检索结果-内蒙古大学图书馆

Exact Sparse Approximation Problems via mixed-integer programming: Formulations and Computational Performance

IEEE TRANSACTIONS ON SIGNAL PROCESSING 2016年第6期64卷 1405-1419页

作者： Bourguignon, Sebastien Ninin, Jordan Carfantan, Herve Mongeau, Marcel Ecole Cent Nantes CNRS UMR 6597 IRCCyN F-44321 Nantes 3 France ENSTA Bretagne Lab STICC CNRS UMR 6285 F-29806 Brest France Univ Toulouse 3 CNRS IRAP UMR 5277 F-31400 Toulouse France Univ Toulouse ENAC MAIAA F-31055 Toulouse 4 France

Sparse approximation addresses the problem of approximately fitting a linear model with a solution having as few non-zero components as possible. While most sparse estimation algorithms rely on suboptimal formulations, this work studies the performance of exact optimization of l(0)-norm-based problems through mixed-integer Programs (MIPs). Nine different sparse optimization problems are formulated based on l(1), l(2) or l(infinity) data misfit measures, and involving whether constrained or penalized formulations. For each problem, MIP reformulations allow exact optimization, with optimality proof, for moderate-size yet difficult sparse estimation problems. Algorithmic efficiency of all formulations is evaluated on sparse deconvolution problems. This study promotes error-constrained minimization of the l(0) norm as the most efficient choice when associated with l(0) and l(infinity) misfits, while the l(2) misfit is more efficiently optimized with sparsity-constrained and sparsity-penalized problems. Exact l(0)-norm optimization is shown to outperform classical methods in terms of solution quality, both for over-and underdetermined problems. Numerical simulations emphasize the relevance of the different l(p) fitting possibilities as a function of the noise statistical distribution. Such exact approaches are shown to be an efficient alternative, in moderate dimension, to classical (suboptimal) sparse approximation algorithms with l(2) data misfit. They also provide an algorithmic solution to less common sparse optimization problems based on l(1) and l(infinity) misfits. For each formulation, simulated test problems are proposed where optima have been successfully computed. Data and optimal solutions are made available as potential benchmarks for evaluating other sparse approximation methods.

关键词： Deconvolution mixed-integer programming l(0)-norm-based problems optimization sparse approximation

来源：评论

学校读者我要写书评

暂无评论

An exact penalty global optimization approach for mixed-integer programming problems

引用

OPTIMIZATION LETTERS 2013年第2期7卷 297-307页

作者： Lucidi, S. Rinaldi, F. Univ Roma La Sapienza Dipartimento Informat & Sistemist I-00185 Rome Italy

In this work, we propose a global optimization approach for mixed-integer programming problems. To this aim, we preliminarily define an exact penalty algorithm model for globally solving general problems and we show its convergence properties. Then, we describe a particular version of the algorithm that solves mixed-integer problems and we report computational results on some MINLP problems.

关键词： mixed-integer programming Global optimization Exact penalty functions

来源：评论

学校读者我要写书评

暂无评论

Topology optimization of truss structure considering kinematic stability based on mixed-integer programming approach

引用

STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2024年第7期67卷 112-112页

作者： Cai, Qi Feng, Ruoqiang Zhang, Zhijie Wang, Xi Southeast Univ Key Lab Concrete & Prestressed Concrete Struct Minist Educ Nanjing 211189 Jiangsu Peoples R China Hohai Univ Coll Mech & Engn Sci Nanjing 211189 Jiangsu Peoples R China

Kinematic instability due to unstable nodes is an often neglected but critical aspect of mathematical optimization models in truss topology optimization problems. On the one hand, kinematically unstable structures cannot be used in the actual structural design. On the other hand, unstable nodes within continuous parallel bars can make the calculation of bar length wrong and affect the optimization effect. To avoid kinematic instability, a computationally efficient nominal disturbing force (NDF) approach for truss topology optimization is presented in this paper. Using the NDF approach, the most favorable structure for the optimization goal can be selected in three schemes: (1) adding bracings at unstable nodes, (2) removing unstable nodes and replacing short bars with long ones, or (3) selecting a new topology form to avoid containing unstable nodes. Compared with the widely used nominal lateral force (NLF) approach in the literature, the NDF approach can not only improve the optimization efficiency but also obtain lighter optimization results. Moreover, using the NDF approach, a mixed-integer linear optimization model for minimizing the weight of truss with discrete cross-sectional areas subject to constraints on kinematic stability, bar buckling, allowable stress, nodal displacement, bar crossing, and overlapping is proposed in this study. Because the objective and constraint functions are linear expressions in terms of variables, the globally optimal structures can be obtained by using the proposed model. In addition, two necessary conditions for kinematic stability are proposed to speed up the computational efficiency and delete unnecessary nodes within consecutive tension bars. Finally, the effectiveness of the proposed NDF method and the necessary conditions for kinematic stability are studied on four truss topology optimization problems in two and three dimensions.

