efficiency significantly. In this paper, a MILP method utilizing the hierarchical relationship between design and operation 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 independently at each period 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 = {en} } @incollection{YokoyamaShinano, author = {Yokoyama, Ryohei and Shinano, Yuji}, title = {MILP Approaches to Optimal Design and Operation of Distributed Energy Systems}, series = {Optimization in the Real World}, volume = {Volume 13}, booktitle = {Optimization in the Real World}, publisher = {Springer}, isbn = {978-4-431-55419-6}, doi = {10.1007/978-4-431-55420-2_9}, pages = {157 -- 176}, abstract = {Energy field is one of the practical areas to which optimization can contribute significantly. In this chapter, the application of mixed-integer linear programming (MILP) approaches to optimal design and operation of distributed energy systems is described. First, the optimal design and operation problems are defined, and relevant previous work is reviewed. Then, an MILP method utilizing the hierarchical relationship between design and operation variables is presented. In the optimal design problem, integer variables are used to express the types, capacities, numbers, operation modes, and on/off states of operation of equipment, and the number of these variables increases with those of equipment and periods for variations in energy demands, and affects the computation efficiency significantly. The presented method can change the enumeration tree for the branching and bounding procedures, and can search the optimal solution very efficiently. Finally, future work in relation to this method is described.}, language = {en} } @article{YokoyamaShinanoTaniguchietal., author = {Yokoyama, Ryohei and Shinano, Yuji and Taniguchi, Syusuke and Ohkura, Masashi and Wakui, Tetsuya}, title = {Optimization of energy supply systems by MILP branch and bound method in consideration of hierarchical relationship between design and operation}, series = {Energy Conversion and Management}, volume = {92}, journal = {Energy Conversion and Management}, doi = {10.1016/j.enconman.2014.12.020}, pages = {92 -- 104}, abstract = {To attain the highest performance of energy supply systems, it is necessary to rationally determine types, capacities, and numbers of equipment in consideration of their operational strategies corresponding to seasonal and hourly variations in energy demands. In the combinatorial optimization method based on the mixed-integer linear programming (MILP), integer variables are used to express the selection, numbers, and on/off status of operation of equipment, and the number of these variables increases with those of equipment and periods for variations in energy demands, and affects the computation efficiency significantly. In this paper, a MILP method utilizing the hierarchical relationship between design and operation 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 independently at each period 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 to be minimized 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 = {en} } @inproceedings{YokoyamaShinanoTaniguchietal., author = {Yokoyama, Ryohei and Shinano, Yuji and Taniguchi, Syusuke and Ohkura, Masashi and Wakui, Tetsuya}, title = {Generation of multiple best solutions in multiobjective optimal design of energy supply systems}, series = {Proceedings of the 15th International Conference on Power Engineering. ICOPE 2015}, booktitle = {Proceedings of the 15th International Conference on Power Engineering. ICOPE 2015}, doi = {10.1299/jsmeicope.2015.12._ICOPE-15-_56}, abstract = {Optimization approaches based on the mixed-integer linear programming (MILP) have been utilized to design energy supply systems. In this paper, an MILP method utilizing the hierarchical relationship between design and operation is extended to search not only the optimal solution but also suboptimal ones which follow the optimal one without any omissions, what are called K-best solutions, efficiently in a multiobjective optimal design problem. At the upper level, the values of design variables for the K-best solutions are searched by the branch and bound method. At the lower level, the values of operation variables are optimized independently at each period by the branch and bound method under the values of design variables given tentatively. Incumbents for the K-best solutions and an upper bound for all the values of the objective function for the K-best solutions are renewed if necessary between both the levels. This method is implemented into a commercial MILP solver. A practical case study on the multiobjective optimal design of a cogeneration system is conducted, and the validity and effectiveness of the method are clarified.