Refine
Year of publication
Document Type
- Article (41)
- In Proceedings (20)
- Book chapter (2)
- In Collection (1)
- Proceedings (1)
Has Fulltext
- no (65) (remove)
この論文ではソフトウェア・パッケージSCIP Optimization Suite を紹介し,その3つの構成要素:モデリン グ言語Zimpl, 線形計画(LP: linear programming) ソルバSoPlex, そして,制約整数計画(CIP: constraint integer programming) に対するソフトウェア・フレームワークSCIP, について述べる.本論文では,この3つの 構成要素を利用して,どのようにして挑戦的な混合整数線形計画問題(MIP: mixed integer linear optimization problems) や混合整数非線形計画問題(MINLP: mixed integer nonlinear optimization problems) をモデル化 し解くのかを説明する.SCIP は,現在,最も高速なMIP,MINLP ソルバの1つである.いくつかの例により, Zimpl, SCIP, SoPlex の利用方法を示すとともに,利用可能なインタフェースの概要を示す.最後に,将来の開 発計画の概要について述べる.
The purpose of this work is to improve the throughput of step-and-scan lithography equipment to shorten the production time of a wafer. For this purpose, we propose a method for solving the MSOP (Movement Sequence Optimization Problem), which is the problem of computing the fastest schedule for visiting all shots on a wafer. It is well-known that the MSOP on step-and-repeat lithography equipment can be modeled as a traveling salesman problem. In contrast to step-and-repeat lithography equipment, a schedule for step-and-scan lithography equipment must also indicate the scanning direction of each shot, in addition to the sequence of the shots. For this reason, the traveling salesman problem formulation for step-and-repeat lithography equipment cannot be applied to solve the MSOP on step-and-scan lithography equipment directly. We overcame this difficulty by introducing auxiliary vertices to model the scanning directions in the traveling salesman problem formulation. By this method, we were able to compute exact optimal sequences considering the scanning directions of shots for several MSOP instances. Our numerical experiments demonstrated that our proposed method was capable of computing exact optimal solutions for real-world MSOP instances having up to 232 shots on a wafer. These optimal solutions gave a 0.25% to 4.66% improvement in productivity over solutions computed by previously known methods.
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.
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.
This paper describes how we solved 12 previously unsolved mixed-integer program- ming (MIP) instances from the MIPLIB benchmark sets. To achieve these results we used an enhanced version of ParaSCIP, setting a new record for the largest scale MIP computation: up to 80,000 cores in parallel on the Titan supercomputer. In this paper we describe the basic parallelization mechanism of ParaSCIP, improvements of the dynamic load balancing and novel techniques to exploit the power of parallelization for MIP solving. We give a detailed overview of computing times and statistics for solving open MIPLIB instances.
Generation of multiple best solutions in multiobjective optimal design of energy supply systems
(2015)
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.