Refine
Year of publication
- 2020 (224) (remove)
Document Type
- Article (122)
- In Proceedings (35)
- ZIB-Report (30)
- Master's Thesis (9)
- Book chapter (7)
- Book (4)
- Doctoral Thesis (4)
- Other (4)
- In Collection (3)
- Bachelor's Thesis (2)
Keywords
Institute
- Modeling and Simulation of Complex Processes (71)
- Numerical Mathematics (67)
- Visual and Data-centric Computing (37)
- Visual Data Analysis (36)
- Applied Algorithmic Intelligence Methods (33)
- Computational Nano Optics (32)
- Mathematical Optimization (32)
- Mathematical Algorithmic Intelligence (30)
- Distributed Algorithms and Supercomputing (27)
- AI in Society, Science, and Technology (19)
混合整数計画法 (Mixed Integer Programming: MIP) は,MIP を解くソフトウェアである MIP ソルバが大規模な現実問題を解けるようになったこともあり,現実問題を解く有用な OR の手法として広く知られるようになった.しかしながら,MIP ソルバの開発に欠かせないベンチマーク・データセットおよび性能測定方法についてはそれほど広く知られているとは言い難い.ベンチマーク・データセットは注意を払って作成しないと,多くのバイアスがかかってしまう.それらのバイアスを可能な限りのぞき,真に有用なベンチマーク・テストの結果を得るためには複数の人数で多大な労力を割く必要がある.本稿では,そのような MIP ソルバ開発の背景として重要な役割を果たしてきた MIPLIB と Hans Mittelmann’s benchmarks について解説する.また,本稿において Hans Mittelmann’s benchmarks は,BENCHMARKS FOR OPTIMIZATION SOFTWAREのページ (http://plato.asu.edu/bench.html) に示されているベンチマークである.
The temporally and spatially resolved tracking of lithium intercalation and electrode degradation processes are crucial for detecting and understanding performance losses during the operation of lithium-batteries. Here, high-throughput X-ray computed tomography has enabled the identification of mechanical degradation processes in a commercial Li/MnO2 primary battery and the indirect tracking of lithium diffusion; furthermore, complementary neutron computed tomography has identified the direct lithium diffusion process and the electrode wetting by the electrolyte. Virtual electrode unrolling techniques provide a deeper view inside the electrode layers and are used to detect minor fluctuations which are difficult to observe using conventional three dimensional rendering tools. Moreover, the ‘unrolling’ provides a platform for correlating multi-modal image data which is expected to find wider application in battery science and engineering to study diverse effects e.g. electrode degradation or lithium diffusion blocking during battery cycling.
The German high-pressure natural gas transport network consists of thousands of interconnected elements spread over more than 120,000 km of pipelines built during the last 100 years. During the last decade, we have spent many person-years to extract consistent data out of the available sources, both public and private. Based on two case studies, we present some of the challenges we encountered.
Preparing consistent, high-quality data is surprisingly hard, and the effort necessary can hardly be overestimated. Thus, it is particularly important to decide which strategy regarding data curation to adopt. Which precision of the data is necessary? When is it more efficient to work with data that is just sufficiently correct on average?
In the case studies we describe our experiences and the strategies we adopted to deal with the obstacles and to minimize future effort.
Finally, we would like to emphasize that well-compiled data sets, publicly available for research purposes, provide the grounds for building innovative algorithmic solutions to the challenges of the future.
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.
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.
This thesis presents a method for interpolating data using a neural network. The data is sparse and perturbed and is used as training data for a small neural network. For severely perturbed data, the network does not manage to find a smooth interpolation. But as the data resembles the solution to the one-dimensional and time-independent heat equation, the weak form of this PDE and subsequently its functional can be written down. If the functional is minimized, a solution to the weak form of the heat equation is found. The functional is now added to the traditional loss function of a neural network, the mean squared error between the network prediction and the given data, in order to smooth out fluctuations and interpolate between distanced grid points. This way, the network minimizes both the mean squared error and the functional, resulting in a smoother curve that can be used to predict u(x) for any grid point x.
Two essential ingredients of modern mixed-integer programming (MIP) solvers are diving heuristics that simulate a partial depth-first search in a branch-and-bound search tree and conflict analysis of infeasible subproblems to learn valid constraints. So far, these techniques have mostly been studied independently: primal heuristics under the aspect of finding high-quality feasible solutions early during the solving process and conflict analysis for fathoming nodes of the search tree and improving the dual bound. Here, we combine both concepts in two different ways. First, we develop a diving heuristic that targets the generation of valid conflict constraints from the Farkas dual. We show that in the primal this is equivalent to the optimistic strategy of diving towards the best bound with respect to the objective function. Secondly, we use information derived from conflict analysis to enhance the search of a diving heuristic akin to classical coefficient diving. The computational performance of both methods is evaluated using an implementation in the source-open MIP solver SCIP. Experiments are carried out on publicly available test sets including Miplib 2010 and Cor@l.
Conflict learning plays an important role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. A major step for MIP conflict learning is to aggregate the LP relaxation of an infeasible subproblem to a single globally valid constraint, the dual proof, that proves infeasibility within the local bounds. Among others, one way of learning is to add these constraints to the problem formulation for the remainder of the search.
We suggest to not restrict this procedure to infeasible subproblems, but to also use global proof constraints from subproblems that are not (yet) infeasible, but can be expected to be pruned soon. As a special case, we also consider learning from integer feasible LP solutions. First experiments of this conflict-free learning strategy show promising results on the MIPLIB2017 benchmark set.