}, language = {en} } @inproceedings{YokoyamaShinanoWakayamaetal., author = {Yokoyama, Ryohei and Shinano, Yuji and Wakayama, Yuki and Wakui, Tetsuya}, title = {Model Reduction by Time Aggregation for Optimal Design of Energy Supply Systems by an MILP Hierarchical Branch and Bound Method}, series = {Proceedings of the 31st International Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact of Energy Systems (ECOS 2018)}, booktitle = {Proceedings of the 31st International Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact of Energy Systems (ECOS 2018)}, abstract = {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 effi- ciently. An original problem has been solved by dividing it into a relaxed optimal design problem at the upper level and optimal operation problems which are independent of one another at the lower level. In addition, some strategies have been proposed to enhance the computation efficiency furthermore. In this paper, a method of reducing model by time aggregation is proposed as a novel strategy to search design candidates efficiently in the relaxed optimal design problem at the upper level. In addition, the previous strategies are modified in accordance with the novel strategy. This method is realized only by clustering periods and averaging energy demands for clustered periods, while it guarantees to derive the optimal solu- tion. The method can decrease the number of design variables and constraints at the upper level, and thus may decrease the computation time at the upper level. Through a case study on the optimal design of a gas turbine cogeneration system, it is clarified how the model reduction is effective to enhance the computation efficiency in comparison and combination with the modified previous strategies.}, language = {en} } @inproceedings{YokoyamaShinanoWakayamaaetal., author = {Yokoyama, Ryohei and Shinano, Yuji and Wakayamaa, Yuji and Wakui, Tetsuya}, title = {Optimal Design of a Gas Turbine Cogeneration Plant by a Hierarchical Optimization Method With Parallel Computing}, series = {ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition}, volume = {3}, booktitle = {ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition}, abstract = {To attain the highest performance of energy supply systems, it is necessary to rationally determine types, capacities, and numbers of equipment in consideration of their operational strategies corresponding to seasonal and hourly variations in energy demands. Mixed-integer linear programming (MILP) approaches have been applied widely to such optimal design problems. The authors have proposed a MILP method utilizing the hierarchical relationship between design and operation variables to solve the optimal design problems of energy supply systems efficiently. In addition, some strategies to enhance the computation efficiency have been adopted: bounding procedures at both the levels and ordering of the optimal operation problems at the lower level. In this paper, as an additional strategy to enhance the computation efficiency, parallel computing is adopted to solve multiple optimal operation problems in parallel at the lower level. In addition, the effectiveness of each and combinations of the strategies adopted previously and newly is investigated. This hierarchical optimization method is applied to an optimal design of a gas turbine cogeneration plant, and its validity and effectiveness are clarified through some case studies.}, language = {en} } @inproceedings{YokoyamaKamadaShinanoetal.2020, author = {Yokoyama, Ryohei and Kamada, Hiroki and Shinano, Yuji and Wakui, Tetsuya}, title = {A Hierarchical Optimization Approach to Robust Design of Energy Supply Systems Based on a Mixed-Integer Linear Model}, series = {Conference}, booktitle = {Conference}, pages = {601 -- 613}, year = {2020}, abstract = {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 hierarchi- cal mixed-integer linear programming (MILP) method is proposed to maximize the robustness of energy sup- ply 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 cri- terion, and considering relationships among integer design variables, uncertain energy demands, and inte- ger 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. Since these different types of optimization problems are difficult to solve even using commercial MILP solvers, they are solved by applying a hierarchi- cal MILP method developed for ordinary optimal design problems 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.}, language = {en} } @inproceedings{YokoyamaTakeuchiShinanoetal., author = {Yokoyama, Ryohei and Takeuchi, Kotaro and Shinano, Yuji and Wakui, Tetsuya}, title = {Effect of Model Reduction by Time Aggregation in Multiobjective Optimal Design of Energy Supply Systems by a Hierarchical MILP Method}, series = {Conference}, booktitle = {Conference}, pages = {627 -- 639}, abstract = {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 effi- ciently. As one of the strategies to enhance the computation efficiency furthermore, a method of reducing model by time aggregation has been proposed to search design candidates accurately and efficiently in the relaxed optimal design problem at the upper level. In this paper, the hierarchical MILP method and model reduction by time aggregation are applied to the multiobjective optimal design. In applying the model reduc- tion, the methods of clustering periods by the order of time series, based on an operational strategy, and by the k-medoids method are applied. As a case study, the multiobjective optimal design of a gas turbine cogeneration system with a practical configuration is investigated by adopting the annual total cost and pri- mary energy consumption as the objective functions to be minimized simultaneously, 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. It also turns out that the model reduction only by the k- medoids method is effective very limitedly when importance is given to minimizing the second objective function.