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An Approach of Epistasis Detection Using integer linear programming Optimizing Bayesian Network

IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2022年第5期19卷 2654-2671页

作者： Yang, Xuan Yang, Chen Lei, Jimeng Liu, Jianxiao Huazhong Agr Univ Coll Informat Wuhan 430070 Hubei Peoples R China

Proposing a more effective and accurate epistatic loci detection method in large-scale genomic data has important research significance for improving crop quality, disease treatment, etc. Due to the characteristics of high accuracy and processing non-linear relationship, Bayesian network (BN) has been widely used in constructing the network of SNPs and phenotype traits and thus to mine epistatic loci. However, the shortcoming of BN is that it is easy to fall into local optimum and unable to process large-scale of SNPs. In this work, we transform the problem of learning Bayesian network into the optimization of integer linear programming (ILP). We use the algorithms of branch-and-bound and cutting planes to get the global optimal Bayesian network (ILPBN), and thus to get epistatic loci influencing specific phenotype traits. In order to handle large-scale of SNP loci and further to improve efficiency, we use the method of optimizing Markov blanket to reduce the number of candidate parent nodes for each node. In addition, we use alpha-BIC that is suitable for processing the epistatis mining to calculate the BN score. We use four properties of BN decomposable scoring functions to further reduce the number of candidate parent sets for each node. Experiment results show that ILPBN can not only process 2-locus and 3-locus epistasis mining, but also realize multi-locus epistasis detection. Finally, we compare ILPBN with several popular epistasis mining algorithms by using simulated and real Age-related macular disease (AMD) dataset. Experiment results show that ILPBN has better epistasis detection accuracy, F1-score and false positive rate in premise of ensuring the efficiency compared with other methods. Availability: Codes and dataset are available at: http://122.205.95.139/ILPBN/.

关键词： Bayes methods Markov processes integer linear programming Optimization Statistical analysis Search problems Genomics Epistasis integer linear programming bayesian network markov blanket multi-locus

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A Global Optimal Gaussian Mixture Reduction Approach Based on integer linear programming

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CHINESE JOURNAL OF ELECTRONICS 2013年第4期22卷 763-768页

作者： Zhu Hongyan Zhai Qiaozhu Xi An Jiao Tong Univ Sch Elect & Informat Engn Xian 710049 Peoples R China Xi An Jiao Tong Univ Minist Educ Key Lab Intelligent Networks & Network Secur Xian 710049 Peoples R China

In many applications, the Gaussian mixture serves as an important probabilistic representation of the system state. A global optimal Gaussian mixture reduction (GMR) approach based on integer linear programming (ILP) is developed in this paper. Firstly, a Gaussian base set is constructed with partial merging of components of the original mixture. Secondly, by introducing auxiliary variables reasonably, the original problem of selecting the best candidates from the given Gaussian base set is formulated as an ILP problem. Finally, a global optimal solution to GMR is obtained by solving the ILP problem. The global optimum property enables it as a basis for performance comparison with different GMR algorithms.

关键词： Gaussian mixture reduction integer linear programming Component merging Integral squared difference Global optimal solution

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One-dimensional cutting stock with a limited number of open stacks: bounds and solutions from a new integer linear programming model

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INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH 2016年第1-2期23卷 47-63页

作者： Arbib, Claudio Marinelli, Fabrizio Ventura, Paolo Univ Aquila I-67010 Laquila Italy Univ Politecn Marche Dipartimento Ingn Informaz I-60121 Ancona Italy CNR Ist Anal Sistemi & Informat I-00185 Rome Italy

We address a one-dimensional cutting stock problem where, in addition to trim-loss minimization, cutting patterns must be sequenced so that no more than s different part types are in production at any time. We propose a new integer linear programming formulation whose constraints grow quadratically with the number of distinct part types and whose linear relaxation can be solved by a standard column generation procedure. The formulation allowed us to solve problems with 20 part types for which an optimal solution was unknown.

关键词： cutting stock open stacks pattern sequencing integer linear programming

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A parallel domain decomposition algorithm for coastal ocean circulation models based on integer linear programming

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OCEAN DYNAMICS 2017年第5期67卷 639-649页

作者： Jordi, Antoni Georgas, Nickitas Blumberg, Alan Stevens Inst Technol Davidson Lab Hoboken NJ 07030 USA

