检索结果-内蒙古大学图书馆

mixed-integer quadratic optimization for waste flow quantification

optimization AND ENGINEERING 2022年第4期23卷 2177-2201页

作者： Somplak, R. Smejkalova, V Kudela, J. Brno Univ Technol Fac Mech Engn Inst Proc Engn Brno Czech Republic Brno Univ Technol Fac Mech Engn Inst Automat & Comp Sci Brno Czech Republic

The transition to a circular economy can be realized with higher waste recycling. With the knowledge of waste flows and the links between them, it is possible to plan the infrastructure of the entire system and set the goals needed for the transition to a circular economy. If the statistical analysis does not provide quality models, it is possible to describe waste flows using basic balance relationships. This contribution presents an optimization model based on quadratic programming. The output of the model is an estimate of the waste amount that was managed to divert from mixed municipal waste to separate fractions in the past period. A key input is an estimate of the composition of mixed municipal waste. For a more detailed territorial model, composition estimates are often not available, so an optimization model using the principle of credibility has been proposed. Uncertain information for lower territorial units is corrected by aggregated results for the national level. The resulting optimization models were tested on the data of the Czech Republic for the period 2010-2018 in annual detail. The result interprets what part of the newly separated waste comes from mixed municipal waste. For the significant monitored fractions this value is low, 0.26 for bio-waste in the Czech Republic. On the contrary, the high part of the shift from mixed municipal waste is for plastic, 0.82. The results showed the advantage of correction at lower territory levels due to the high variability of the input data.

关键词： Data reconciliation mixed-integer quadratic optimization Data aggregation Waste production mixed municipal waste Waste flow

来源：评论

学校读者我要写书评

暂无评论

mixed-integer quadratic optimization and iterative clustering techniques for semi-supervised support vector machines

引用

TOP 2024年第3期32卷 391-428页

作者： Burgard, Jan Pablo Pinheiro, Maria Eduarda Schmidt, Martin Trier Univ Dept Econ & Social Stat Univ Sring 15 D-54296 Trier Germany Trier Univ Dept Math Universitatsring 15 D-54296 Trier Germany

Among the most famous algorithms for solving classification problems are support vector machines (SVMs), which find a separating hyperplane for a set of labeled data points. In some applications, however, labels are only available for a subset of points. Furthermore, this subset can be non-representative, e.g., due to self-selection in a survey. Semi-supervised SVMs tackle the setting of labeled and unlabeled data and can often improve the reliability of the results. Moreover, additional information about the size of the classes can be available from undisclosed sources. We propose a mixed-integer quadratic optimization (MIQP) model that covers the setting of labeled and unlabeled data points as well as the overall number of points in each class. Since the MIQP's solution time rapidly grows as the number of variables increases, we introduce an iterative clustering approach to reduce the model's size. Moreover, we present an update rule for the required big-M values, prove the correctness of the iterative clustering method as well as derive tailored dimension-reduction and warm-starting techniques. Our numerical results show that our approach leads to a similar accuracy and precision than the MIQP formulation but at much lower computational cost. Thus, we can solve larger problems. With respect to the original SVM formulation, we observe that our approach has even better accuracy and precision for biased samples.

关键词： Semi-supervised learning Support vector machines Clustering mixed-integer quadratic optimization

来源：评论

学校读者我要写书评

暂无评论

quadratic convex reformulations for a class of complex quadratic programming problems

引用

COMPUTATIONAL optimization AND APPLICATIONS 2025年第1期91卷 125-144页

作者： Lu, Cheng Kang, Gaojian Qu, Guangtai Deng, Zhibin North China Elect Power Univ Sch Econ & Management Beijing 102206 Peoples R China Univ Chinese Acad Sci Sch Econ & Management Beijing 100190 Peoples R China Univ Chinese Acad Sci MOE Social Sci Lab Digital Econ Forecasts & Policy Beijing 100190 Peoples R China

We investigate a class of complex quadratic programming problems characterized by unit-modulus and discrete argument constraints. This problem can be reformulated as a mixed-integer quadratic programming problem, which could be addressed using a commercial solver such as Gurobi. However, the solver's efficiency is often unsatisfying if the problem formulation is inadequately designed. In this paper, we introduce several quadratic convex reformulations aimed at enhancing the solver's performance. We extend the classical diagonal perturbation-based reformulation technique to this problem. Additionally, by leveraging the unique structure of the problem, we derive a new quadratic convex reformulation that provides a tighter continuous relaxation compared to the diagonal perturbation-based approach. The numerical tests on random instances and the unimodular code design problem demonstrate the superiority of the newly proposed reformulation.

