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Regularity of Maximum Distance Minimizers

Journal of Mathematical Sciences (United States) 2018年第2期232卷 164-169页

作者： Teplitskaya, Y. Chebyshev Laboratory St.Petersburg State University St.Petersburg Russian Federation

We study properties of sets having the minimum length (one-dimensional Hausdorff measure) in the class of closed connected sets Σ ⊂ ℝ2 satisfying the inequality maxyϵM dist (y, Σ) ≤ r for a given compact set M ⊂ ℝ2... 详细信息

We study properties of sets having the minimum length (one-dimensional Hausdorff measure) in the class of closed connected sets Σ ⊂ ℝ² satisfying the inequality max_yϵM dist (y, Σ) ≤ r for a given compact set M ⊂ ℝ² and given r > 0. Such sets play the role of the shortest possible pipelines arriving at a distance at most r to every point of M where M is the set of customers of the pipeline. In this paper, it is announced that every maximum distance minimizer is a union of finitely many curves having one-sided tangent lines at every point. This shows that a maximum distance minimizer is isotopic to a finite Steiner tree even for a “bad” compact set M, which distinguishes it from a solution of the Steiner problem (an example of a Steiner tree with infinitely many branching points can be found in a paper by Paolini, Stepanov, and Teplitskaya). Moreover, the angle between these lines at each point of a maximum distance minimizer is at least 2π/3. Also, we classify the behavior of a minimizer Σ in a neighborhood of any point of Σ. In fact, all the results are proved for a more general class of local minimizers. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.

关键词： REGULARIZATION (Mathematics) HAUSDORFF measures branch & bound algorithms SET theory COMPACT spaces (Topology)

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Discrete and geometric branch and bound algorithms for medical image registration

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ANNALS OF OPERATIONS RESEARCH 2012年第1期196卷 737-765页

作者： Pfeuffer, Frank Stiglmayr, Michael Klamroth, Kathrin Univ Wuppertal Dept Math & Informat D-42119 Wuppertal Germany Univ Magdeburg Dept Math Inst Math Optimizat D-39106 Magdeburg Germany

Aiming at the development of an exact solution method for registration problems, we present two different branch & bound algorithms for a mixed integer programming formulation of the problem. The first B&B algorithm branches on binary assignment variables and makes use of an optimality condition that is derived from a graph matching formulation. The second, geometric B&B algorithm applies a geometric branching strategy on continuous transformation variables. The two approaches are compared for synthetic test examples as well as for 2-dimensional medical data. The results show that medium sized problem instances can be solved to global optimality in a reasonable amount of time.

关键词： branch & bound algorithms algorithms INTEGER programming MATHEMATICAL programming VARIABLES (Mathematics)

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A Hybrid branch-and-bound and Benders Decomposition Algorithm for the Network Design Problem

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COMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING 2017年第4期32卷 319-343页

作者： Bagloee, Saeed Asadi Sarvi, Majid Patriksson, Michael Univ Melbourne Melbourne Sch Engn Melbourne Vic 3010 Australia Chalmers Univ Technol SE-41296 Gothenburg Sweden Univ Gothenburg SE-41296 Gothenburg Sweden

Given a set of candidate road projects associated with costs, finding the best subset with respect to a limited budget is known as the network design problem (NDP). The NDP is often cast in a bilevel programming problem which is known to be NP-hard. In this study, we tackle a special case of the NDP where the decision variables are integers. A variety of exact solutions has been proposed for the discrete NDP, but due to the combinatorial complexity, the literature has yet to address the problem for large-size networks, and accounting for the multimodal and multiclass traffic flows. To this end, the bilevel problem is solved by branch-and-bound. At each node of the search tree, a valid lower bound based on system optimal (SO) traffic flow is calculated. The SO traffic flow is formulated as a mixed integer, non-linear programming (MINLP) problem for which the Benders decomposition method is used. The algorithm is coded on a hybrid and synchronized platform consisting of MATLAB (optimization engine), EMME 3 (transport planning module), MS Access (database), and MS Excel (user interface). The proposed methodology is applied to three examples including Gao's network, the Sioux-Falls network, and a real size network representing the city of Winnipeg, Canada. Numerical tests on the network of Winnipeg at various budget levels have shown promising results.