This paper presents a new parallel domain decomposition algorithm based on integer linear programming (ILP), a mathematical optimization method. To minimize the computation time of coastal ocean circulation models, the ILP decomposition algorithm divides the global domain in local domains with balanced work load according to the number of processors and avoids computations over as many as land grid cells as possible. In addition, it maintains the use of logically rectangular local domains and achieves the exact same results as traditional domain decomposition algorithms (such as Cartesian decomposition). However, the ILP decomposition algorithm may not converge to an exact solution for relatively large domains. To overcome this problem, we developed two ILP decomposition formulations. The first one (complete formulation) has no additional restriction, although it is impractical for large global domains. The second one (feasible) imposes local domains with the same dimensions and looks for the feasibility of such decomposition, which allows much larger global domains. Parallel performance of both ILP formulations is compared to a base Cartesian decomposition by simulating two cases with the newly created parallel version of the Stevens Institute of Technology's Estuarine and Coastal Ocean Model (sECOM). Simulations with the ILP formulations run always faster than the ones with the base decomposition, and the complete formulation is better than the feasible one when it is applicable. In addition, parallel efficiency with the ILP decomposition may be greater than one.

关键词： Coastal ocean circulation model Parallel computing Domain decomposition integer linear programming Urban ocean ECOM

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Resolving Logical Contradictions in Description Logic Ontologies Based on integer linear programming

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IEEE ACCESS 2019年 7卷 71500-71510页

作者： Ji, Qiu Boutouhami, Khaoula Qi, Guilin Nanjing Univ Posts & Telecommun Sch Modern Posts Nanjing 210023 Jiangsu Peoples R China Nanjing Univ Posts & Telecommun Inst Modern Posts Nanjing 210023 Jiangsu Peoples R China Southeast Univ Sch Comp Sci & Engn Nanjing 211189 Jiangsu Peoples R China Southeast Univ Key Lab Comp Network & Informat Integrat Minist Educ Nanjing 211189 Jiangsu Peoples R China

When resolving logical contradictions in ontologies, Reiter's hitting set tree algorithm is often applied to satisfy the minimal change principle. To improve the efficiency, the researchers have proposed various algorithms by using a scoring function, defining new semantics or applying some heuristic strategies. However, these algorithms either sacrifice minimal change or are designed for less expressive ontologies like DL-Lite. In this paper, we propose a mathematic approach based on integer linear programming, which is an optimization problem of maximizing or minimizing a linear objective function, to deal with DL ontologies. Specifically, we define the integer linear programming-based model to resolve logical contradictions. To realize the model, we propose one algorithm to find a cardinality-minimal solution and two algorithms dealing with weighted ontologies. Our experiments are conducted over 70 real-life and artificial ontologies to compare our algorithms with those hitting set tree-based ones. Through the experiments, the prominent efficiency and effectiveness have been exhibited by our algorithms. They usually take about 0.4 s to find a solution while others spend more than 100 s in many cases. The experimental results also show that the first two algorithms could find the cardinality-minimal solutions and those with a minimal sum of weights, respectively.

关键词： Logical contradictions inconsistency handling ontology repair semantic web integer linear programming

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Reservation table scheduling: Branch-and-bound based optimization vs. integer linear programming techniques

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RAIRO-OPERATIONS RESEARCH 2007年第4期41卷 427-454页

作者： Cherroun, Hadda Darte, Alain Feautrier, Paul Amar Telidji Univ Laghouat 03000 Algeria UCBL CNRS INRIA LIPENS Lyon F-69007 Lyon France

The recourse to operation research solutions has strongly increased the performances of scheduling task in the High-Level Synthesis ( called hardware compilation). Scheduling a whole program is not possible as too many constraints and objectives interact. We decompose high-level scheduling in three steps. Step 1: Coarse-grain scheduling tries to exploit parallelism and locality of the whole program ( in particular in loops, possibly imperfectly nested) with a rough view of the target architecture. This produces a sequence of logical steps, each of which contains a pool of macro-tasks. Step 2: Micro-scheduling maps and schedules each macro-task independently taking into account all peculiarities of the target architecture. This produces a reservation table for each macro-task. Step 3: Fine-grain scheduling refines each logical step by scheduling all its macro-tasks. This paper focuses on the third step. As tasks are modeled as reservation tables, we can express resource constraints using dis-equations (i.e., negations of equations). As most scheduling problems, scheduling tasks with reservation tables to minimize the total duration is NP-complete. Our goal here is to design different strategies and to evaluate them, on practical examples, to see if it is possible to find optimal solution in reasonable time. The first algorithm is based on integer linear programming techniques for scheduling, which we adapt to our specific problem. Our main algorithmic contribution is an exact branch-and-bound algorithm, where each evaluation is accelerated by variant of Dijkstra's algorithm. A simple greedy heuristic is also proposed for comparisons. The evaluation and comparison are done on pieces of scientific applications from the PerfectClub and the HLSynth95 benchmarks. The results demonstrate the suitability of these solutions for high-level synthesis scheduling.