关键词： Truss Topology optimization Kinematic stability mixed-integer programming

来源：评论

学校读者我要写书评

暂无评论

A Stochastic-Goal mixed-integer programming approach for integrated stock and bond portfolio optimization

引用

COMPUTERS & INDUSTRIAL ENGINEERING 2011年第4期61卷 1285-1295页

作者： Stoyan, Stephen J. Kwon, Roy H. Univ So Calif Daniel J Epstein Dept Ind & Syst Engn Los Angeles CA 90089 USA Univ Toronto Dept Mech & Ind Engn Toronto ON Canada

We consider a Stochastic-Goal mixed-integer programming (SGMIP) approach for an integrated stock and bond portfolio problem. The portfolio model integrates uncertainty in asset prices as well as several important real-world trading constraints. The resulting formulation is a structured large-scale problem that is solved using a model specific algorithm that consists of a decomposition, warm-start, and iterative procedure to minimize constraint violations. We present computational results and portfolio return values in comparison to a market performance measure. For many of the test cases the algorithm produces optimal solutions, where CPU time is improved greatly. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Stochastic programming Goal programming mixed-integer programming Geographical decomposition

来源：评论

学校读者我要写书评

暂无评论

Algorithms for generating Pareto fronts of multi-objective integer and mixed-integer programming problems

引用

ENGINEERING OPTIMIZATION 2022年第8期54卷 1413-1425页

作者： Burachik, Regina S. Kaya, C. Yalcin Rizvi, Mohammed Mustafa Univ South Australia Math UniSA STEM Adelaide SA Australia Univ Chittagong Dept Math Chittagong Bangladesh

Multi-objective integer or mixed-integer programming problems typically have disconnected feasible domains, making the task of constructing an approximation of the Pareto front challenging. The present article shows that certain algorithms that were originally devised for continuous problems can be successfully adapted to approximate the Pareto front for integer, and mixed-integer, multi-objective problems. Relationships amongst various scalarization techniques are established to motivate the choice of a particular scalarization in these algorithms. The proposed algorithms are tested by means of two-, three- and four-objective integer and mixed-integer problems, and comparisons are made. In particular, a new four-objective algorithm is used to solve a rocket injector design problem with a discrete variable, which is a challenging mixed-integer programming problem.

关键词： Multi-objective optimization mixed-integer programming scalarization Pareto front numerical methods

来源：评论

学校读者我要写书评

暂无评论

Forestry production and logistics planning: an analysis using mixed-integer programming

引用

FOREST POLICY AND ECONOMICS 2005年第4期7卷 625-633页

作者： Troncoso, JJ Garrido, RA Pontificia Univ Catolica Chile Dept Forest Sci Santiago Chile Pontificia Univ Catolica Chile Dept Transport Engn Santiago Chile

This article presents a mathematical model for the problem of production and logistics in the forest industry. Specifically, a dynamic model of mixed-integer programming was formulated to solve three common problems in the forest sector: forest production, forest facilities location and forest freight distribution. The implemented mathematical model allows the strategic selection of the optimal location and size of a forest facility, in addition to the identification of the production levels and freight flows that will be generated in the considered planning horizon. A practical application of the model was carried out, validating its utility in the location of a sawmill. The model was optimally solved using LINGO, which also allowed to evaluate its response capacity in relation to changes in information considered in the initial planning, as well as the comparison of the decisions and the solution times for different scenarios such as demand, transportation costs, timber prices and yields of the sawn process. (c) 2004 Elsevier B.V. All rights reserved.

关键词： forest planning production and logistics plant location problem mixed-integer programming

来源：评论

学校读者我要写书评

暂无评论

Further results on an abstract model for branching and its application to mixed integer programming

引用

MATHEMATICAL programming 2021年第1-2期190卷 811-841页

作者： Anderson, Daniel Le Bodic, Pierre Morgan, Kerri Carnegie Mellon Univ Comp Sci Dept Pittsburgh PA 15213 USA Monash Univ Fac Informat Technol Caulfield Australia Deakin Univ Fac Sci Engn & Built Environm Sch Informat Technol Geelong Vic Australia

A key ingredient in branch and bound (B&B) solvers for mixed-integer programming (MIP) is the selection of branching variables since poor or arbitrary selection can affect the size of the resulting search trees by orders of magnitude. A recent article by Le Bodic and Nemhauser (Math Program 166(1-2):369-405, 2017) investigated variable selection rules by developing a theoretical model of B&B trees from which they developed some new, effective scoring functions for MIP solvers. In their work, Le Bodic and Nemhauser left several open theoretical problems, solutions to which could guide the future design of variable selection rules. In this article, we first solve many of these open theoretical problems. We then implement an improved version of the model-based branching rules in SCIP 6.0, a state-of-the-art academic MIP solver, in which we observe an 11% geometric average time and node reduction on instances of the MIPLIB 2017 Benchmark Set that require large B&B trees.