关键词： BILEVEL programming branch & bound algorithms TRAFFIC flow NONLINEAR programming DECOMPOSITION (Mathematics)

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Neurofuzzy c-Means Network-Based SCARA Robot for Head Gimbal Assembly (HGA) Circuit Inspection

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COMPUTATIONAL INTELLIGENCE AND NEUROSCIENCE 2018年第1期2018卷 1-10页

作者： Kiatwanidvilai, Somyot Praserttaweelap, Rawinun King Mongkuts Inst Technol Ladkrabang Fac Engn Dept Elect Engn Bangkok Thailand

Decision and control of SCARA robot in HGA (head gimbal assembly) inspection line is a very challenge issue in hard disk drive (HDD) manufacturing. The HGA circuit called slider FOS is a part of HDD which is used for reading and writing data inside the disk with a very small dimension, i.e., 45 x 64 mu m. Accuracy plays an important role in this inspection, and classification of defects is very crucial to assign the action of the SCARA robot. The robot can move the inspected parts into the corresponding boxes, which are divided into 5 groups and those are Good, Bridging, Missing, Burn, and No connection. A general image processing technique, blob analysis, in conjunction with neurofuzzy c-means (NFC) clustering with branch and bound (BNB) technique to find the best structure in all possible candidates was proposed to increase the performance of the entire robotics system. The results from two clustering techniques which are K-means, Kohonen network, and neurofuzzy c-means were investigated to show the effectiveness of the proposed algorithm. Training results from the 30x microscope inspection with 300 samples show that the best accuracy for clustering is 99.67% achieved from the NFC clustering with the following features: area, moment of inertia, and perimeter, and the testing results show 92.21% accuracy for the conventional Kohonen network. The results exhibit the improvement on the clustering when the neural network was applied. This application is one of the progresses in neurorobotics in industrial applications. This system has been implemented successfully in the HDD production line at Seagate Technology (Thailand) Co. Ltd.

关键词： INDUSTRIAL robots HARD disks IMAGE processing branch & bound algorithms K-means clustering

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An Optimization Method of Passenger Assignment for Customized Bus

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MATHEMATICAL PROBLEMS IN ENGINEERING 2017年第1期2017卷 1-9页

作者： Cao, Yang Wang, Jian Harbin Inst Technol Sch Transportat Sci & Engn Harbin 150090 Peoples R China

This study proposes an optimization method of passenger assignment on customized buses (CB). Our proposed method guarantees benefits to passengers by balancing the elements of travel time, waiting time, delay, and economic cost. The optimization problem was solved using a branch and bound (B& B) algorithm based on the shortest path for the selected stations. A simulation-based evaluation of the proposed optimization method was conducted. We find that a CB service can save 38.33% in average travel time, 38.33% in average waiting time, and 27.78% in delay penalties, all at an acceptable ticket price. The variations are caused by different degrees of busload. A detailed investigation revealed that a CB can significantly reduce travel time, waiting time, and delays, with the degree of benefits showing a decreasing trend with corresponding increases in busload. This finding indicates that CBs with smaller busloads can more flexibly transport passengers and provide a greater level of benefits. At the same time, a small busload strategy can be implemented more easily and in the near future on a test basis in urban China areas.

关键词： MATHEMATICAL optimization BUSES MATHEMATICAL models branch & bound algorithms NETWORK analysis (Planning) METROPOLITAN areas TRANSPORTATION CHINA

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Global Optimization Algorithm for Large-Scale Refinery Planning Models with Bilinear Terms

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INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH 2017年第2期56卷 530-548页

作者： Castillo, Pedro Castillo Castro, Pedro M. Mahalec, Vladimir McMaster Univ Dept Chem Engn Hamilton ON L8S 4A7 Canada Univ Lisbon Fac Ciencias Ctr Matemat Aplicacoes Fundamentais & Invest Oper P-1749016 Lisbon Portugal

We propose a global optimization algorithm for mixed-integer nonlinear programming (MINLP) problems arising from oil refinery planning. It relies on tight mixed-integer linear programming (MILP) relaxations that discretize the bilinear terms dynamically using either piecewise McCormick (PMCR) or normalized multiparametric disaggregation (NMDT). Tight relaxations help finding a feasible solution of the original problem via a local nonlinear solver, with the novelty being the generation of multiple starting points from CPLEXs solution pool and the parallel execution. We show that optimality-based bound tightening (OBBT) is essential for large-scale problems, even though it is computationally expensive. To reduce execution times, OBBT is implemented in parallel. The results for a refinery case study, featuring units with alternative operating modes, intermediate storage tanks, and single- and multiple-period supply and demand scenarios, show that the algorithms performance is comparable to commercial solvers BARON and ANTIGONE.