}, language = {en} } @inproceedings{YokoyamaShinanoWakayamaetal., author = {Yokoyama, Ryohei and Shinano, Yuji and Wakayama, Yuki and Wakui, Tetsuya}, title = {Multiobjective Optimal Design of a Gas Turbine Cogeneration Plant by a Revised Hierarchical Optimization Method}, series = {ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition}, volume = {3}, booktitle = {ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition}, doi = {doi:10.1115/GT2017-64296}, pages = {1 -- 14}, abstract = {To attain the highest performance of energy supply systems, it is necessary to rationally determine design specifications in consideration of operational strategies corresponding to energy demands. Mixed-integer linear programming (MILP) approaches have been applied widely to such optimal design problems. A MILP method utilizing the hierarchical relationship between design and operation variables have been proposed to solve them efficiently. However, it cannot necessarily be effective to multi-objective optimal design problems because of the existence of a large number of competing design candidates. In this paper, the hierarchical MILP method is revised from the viewpoint of computation efficiency so that it can be applied practically to multi-objective optimal design problems. At the lower level, the order of the optimal operation problems to be solved is changed based on incumbents obtained previously to increase a lower bound for the optimal value of the combined objective function and reduce the number of the optimal operation problems to be solved. At the upper level, a lower bound for the optimal value of the combined objective function is incorporated into the solution method to reduce the number of the design candidates to be generated. This revised hierarchical MILP method is applied to a multiobjective optimal design of a gas turbine cogeneration plant, and its validity and effectiveness are clarified.}, language = {en} } @inproceedings{YokoyamaNakamuraWakuietal., author = {Yokoyama, Ryohei and Nakamura, Ryo and Wakui, Tetsuya and Shinano, Yuji}, title = {Evaluation of Performance Robustness of a Gas Turbine Cogeneration Plant Based on a Mixed-Integer Linear Model}, series = {ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition}, volume = {3}, booktitle = {ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition}, doi = {doi:10.1115/GT2016-56217}, pages = {1 -- 9}, abstract = {In designing energy supply systems, designers are requested to rationally determine equipment types, capacities, and numbers in consideration of equipment operational strategies corresponding to seasonal and hourly variations in energy demands. However, energy demands have some uncertainty at the design stage, and the energy demands which become certain at the operation stage may differ from those estimated at the design stage. Therefore, designers should consider that energy demands have some uncertainty, evaluate the performance robustness against the uncertainty, and design the systems to heighten the robustness. Especially, this issue is important for cogeneration plants, because their performances depend significantly on both heat and power demands. Although robust optimal design methods of energy supply systems under uncertain energy demands were developed, all of them are based on linear models for energy supply systems. However, it is still a hard challenge to develop a robust optimal design method even based on a mixed-integer linear model. At the first step for this challenge, in this paper, a method of evaluating the performance robustness of energy supply systems under uncertain energy demands is proposed based on a mixed-integer linear model. This problem is formulated as a bilevel mixed-integer linear programming one, and a sequential solution method is applied to solve it approximately by discretizing uncertain energy demands within their intervals. In addition, a hierarchical optimization method in consideration of the hierarchical relationship between design and operation variables is applied to solve large scale problems efficiently. Through a case study on a gas turbine cogeneration plant for district energy supply, the validity and effectiveness of the proposed method and features of the performance robustness of the plant are clarified.}, language = {en} } @article{YokoyamaTakeuchiShinanoetal., author = {Yokoyama, Ryohei and Takeuchi, Kotaro and Shinano, Yuji and Wakui, Tetsuya}, title = {Effect of model reduction by time aggregation in multiobjective optimal design of energy supply systems by a hierarchical MILP method}, series = {Energy}, volume = {228}, journal = {Energy}, doi = {https://doi.org/10.1016/j.energy.2021.120505}, abstract = {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.}, language = {en} } @article{YokoyamaKamadaShinanoetal., author = {Yokoyama, Ryohei and Kamada, Hiroki and Shinano, Yuji and Wakui, Tetsuya}, title = {A hierarchical optimization approach to robust design of energy supply systems based on a mixed-integer linear model}, series = {Energy}, volume = {229}, journal = {Energy}, doi = {https://doi.org/10.1016/j.energy.2021.120343}, abstract = {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.