关键词： scheduling resource constraints reservation tables disequations branch-and-bound Dijkstra integer linear programming high-level synthesis

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Adaptive integer linear programming Model for Optimal Qubit Permutation

IEEE DESIGN & TEST

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IEEE DESIGN & TEST 2021年第4期38卷 78-84页

作者： de Almeida, Alexandre A. A. Dueck, Gerhard W. Sao Paulo State Univ UNESP Sch Engn BR-01049010 Sao Paulo Brazil Univ New Brunswick Fac Comp Sci Fredericton NB E3B 5A3 Canada

Editor's notes: Quantum computer performance is often limited by the maximum number of pairs of qubits that can interact. This article expresses the problem in terms of integer linear programming, showing that in this way we can identify an optimal solution. -Marcelo Lubaszewki, Universidade Federal do Rio Grande do Sul -Matteo Sonza Reorda, Politecnico di Torino

关键词： Logic gates Qubit Integrated circuit modeling Quantum circuit Manganese Computer architecture Mathematical model integer linear programming IBM quantum processors quantum circuits reversible circuits

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Novel integer linear programming models for the facility layout problem with fixed-size rectangular departments

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COMPUTERS & OPERATIONS RESEARCH 2018年第Jul.期95卷 163-171页

作者： Feng, Jianguang Che, Ada Northwestern Polytech Univ Sch Management Xian 710072 Shaanxi Peoples R China

This paper considers the facility layout problem (FLP) that places a set of fixed-size rectangular departments on a given rectangular site in such a way that the total material flow between adjacent departments is maximized. We demonstrate that an existing integer linear programming (ILP) model for this problem is flawed. Then, two novel ILP models are developed by reformulating some constraints of the existing model from different perspectives. They both significantly reduce the quantity of decision variables. It is also shown that the proposed models can be simplified if all departments have the same size. Numerical experiments conducted on several benchmark instances show that the proposed models outperform the existing one with promising results. Our models can solve all tested instances to optimality within reasonable time, while the existing one cannot. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Facility layout Adjacency constraints integer linear programming

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An Efficient Fault Diagnosis Approach Based on integer linear programming for Labeled Petri Nets

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2021年第5期66卷 2393-2398页

作者： Zhu, Guanghui Feng, Lei Li, Zhiwu Wu, Naiqi Macau Univ Sci & Technol Inst Syst Engn Taipa 999078 Macao Peoples R China Macau Univ Sci & Technol Collaborat Lab Intelligent Sci & Syst Taipa 999078 Macao Peoples R China Aix Marseille Univ Univ Toulon LIS CNRS F-13007 Marseille France KTH Royal Inst Technol Dept Machine Design S-10044 Stockholm Sweden Xidian Univ Sch Electromech Engn Xian 710071 Peoples R China Guangdong Univ Technol State Key Lab Precis Elect Mfg Technol & Equipmen Guangzhou 510006 Peoples R China

In this article, we present a fault diagnosis approach for discrete event systems using labeled Petri nets. In contrast to the existing works, a new fault class containing all the fault transitions is additionally introduced in the diagnosis function, leading to a more informative and precise diagnosis result. An integer linear programming (ILP) problem is built according to an observed word. By specifying different objective functions to the ILP problem, the diagnosis result is obtained without enumerating all observable transition sequences consistent with the observed word, which is more efficient in comparison with the existing ILP-based approaches.

关键词： Petri nets Fault diagnosis integer linear programming Discrete-event systems Labeling linear programming Modeling Discrete event system fault diagnosis integer linear programming (ILP) Petri net

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Power Minimization for Dual- and Triple-Supply Digital Circuits via integer linear programming

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2009年第9期E92A卷 2318-2325页

作者： Ahn, Ki-Yong Kyung, Chong-Min Korea Adv Inst Sci & Technol Sch Elect Engn & Comp Sci Taejon South Korea

This paper proposes an integer linear programming (ILP)-based power minimization method by partitioning into regions, first, with three different V-DD's(PM3V), and, secondly, with two different V-DD's(PM2V). To reduce the solving time of triple-V-DD case (PM3V), we also proposed a partitioned ILP method(p-PM3V). The proposed method provides 29% power saving on the average in the case of triple-V-DD compared to the case of single V-DD. Power reduction of PM3V compared to Clustered Voltage Scaling (CVS) was about 18%. Compared to the un-partitioned ILP formulation(PM3V), the partitioned ILP method(p-PM3V) reduced the total solution time by 46% at the cost of additional power consumption within 1.3%.

关键词： system on chip low power design partitioning integer linear programming

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