关键词： Branch and bound mixed-integer programming Algorithm analysis Branching rules

来源：评论

学校读者我要写书评

暂无评论

Assignments of Pavement Treatment Options: Genetic Algorithms versus mixed-integer programming

引用

JOURNAL OF TRANSPORTATION ENGINEERING PART B-PAVEMENTS 2020年第2期146卷

作者： Sindi, Wadea Agbelie, Bismark Catholic Univ Amer Dept Civil Engn Washington DC 20064 USA Royal Commiss Jubail & Yanbu Tech Affairs Yanbu 46451 Saudi Arabia

Assigning specific maintenance treatments is an important process in a pavement management system (PMS). A decision-making method to support this process should be based on an objective of optimizing the service life and cost of each treatment, which becomes a multiobjective process when applied to a road network. This paper explored the expected accuracy rates of network treatment options through a multiobjective optimization methodology which utilized genetic algorithms (GAs) and mixed-integer programming (MIP). This paper demonstrated the application of GAs and MIP based on the common indicators of distress for evaluating pavement condition (rutting, raveling, potholes, cracks, and roughness). The results indicated that the proposed method is capable of effectively assigning pavement maintenance while considering optimal service life and minimal cost.

关键词： Pavement treatment Genetic algorithms mixed-integer programming Pavement management Pavement assessment

来源：评论

学校读者我要写书评

暂无评论

Computation of Systemic Risk Measures: A mixed-integer programming Approach

引用

OPERATIONS RESEARCH 2023年第6期71卷 2130页

作者： Ararat, Cagin Meimanjan, Nurtai Bilkent Univ Dept Ind Engn TR-06800 Ankara Turkiye Vienna Univ Econ & Business Inst Stat & Math A-1020 Vienna Austria

Systemic risk is concerned with the instability of a financial system whose members are interdependent in the sense that the failure of a few institutions may trigger a chain of defaults throughout the system. Recently, several systemic risk measures have been proposed in the literature that are used to determine capital requirements for the members subject to joint risk considerations. We address the problem of computing systemic risk measures for systems with sophisticated clearing mechanisms. In particular, we consider an extension of the Rogers-Veraart network model where the operating cash flows are unrestricted in sign. We propose a mixed-integer programming problem that can be used to compute clearing vectors in this model. Because of the binary variables in this problem, the corresponding (set-valued) systemic risk measure fails to have convex values in general. We associate nonconvex vector optimization problems with the systemic risk measure and provide theoretical results related to the weighted-sum and Pascoletti-Serafini scalarizations of this problem. Finally, we test the proposed formulations on computational examples and perform sensitivity analyses with respect to some model-specific and structural parameters.

关键词： systemic risk measure set-valued risk measure Eisenberg-Noe model Rogers-Veraart model mixed-integer programming vector optimization

来源：评论

学校读者我要写书评

暂无评论

A grey-forecasting interval-parameter mixed-integer programming approach for integrated electric-environmental management-A case study of Beijing

引用

ENERGY 2013年 63卷 334-344页

作者： Wang, Xingwei Cai, Yanpeng Chen, Jiajun Dai, Chao Beijing Normal Univ Sch Environm Minist Educ Key Lab Water & Sediment Sci Beijing 100875 Peoples R China Univ Regina Inst Energy Environm & Sustainable Communities Regina SK S4S 7H9 Canada Peking Univ Dept Environm Sci Beijing 100871 Peoples R China

In this study, a GFIPMIP (grey-forecasting interval-parameter mixed-integer programming) approach was developed for supporting IEEM (integrated electric-environmental management) in Beijing. It was an attempt to incorporate an energy-forecasting model within a general modeling framework at the municipal level. The developed GFIPMIP model can not only forecast electric demands, but also reflect dynamic, interactive, and uncertain characteristics of the IEEM system in Beijing. Moreover, it can address issues regarding power supply, and emission reduction of atmospheric pollutants and GHG (greenhouse gas). Optimal solutions were obtained related to power generation patterns and facility capacity expansion schemes under a series of system constraints. Two scenarios were analyzed based on multiple environmental policies. The results were useful for helping decision makers identify desired management strategies to guarantee the city's power supply and mitigate emissions of GHG and atmospheric pollutants. The results also suggested that the developed GFIPMIP model be applicable to similar engineering problems. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Interval-parameter programming mixed-integer programming Grey-forecasting model Integrated electric-environmental management Beijing Uncertainties

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：