}, language = {en} } @article{YokoyamaHiramatsuShinanoetal., author = {Yokoyama, Ryohei and Hiramatsu, Yuto and Shinano, Yuji and Wakui, Tetsuya}, title = {Evaluation of robustness in multiple performance criteria for designing energy supply systems based on a mixed-integer linear model}, series = {Proceedings of the 35th International Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact of Energy Systems (ECOS 2022)}, journal = {Proceedings of the 35th International Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact of Energy Systems (ECOS 2022)}, pages = {1937 -- 1948}, abstract = {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.}, language = {en} } @article{YokoyamaShinanoWakui, author = {Yokoyama, Ryohei and Shinano, Yuji and Wakui, Tetsuya}, title = {Day and time aggregations for optimal design of energy supply systems with storage units by a hierarchical MILP method}, series = {PROCEEDINGS OF ECOS 2022 - THE 35 TH INTERNATIONAL CONFERENCE ON EFFICIENCY, COST, OPTIMIZATION, SIMULATION AND ENVIRONMENTAL IMPACT OF ENERGY SYSTEMS}, journal = {PROCEEDINGS OF ECOS 2022 - THE 35 TH INTERNATIONAL CONFERENCE ON EFFICIENCY, COST, OPTIMIZATION, SIMULATION AND ENVIRONMENTAL IMPACT OF ENERGY SYSTEMS}, pages = {1891 -- 1902}, abstract = {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.}, language = {en} } @article{YokoyamaShinanoWakui, author = {Yokoyama, Ryohei and Shinano, Yuji and Wakui, Tetsuya}, title = {Evaluation of Design Alternatives for a Gas Turbine Cogeneration Plant Based on Multiobjective K-Best Solutions}, series = {International Conference on Power Engineering-2019}, journal = {International Conference on Power Engineering-2019}, pages = {1112 -- 1117}, abstract = {To realize the best performance in energy supply, it is an important task to determine types, capacities, and numbers of energy conversion equipment appropriately. It is also necessary to take account of seasonal and hourly variations in energy demands and corresponding operational strategies of equipment. The mixed-integer linear programming (MILP) method has been utilized widely to derive the optimal solution for such a design problem. From the design viewpoint, it is important to generate not only the optimal solution but also suboptimal ones which follow the optimal one without omission, what are called K-best solutions. In this paper, an MILP method utilizing the hierarchical relationship between design and operation variables is applied along with some strategies to efficiently drive K-best solutions of a multiobjective optimal design problem of a gas turbine cogeneration system for district energy supply. The annual total cost and primary energy consumption are adopted as the objective functions to be minimized. A case study is conducted, and K-best solutions with an allowable increase in the value of the combined objective function are derived for each value of the weight for the annual total cost. Through the study, it is clarified how the weight affects the computation time, the number of the K-best solutions, and the design specifications and the values of the objective functions for the K-best solutions.}, language = {en} } @article{YokoyamaHiramatsuShinanoetal., author = {Yokoyama, Ryohei and Hiramatsu, Yuto and Shinano, Yuji and Wakui, Tetsuya}, title = {Evaluation of robustness in multiple performance criteria for designing energy supply systems based on a mixed-integer linear model}, series = {The 35th International Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact of Energy Systems (ECOS 2022)}, journal = {The 35th International Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact of Energy Systems (ECOS 2022)}, pages = {1937 -- 1948}, abstract = {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.}, language = {en} } @article{YokoyamaShinanoTaniguchietal., author = {Yokoyama, Ryohei and Shinano, Yuji and Taniguchi, Syusuke and Wakui, Tetsuya}, title = {Search for K-best solutions in optimal design of energy supply systems by an extended MILP hierarchical branch and bound method}, series = {Energy}, volume = {184}, journal = {Energy}, doi = {https://doi.org/10.1016/j.energy.2018.02.077}, pages = {45 -- 57}, abstract = {For the purpose of making a decision in the optimal design of an energy supply system, it is important to investigate not only the optimal solution but also suboptimal ones which follow the optimal one without any omissions, what are called K-best solutions. In this paper, a mixed-integer linear programming method utilizing the hierarchical relationship between design and operation variables proposed previ- ously is extended to search the K-best solutions very efficiently. In addition, methods for updating the incumbents are incorporated into the extended method for three options for the criterion set newly in deriving the K-best solutions. This extended method is implemented into open and commercial MILP solvers, and is applied to illustrative and practical case studies, respectively, on the optimal design of cogeneration systems. Through the studies, it turns out that the proposed method is much superior in terms of solution optimality and computation efficiency to a conventional method, and that the computation efficiency to derive one of the K-best solutions by the proposed method increases with the number of K-best solutions. In addition, features of the K-best solutions in the value of objective function are clarified.