关键词： mixed-integer quadratic optimization Convex quadratic reformulation Semidefinite relaxation

来源：评论

学校读者我要写书评

暂无评论

On Tractable Convex Relaxations of Standard quadratic optimization Problems under Sparsity Constraints

引用

JOURNAL OF optimization THEORY AND APPLICATIONS 2025年第3期204卷 1-36页

作者： Bomze, Immanuel Peng, Bo Qiu, Yuzhou Yildirim, E. Alper Univ Vienna Fac Math & Res Network Data Sci Oskar Morgenstern Pl 1 A-1090 Vienna Austria Univ Vienna VGSCO Oskar Morgenstern Pl 1 A-1090 Vienna Austria Univ Vienna ISOR Oskar Morgenstern Pl 1 A-1090 Vienna Austria Univ Edinburgh Sch Math Peter Guthrie Tait Rd Edinburgh EH9 3FD Scotland

Standard quadratic optimization problems (StQPs) provide a versatile modelling tool in various applications. In this paper, we consider StQPs with a hard sparsity constraint, referred to as sparse StQPs. We focus on various tractable convex relaxations of sparse StQPs arising from a mixed-binary quadratic formulation, namely, the linear optimization relaxation given by the reformulation-linearization technique, the Shor relaxation, and the relaxation resulting from their combination. We establish several structural properties of these relaxations in relation to the corresponding relaxations of StQPs without any sparsity constraints, and pay particular attention to the rank-one feasible solutions retained by these relaxations. We then utilize these relations to establish several results about the quality of the lower bounds arising from different relaxations. We also present several conditions that ensure the exactness of each relaxation.

关键词： Standard quadratic optimization problems Sparsity mixed-integer quadratic optimization Reformulation-linearization technique Shor relaxation

来源：评论

学校读者我要写书评

暂无评论

Explicit convex hull description of bivariate quadratic sets with indicator variables

引用

MATHEMATICAL PROGRAMMING 2024年 1-43页

作者： De Rosa, Antonio Khajavirad, Aida Bocconi Univ Dept Decis Sci Milan Italy Bocconi Univ BIDSA Milan Italy Lehigh Univ Dept Ind & Syst Engn Bethlehem PA 18015 USA

We consider the nonconvex set Sn={(x,X,z):X=xxT,x(1-z)=0,x >= 0,z is an element of{0,1}n}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal {S}}}_n = \{(x,X,z): X = x x<^>T, \;x (1-z) =0,\;x \ge 0,\;z \in \{0,1\}<^>n\}$$\end{document}, which is closely related to the feasible region of several difficult nonconvex optimization problems such as the best subset selection and constrained portfolio optimization. Utilizing ideas from convex analysis and disjunctive programming, we obtain an explicit description for the closure of the convex hull of S2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal {S}}}_2$$\end{document} in the space of original variables. In order to generate valid inequalities corresponding to supporting hyperplanes of the convex hull of S2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal {S}}}_2$$\end{document}, we present a simple separation algorithm that can be incorporated in branch-and-cut based solvers to enhance the quality of existing relaxations.

关键词： mixed-integer quadratic optimization Indicator variables Convex hull Disjunctive programming Perspective function Projection

来源：评论

学校读者我要写书评

暂无评论

The equivalence of optimal perspective formulation and Shor's SDP for quadratic programs with indicator variables

引用

OPERATIONS RESEARCH LETTERS 2022年第2期50卷 195-198页

作者： Han, Shaoning Gomez, Andres Atamturk, Alper Univ Southern Calif Viterbi Sch Engn Daniel J Epstein Dept Ind & Syst Engn Los Angeles CA 90089 USA Univ Calif Berkeley Dept Ind Engn & Operat Res Berkeley CA 94720 USA

In this paper, we compare the strength of the optimal perspective relaxation and Shor's SDP relaxation for convex quadratic optimization problems with indicator variables and prove that they are equivalent. (C) 20... 详细信息

关键词： mixed-integer quadratic optimization Semidefinite programming Perspective formulation Indicator variables Convexification