关键词： MIXED integer linear programming PETROLEUM refineries GLOBAL optimization NONLINEAR programming branch & bound algorithms LARGE scale systems

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Optimal demand response strategy of a portfolio of multiple commercial buildings: Methods and a case study

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SCIENCE AND TECHNOLOGY FOR THE BUILT ENVIRONMENT 2016年第6期22卷 655-665页

作者： Li, Weilin Xu, Peng Jiao, Feifei Tongji Univ Sch Mech Engn A434 Caoan Rd 4800 Shanghai 201804 Peoples R China

Commercial building demand response control is an effective way to reduce summer electrical peak demand in cities. However, a portfolio of a large number of buildings has different demand response control strategies than individual buildings. In this article, an optimization method is proposed for scheduling demand response strategies for multiple commercial buildings that can be recognized as a multi-building portfolio during demand response. Through this optimal scheduling, decision makers can determine which buildings should participate in the demand response program that controls the strategies that should be used as well as the corresponding optimum starting/ending time. In this article, the optimal scheduling problem is converted into a time series 0-1 programming problem and is solved by the branch and bound method, with three optimization objectives of smooth reduction, maximum reduction, and maximum economic benefits. As a pilot demand response case test, the measured data for 18 large commercial buildings (as a multi-building portfolio) in a recent large-scale demand response experiment were used to evaluate the effectiveness of the optimal scheduling method. The results demonstrated that the optimal scheduling scheme can significantly improve the demand response effectiveness of a large number of buildings together.

关键词： INVESTMENTS COMMERCIAL buildings DEMAND (Economic theory) MATHEMATICAL optimization branch & bound algorithms CASE studies

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branch-and-bound algorithm applied to uncertainty quantification of a Boiling Water Reactor Station Blackout

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NUCLEAR ENGINEERING AND DESIGN 2015年 295卷 283-304页

作者： Nielsen, Joseph Tokuhiro, Akira Hiromoto, Robert Tu, Lei Idaho Natl Lab Idaho Falls ID 83415 USA Univ Idaho Dept Mech Engn Idaho Falls ID 83402 USA Univ Idaho Nucl Engn Program Idaho Falls ID 83402 USA Univ Idaho Dept Comp Sci Idaho Falls ID 83402 USA

Evaluation of the impacts of uncertainty and sensitivity in modeling presents a significant set of challenges in particular to high fidelity modeling. Computational costs and validation of models creates a need for cost effective decision making with regards to experiment design. Experiments designed to validate computation models can be used to reduce uncertainty in the physical model. In some cases, large uncertainty in a particular aspect of the model may or may not have a large impact on the final results. For example, modeling of a relief valve may result in large uncertainty, however, the actual effects on final peak clad temperature in a reactor transient may be small and the large uncertainty with respect to valve modeling may be considered acceptable. Additionally, the ability to determine the adequacy of a model and the validation supporting it should be considered within a risk informed framework. Low fidelity modeling with large uncertainty may be considered adequate if the uncertainty is considered acceptable with respect to risk. In other words, models that are used to evaluate the probability of failure should be evaluated more rigorously with the intent of increasing safety margin. Probabilistic risk assessment (PRA) techniques have traditionally been used to identify accident conditions and transients. Traditional classical event tree methods utilize analysts' knowledge and experience to identify the important timing of events in coordination with thermal-hydraulic modeling. These methods lack the capability to evaluate complex dynamic systems. In these systems, time and energy scales associated with transient events may vary as a function of transition times and energies to arrive at a different physical state. Dynamic PRA (DPRA) methods provide a more rigorous analysis of complex dynamic systems. Unfortunately DPRA methods introduce issues associated with combinatorial explosion of states. This paper presents a methodology to address combinatorial

关键词： branch & bound algorithms UNCERTAINTY (Information theory) BOILING water reactor design & construction ELECTRIC power failures RISK assessment

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Global Optimization for Solving Linear Multiplicative Programming Based on a New Linearization Method

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SCIENTIFIC PROGRAMMING 2016年第1期2016卷 1-9页

作者： Wang, Chun-Feng Bai, Yan-Qin Shanghai Univ Coll Sci Dept Math Shanghai 200444 Peoples R China Henan Normal Univ Dept Math Xinxiang 453007 Peoples R China

This paper presents a new global optimization algorithm for solving a class of linear multiplicative programming (LMP) problem. First, a new linear relaxation technique is proposed. Then, to improve the convergence speed of our algorithm, two pruning techniques are presented. Finally, a branch and bound algorithm is developed for solving the LMP problem. The convergence of this algorithm is proved, and some experiments are reported to illustrate the feasibility and efficiency of this algorithm.

关键词： MATHEMATICAL programming MATHEMATICAL optimization branch & bound algorithms algorithms boundS (Mathematics)

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Associated branched Continued Fractions with Two Independent Variables

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UKRAINIAN MATHEMATICAL JOURNAL 2015年第9期66卷 1312-1323页

作者： Dmytryshyn, R. I. Vasyl Stefanyk Precarpathian Natl Univ Ivano Frankivsk Ukraine

An algorithm for the expansion of a given formal double power series in the associated branched continued fraction with two independent variables is constructed and the conditions for the existence of this expansion a... 详细信息

关键词： INDEPENDENT variables branch & bound algorithms COMPLEX numbers FRACTIONS GENERALIZATION

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