}, language = {en} } @article{YokoyamaShinanoWakayamaetal., author = {Yokoyama, Ryohei and Shinano, Yuji and Wakayama, Yuki and Wakui, Tetsuya}, title = {Model reduction by time aggregation for optimal design of energy supply systems by an MILP hierarchical branch and bound method}, series = {Energy}, volume = {181}, journal = {Energy}, doi = {https://doi.org/10.1016/j.energy.2019.04.066}, pages = {782 -- 792}, abstract = {Mixed-integer linear programming (MILP) methods have been applied widely to optimal design of energy supply systems in consideration of multi-period operation. A hierarchical MILP method has been proposed to solve such optimal design problems efficiently. An original problem has been solved by dividing it into a relaxed optimal design problem at the upper level and optimal operation problems which are independent of one another at the lower level. In addition, some strategies have been proposed to enhance the computation efficiency furthermore. In this paper, a method of reducing model by time aggregation is proposed as a novel strategy to search design candidates efficiently in the relaxed optimal design problem at the upper level. In addition, the previous strategies are modified in accordance with the novel strategy. This method is realized only by clustering periods and averaging energy demands for clustered periods, while it guarantees to derive the optimal solution. Thus, it may decrease the computation time at the upper level. Through a case study on the optimal design of a gas turbine cogeneration system, it is clarified how the model reduction is effective to enhance the computation efficiency in comparison and combination with the modified previous strategies.}, language = {en} } @article{YokoyamaShinanoTakeuchietal., author = {Yokoyama, Ryohei and Shinano, Yuji and Takeuchi, Kotaro and Wakui, Tetsuya}, title = {Operation-based time-period clustering for optimal design of energy supply systems by a hierarchical MILP method}, series = {THE 32ND INTERNATIONAL CONFERENCE ON EFFICIENCY, COST, OPTIMIZATION, SIMULATION AND ENVIRONMENTAL IMPACT OF ENERGY SYSTEMS(ECOS 2019)}, journal = {THE 32ND INTERNATIONAL CONFERENCE ON EFFICIENCY, COST, OPTIMIZATION, SIMULATION AND ENVIRONMENTAL IMPACT OF ENERGY SYSTEMS(ECOS 2019)}, pages = {527 -- 539}, abstract = {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, a method of clustering periods has been proposed based on the optimal operational strategies of the systems to avoid a large decrease in the lower bound for the optimal value of the objective function by model reduction. This method has been realized only by solving the relaxed optimal design problem at the upper level in advance. The method can decrease the number of operation variables and constraints at the upper level, and thus can decrease the computation time at the upper level. Through a case study on the optimal design of a gas turbine cogeneration system, it is clarified how the proposed clustering method is effective to enhance the computation efficiency in comparison with the conventional one which clusters periods regularly in time series.}, language = {en} } @article{YokoyamaShinanoWakui, author = {Yokoyama, Ryohei and Shinano, Yuji and Wakui, Tetsuya}, title = {Day and time aggregations for optimal design of energy supply systems with storage units by a hierarchical MILP method}, series = {The 35th International Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact of Energy Systems (ECOS 2022)}, journal = {The 35th International Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact of Energy Systems (ECOS 2022)}, pages = {1891 -- 1902}, abstract = {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.}, language = {en} } @article{YokoyamaShinanoWakayamaetal., author = {Yokoyama, Ryohei and Shinano, Yuji and Wakayama, Yuki and Wakui, Tetsuya}, title = {Model reduction by time aggregation for optimal design of energy supply systems by an MILP hierarchical branch and bound method}, series = {Energy}, volume = {181}, journal = {Energy}, pages = {782 -- 792}, abstract = {Mixed-integer linear programming (MILP) methods have been applied widely to optimal design of en- ergy supply systems in consideration of multi-period operation. A hierarchical MILP method has been proposed to solve such optimal design problems efficiently. An original problem has been solved by dividing it into a relaxed optimal design problem at the upper level and optimal operation problems which are independent of one another at the lower level. In addition, some strategies have been pro- posed to enhance the computation efficiency furthermore. In this paper, a method of reducing model by time aggregation is proposed as a novel strategy to search design candidates efficiently in the relaxed optimal design problem at the upper level. In addition, the previous strategies are modified in accor- dance with the novel strategy. This method is realized only by clustering periods and averaging energy demands for clustered periods, while it guarantees to derive the optimal solution. Thus, it may decrease the computation time at the upper level. Through a case study on the optimal design of a gas turbine cogeneration system, it is clarified how the model reduction is effective to enhance the computation efficiency in comparison and combination with the modified previous strategies.