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FINDING MAXIMUM CLIQUES IN ARBITRARY AND IN SPECIAL GRAPHS

COMPUTING 1991年第4期46卷 321-341页

作者： BABEL, L Mathematisches Institut Technische Universität München München 2 Federal Republic of Germany

The classical problem of finding a clique of largest cardinality in an arbitrary graph is NP-complete. For that reason earlier work diverges into two directions. The first concerns algorithms solving the problem for arbitrary graphs in reasonable (but exponential) time, the other restricts to special classes of graphs where polynomial methods can be found. Here, the two directions are combined in a way. A branch and bound algorithm is developed treating the general case. Computational experiments on random graphs show that this algorithm compares favorable to the fastest known method. Furthermore, it consumes only polynomial time for quite a few graph classes. For some of them no polynomial solution method is given so far.

关键词： MAXIMUM CLIQUE PROBLEM branch and bound algorithm POLYNOMIAL SOLVABLE PROBLEMS

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JOINTLY CONSTRAINED BICONVEX PROGRAMMING

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MATHEMATICS OF OPERATIONS RESEARCH 1983年第2期8卷 273-286页

作者： ALKHAYYAL, FA FALK, JE GEORGE WASHINGTON UNIV DEPT OPERAT RESWASHINGTONDC 20052

This paper presents a branch-and-bound algorithm for minimizing the sum of a convex function in x , a convex function in y and a bilinear term in x and y over a closed set. Such an objective function is called biconvex with biconcave functions similarly defined. The feasible region of this model permits joint constraints in x and y to be expressed. The bilinear programming problem becomes a special case of the problem addressed in this paper. We prove that the minimum of a biconcave function over a nonempty compact set occurs at a boundary point of the set and not necessarily an extreme point. The algorithm is proven to converge to a global solution of the nonconvex program. We discuss extensions of the general model and computational experience in solving jointly constrained bilinear programs, for which the algorithm has been implemented.

关键词： bilinear programming nonconvex programming global convergence branch and bound algorithm biconvex functions

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Material Identification From Radiographs Without Energy Resolution

IEEE TRANSACTIONS ON COMPUTATIONAL IMAGING

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IEEE TRANSACTIONS ON COMPUTATIONAL IMAGING 2023年 9卷 314-326页

作者： McCann, Michael T. T. Guardincerri, Elena Gonzales, Samuel M. M. Misurek, Lauren A. A. Schei, Jennifer L. L. Klasky, Marc L. L. Los Alamos Natl Lab Theoret Div Los Alamos NM 87545 USA Los Alamos Natl Lab Phys Div Los Alamos NM 87545 USA Los Alamos Natl Lab Nucl Engn & Nonproliferat Div Los Alamos NM 87545 USA Los Alamos Natl Lab Integrated Weap Expt Div Los Alamos NM 87545 USA

We propose a method for performing material identification from radiographs without energy-resolved measurements. Material identification has a wide variety of applications, including in biomedical imaging, nondestructive testing, and security. While existing techniques for radiographic material identification make use of dual energy sources, energy-resolving detectors, or additional (e.g., neutron) measurements, such setups are not always practical- requiring additional hardware and complicating imaging. We tackle material identification without energy resolution, allowing standard X-ray systems to provide material identification information without requiring additional hardware. Assuming a setting where the geometry of each object in the scene is known and the materials come from a known set of possible materials, we pose the problem as a combinatorial optimization with a loss function that accounts for the presence of scatter and an unknown gain and propose a branch and bound algorithm to efficiently solve it. We present experiments on both synthetic data and real, experimental data with relevance to security applications- thick, dense objects imaged with MeV X-rays. We show that material identification can be efficient and accurate, for example, in a scene with three shells (two copper, one aluminum), our algorithm ran in six minutes on a consumer-level laptop and identified the correct materials as being among the top 10 best matches out of 8,000 possibilities.

关键词： Radiography X-ray imaging Security Imaging Detectors Predictive models Energy resolution X-ray radiography material identification combinatorial optimization branch and bound algorithm

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On Blade Matching Following Batch Production

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WIND ENGINEERING 2010年第3期34卷 325-333页

作者： Hitz, K. L. Wood, D. H. Univ Newcastle Sch Engn Newcastle Upon Tyne Tyne & Wear 2308 England Aerogenesis Australia Sydney NSW Australia

Wind turbine blades are usually made in batches and then matched in pairs or triples to form the rotor. This paper considers matching with the aim of avoiding or reducing the need for further adjustment of, say, the blade mass. Matching is considered optimal when it minimises the sum of the squared differences in the chosen matching parameter for all blade pairs or triples in a batch. It is proved that use of a simple parameter such as blade mass, or centre of mass, leads to optimal matching by ordering in terms of that parameter. More complex matching based on, say, minimising the eccentricity of the centre of mass, causes the parameter for one blade to depend on at least one other blade. Then ordering does not necessarily produce the optimal matching but, in all cases considered, it comes very close. A branch and bound algorithm is developed for complex matching and is shown to provide the optimal matching in a realistic time for batches of at least 20 blades.

关键词： Wind turbine blades rotor matching branch and bound algorithm

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OPTIMIZING STANDBY RELIABILITY SYSTEMS HAVING NON-DECREASING FAILURE RATES

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MANAGEMENT SCIENCE 1979年第6期25卷 577-582页

作者： MCLEAVEY, DW MCLEAVEY, JA US COAST GUARD ACAD DEPT MATHNEW LONDONCT 06320 WARREN ROGERS & ASSOCIATES NEWPORTRI

In this article we develop a bounding procedure which is applied in an algorithm for determining the number of back-up components to include in a series system. Operating only when original units fail, back-up components increase system reliability. They also add weight, take up space, and cost money. Maximizing the reliability of nuclear power plants, ships, aircraft, life support systems and electronic instruments leads to this class of resource allocation problem. Because the procedure requires only that the rate of failure of individual components remains constant or increases with time, the algorithm can accommodate a wide variety of failure probability distributions. In applications, the failure probability for various types of components might belong to different families and this can be readily handled by the algorithm presented.