}, language = {en} } @article{WakayamaYokoyamaShinanoetal., 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)}, series = {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}, 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}, 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{TakeuchiYokoyamaShinanoetal., 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)}, series = {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}, 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}, 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., 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)}, series = {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}, 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}, 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., 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)}, series = {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}, 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}, 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., 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)}, series = {日本機械学会第11回最適化シンポジウム2014講演論文集}, 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}, 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} } @article{WakayamaYokoyamaShinanoetal., author = {Wakayama, Yuki and Yokoyama, Ryohei and Shinano, Yuji and Wakui, Tetsuya}, title = {階層的最適化によるエネルギ ー供給システムの最適設計・運用 (期間のクラスタリングに よるモデル縮約とその効果)}, series = {日本機械学会関西支部第93期定時総会講演会講演論文集}, journal = {日本機械学会関西支部第93期定時総会講演会講演論文集}, pages = {259 -- 260}, abstract = {Ahierarchical mixed-integer linear programmingmethod has been proposed to solve optimal design problems of energy supply systems efficiently. In this paper, a method of reducing model by clustering periods 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. Through acase study on the optimaldesign of a cogeneration system, ti is clarified how the model reduction si effective ot enhance the computation efficiency.}, language = {ja} } @article{KamadaYokoyamaShinanoetal., author = {Kamada, Hiroki and Yokoyama, Ryohei and Shinano, Yuji and Wakui, Tetsuya}, title = {階層的最適化手法を用いた エネルギー供給システムのロバスト性評価}, series = {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}, journal = {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}, pages = {1 -- 4}, 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. However, this method takes a long computation time, and thus it can be applied only to small-scale problems. In this paper, a hierarchical optimization method is applied to two types of optimization problems for evaluating robustness to solve them efficiently. In a case study, the proposed method is applied to a cogeneration system with a complex configuration, and the validity and effectiveness of the method are ascertained.}, language = {ja} } @article{TaniguchiYokoyamaShinanoetal., 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)}, series = {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}, 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}, 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., 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 設計および運用の階層的関係を考慮した最適化 (多目的最適設計へのモデル縮約の適用)}, series = {エネルギー・資源学会第36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}, journal = {エネルギー・資源学会第36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 = {724 -- 729}, 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 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 based on the optimal operational strategies of equipment has been proposed to search design solution candidates efficiently in the relaxed optimal design problem at the upper level. In this paper, these methods are applied to the multiobjective optimal design of a cogeneration system by considering the annual total cost and primary energy consumption as the objective functions to be minimized. Through a case study, it turns out that the model reduction by the operation-based time-period clustering is effective in terms of the computation efficiency when importance is given to the first objective function, while it is not when importance is given to the second objective function.}, language = {ja} } @article{YokoyamaShinanoTakeuchietal., author = {Yokoyama, Ryohei and Shinano, Yuji and Takeuchi, Kotaro 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 (モデル縮約のための期間クラスタリング手法の比較)}, series = {第38回エネルギー・資源学会研究発表会講演論文集}, journal = {第38回エネルギー・資源学会研究発表会講演論文集}, pages = {109 -- 114}, abstract = {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, three clustering methods are applied to time aggregation and compared with one another in terms of the computation efficiency. Especially, the k-medoids method is applied newly in addition to the time-series and operation-based methods applied previously. A case study is conducted on the optimal design of a gas turbine cogeneration system for district energy supply. Through the study, it turns out the k-medoids method is effective to shorten the computation time as compared with the time-series method, although it is necessary to set the number of clusters artifically in both the methods. It also turns out that the operation-based method is more effective than the k-medoids method in terms of the computation efficiency even with the number of clusters set automatically.}, language = {ja} } @article{YokoyamaShinanoWakui, author = {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 (蓄エネルギー機器を有するシステムへの適用)}, series = {第40回エネルギー・資源学会研究発表会講演論文集}, journal = {第40回エネルギー・資源学会研究発表会講演論文集}, pages = {398 -- 403}, abstract = {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 has been extendedly applied to the optimal design of energy supply systems with storage units. Especially, the method of re- ducing model is extended by aggregating representative days and sampling times differently in consideration of the characteristics of storage units. A case study is conducted on the optimal design of a gas turbine cogeneration system with a thermal storage unit for district energy supply. Through the study, it turns out the hierarchical MILP method is effective to derive the optimal solution as compared with a conventional method. It also turns out that the model reduction with the special time aggregation is effective to shorten the computation time as compared with that without time aggregation in case that the number of candidates for equipment capacities is relatively small.}, language = {ja} } @article{YokoyamaShinanoWakui, author = {Yokoyama, Ryohei and Shinano, Yuji and Wakui, Tetsuya}, title = {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設計解の評価)}, series = {エネルギー・資源学会第38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}, journal = {エネルギー・資源学会第38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 = {468 -- 473}, abstract = {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 solve such an optimal design problem with a large number of periods efficiently 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 provide a time aggregation method for deriving aprroximate optimal design solutions and evaluting their values of the objective function. Especially, a method of evaluating design solutions is presented here using both methods of evaluating the robustness under uncertain energy demands and solving optimal design problems by a hierarchical approach. 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 lower bounds for the optimal value of the objective function as compared with those obtained by a conventional approach.}, language = {ja} } @article{KamadaYokoyamaShinanoetal., author = {Kamada, Hiroki and Yokoyama, Ryohei and Shinano, Yuji and Wakui, Tetsuya}, title = {階層的最適化手法の援用による エネルギー供給システムのロバスト最適設計}, series = {エネルギー・資源学会第36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}, journal = {エネルギー・資源学会第36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 = {730 -- 735}, 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. Since this problem must be solved by a special algorithm and is too difficult to solve even using a commercial solver, a hierarchical optimization approach has been applied to solve the problem but its application is limited only to small scale toy problems. In this paper, some strategies are introduced into the hierarchical optimization approach to enhance the computation efficiency for the purpose of applying the approach to large scale practical problems. In a case study, the proposed approach is applied to the robust optimal design of a cogeneration system with a complex configuration, and the validity and effectiveness of the method are ascertained.}, language = {ja} } @article{YokoyamaShinanoWakui, author = {Yokoyama, Ryohei and Shinano, Yuji and Wakui, Tetsuya}, title = {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)}, series = {第41回エネルギー・資源学会研究発表会講演論文集}, journal = {第41回エネルギー・資源学会研究発表会講演論文集}, pages = {144 -- 148}, abstract = {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.}, language = {ja} } @article{TakeuchiYokoyamaShinanoetal., 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)}, series = {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}, journal = {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}, pages = {1 -- 4}, 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. 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.}, language = {ja} } @article{YokoyamaShinanoWakui, author = {Yokoyama, Ryohei and Shinano, Yuji and Wakui, Tetsuya}, title = {An effective approach for deriving and evaluating approximate optimal design solutions of energy supply systems by time series aggregation}, series = {Frontiers in Energy Research}, volume = {11}, journal = {Frontiers in Energy Research}, doi = {10.3389/fenrg.2023.1128681}, pages = {1 -- 14}, abstract = {It is important to design multi-energy supply systems optimally in consideration of their operations for variations in energy demands. An approach for efficiently solving such an optimal design problem with a large number of periods for variations in energy demands is to derive an approximate optimal design solution by time series aggregation. However, such an approach does not provide any information on the accuracy for the optimal value of the objective function. In this paper, an effective approach for time series aggregation is proposed to derive an approximate optimal design solution and evaluate a proper gap between the upper and lower bounds for the optimal value of the objective function based on a mixed-integer linear model. In accordance with aggregation, energy demands are relaxed to uncertain parameters and the problem for deriving an approximate optimal design solution and evaluating it is transformed to a three-level optimization problem, and it is solved by applying both the robust and hierarchical optimization methods. A case study is conducted on a cogeneration system with a practical configuration, and it turns out that the proposed approach enables one to derive much smaller gaps as compared with those obtained by a conventional approach.}, language = {en} }