关键词： standby redundancy series systems branch and bound algorithm

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Non-Cyclic Scheduling of a Wet Station

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IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING 2014年第4期11卷 1262-1274页

作者： Kim, Hyun-Jung Lee, Jun-Ho Lee, Tae-Eog Korea Adv Inst Sci & Technol Dept Ind & Syst Engn Taejon 305701 South Korea

We examine a non-cyclic scheduling problem of a wet station that performs cleaning processes for removing residual contaminants on wafer surfaces. Several chemical and rinse baths, and multiple robots for transporting jobs are linearly combined in a wet station. A wet station in a fab tends to have different types of jobs. Therefore, it is realistic to consider non-cyclic release of jobs into a wet station. We therefore examine a non-cyclic scheduling problem of a wet station that determines the task sequence of each robot so as to minimize the makespan of a given sequence of different jobs. We develop an efficient branch and bound procedure by examining the scheduling problem. To do this, we first develop a Petri net model for the scheduling problem. By identifying deadlock prevention conditions from the Petri net model, we eliminate partial solutions in advance that eventually will lead to a deadlock. By examining the feasible transition firings or state transition behavior of the Petri net model, we branch only feasible partial solutions or nodes that correspond to feasible state transitions or transition firings. We also develop a tight lower bound based on the bottleneck workload of the baths. We prove computational efficiency of the branch and bound procedure for practical problems.

关键词： branch and bound algorithm cluster tool deadlock no-wait Petri nets wet station

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MINORANT METHODS OF STOCHASTIC GLOBAL OPTIMIZATION

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CYBERNETICS AND SYSTEMS ANALYSIS 2005年第2期41卷 203-214页

作者： Norkin, V. I. Onishchenko, B. O. Natl Acad Sci Ukraine V M Glushkov Inst Cybernet Kiev Ukraine

Generalizations of the branch and bound method and of the Piyavskii method for solution of stochastic global optimization problems are considered. These methods employ the concept of a tangent minorant of an objective... 详细信息

关键词： stochastic global optimization nonconvex stochastic programming branch and bound algorithm Piyavskii method stochastic boundaries tangent minorants

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A heuristic rule for relocating blocks

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COMPUTERS & OPERATIONS RESEARCH 2006年第4期33卷 940-954页

作者： Kim, KH Hong, GP Pusan Natl Univ Dept Ind Engn Pusan 609735 South Korea

One of the most important objectives of the storage and pickup operations in block stacking systems is to minimize the number of relocations during the pickup operation. This study suggests two methods for determining the locations of relocated blocks. First, a branch-and-bound (B&B) algorithm is suggested. Next, a decision rule is proposed by using an estimator for an expected number of additional relocations for a stack. The performance of the decision rule was compared with that of the B&B algorithm. (c) 2004 Elsevier Ltd. All rights reserved.

关键词： relocation block stacking branch and bound algorithm heuristic rule

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Fast feature selection algorithm for poultry skin tumor detection in hyperspectral data

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JOURNAL OF FOOD ENGINEERING 2009年第3-4期94卷 358-365页

作者： Nakariyakul, Songyot Casasent, David P. Thammasat Univ Dept Elect & Comp Engn Khlongluang 12120 Pathumthani Thailand Carnegie Mellon Univ Dept Elect & Comp Engn Pittsburgh PA 15213 USA

Hyperspectral reflectance imaging data are analyzed for poultry skin tumor detection. We consider selecting only a few wavebands from hyperspectral data for potential use in a real-time multispectral camera. To do this, we improve our prior tumor detection system by employing our new adaptive branch and bound algorithm and a support vector machine classifier. Our HS analysis is useful since it provides a guideline for selection of the specific wavelengths for best tumor detection (feature selection). Experimental results demonstrate that our optimal adaptive branch and bound algorithm is significantly faster than other versions of the branch and bound algorithm. We compare the performance of our feature selection algorithm to that of a feature extraction algorithm and show that using our feature selection algorithm gives a better tumor detection rate and a lower false alarm rate. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： branch and bound algorithm Feature selection Feature extraction Hyperspectral data Product inspection Skin tumor detection

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Non-myopic sensor scheduling for low radiation risk tracking using mixed POMDP

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TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL 2017年第2期39卷 230-243页

作者： Shan, Gan-lin Zhang, Zi-ning Shijiazhuang Mech Engn Coll Dept Elect Engn 97 Hepingxilu Rd Shijiazhuang 050003 Peoples R China Aerosp control Ctr Beijing 100094 Peoples R China

This paper addresses a non-myopic sensor-scheduling problem of how to select and assign active sensors for trading off the tracking accuracy and the radiation risk, where the radiation risk is incurred by the fact that the emission energy originating from active sensors for target tracking can be intercepted by the enemy target. This problem is formulated as a mixed partially observable Markov decision process (POMDP) composed of a continuous-state POMDP for target tracking and a discrete-state POMDP for emission control. Based on the idea of foresight optimization, the long-term accuracy reward is evaluated by the combination of unscented transformation sampling and Kalman filtering, whereas the long-term radiation cost is derived from hidden Markov model filter. Because the problem can be converted into a decision tree, a branch and bound algorithm is developed for problem solution. A simulation example illustrates the effectiveness of our approach.

关键词： branch and bound algorithm foresight optimization non-myopic sensor scheduling partially observable Markov decision process unscented transformation sampling

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