来源：评论

学校读者我要写书评

暂无评论

2 x 2-Convexifications for convex quadratic optimization with indicator variables

引用

MATHEMATICAL PROGRAMMING 2023年第1-2期202卷 95-134页

In this paper, we study the convex quadratic optimization problem with indicator variables. For the 2 x 2 case, we describe the convex hull of the epigraph in the original space of variables, and also give a conic quadratic extended formulation. Then, using the convex hull description for the 2 x 2 case as a building block, we derive an extended SDP relaxation for the general case. This new formulation is stronger than other SDP relaxations proposed in the literature for the problem, including the optimal perspective relaxation and the optimal rank-one relaxation. Computational experiments indicate that the proposed formulations are quite effective in reducing the integrality gap of the optimization problems.

关键词： mixed-integer quadratic optimization Semidefinite programming Perspective formulation Indicator variables Convexification

来源：评论

学校读者我要写书评

暂无评论

Innovative approaches to addressing the tradeoff between interpretability and accuracy in ship fuel consumption prediction

引用

TRANSPORTATION RESEARCH PART C-EMERGING TECHNOLOGIES 2023年 157卷

作者： Wang, Haoqing Yan, Ran Wang, Shuaian Zhen, Lu Hong Kong Polytech Univ Fac Business Dept Logist & Maritime Studies Hong Kong Peoples R China Nanyang Technol Univ Sch Civil & Environm Engn Singapore Singapore Shanghai Univ Sch Management Shanghai Peoples R China

Ship fuel consumption is a major component of maritime transport costs and most of its emissions are harmful to the environment. Hence, it is essential to build an accurate ship fuel consumption prediction model, thereby providing reference to the navigation operations. However, maritime industry experts are wary of advanced black-box models since they cannot interpret the outcomes of these models. The application of advanced black-box models in the shipping industry remains limited and it is necessary to develop both accurate and interpretable ship fuel consumption prediction models. This study uses domain knowledge to develop two innovative methods for predicting ship fuel consumption-the first is a physics-informed neural network (PI-NN) model that improves the interpretability of the black-box model while maintaining accuracy and the second is a mixed-integer quadratic optimization (MIO) model that considers more forms of feature variable expressions in an additive white-box model. The proposed approaches address the tradeoff between model interpretability and model accuracy in ship fuel consumption prediction. The experiment results demonstrate that the PI-NN model improves the interpretability of the black-box model while preserving accuracy. The MIO model considers alternative variable expressions, leading to the flexibility of the white-box model. Finally, SHapley Additive exPlanations (SHAP) is used to explain how each feature value contributes to the predictions of the black-box model, thereby providing insights into how each value of feature variables affects fuel consumption. This study provides a solution to the tradeoff between model interpretability and model accuracy and can promote the application of data driven models in ship fuel consumption prediction. Moreover, this study gives implications for the application of explainable machine learning models in practice.

关键词： Maritime transport Interpretable machine learning models Ship fuel consumption prediction Domain knowledge in shipping mixed-integer quadratic optimization

来源：评论

学校读者我要写书评

暂无评论

Sparse and smooth signal estimation: convexification of ℓ0-formulations

The Journal of Machine Learning Research

引用

The Journal of Machine Learning Research 2021年第1期22卷 2370-2412页

作者： Alper Atamtürk Andrés Gómez Shaoning Han Department of Industrial Engineering & Operations Research University of California Berkeley CA Daniel J. Epstein Department of Industrial & Systems Engineering University of Southern California Los Angeles CA

Signal estimation problems with smoothness and sparsity priors can be naturally modeled as quadratic optimization with ℓ0-"norm" constraints. Since such problems are nonconvex and hard-to-solve, the standard approach is, instead, to tackle their convex surrogates based on ℓ1-norm relaxations. In this paper, we propose new iterative (convex) conic quadratic relaxations that exploit not only the ℓ0-"norm" terms, but also the fitness and smoothness functions. The iterative convexification approach substantially closes the gap between the ℓ0-"norm" and its ℓ1 surrogate. These stronger relaxations lead to significantly better estimators than ℓ1-norm approaches and also allow one to utilize affine sparsity priors. In addition, the parameters of the model and the resulting estimators are easily interpretable. Experiments with a tailored Lagrangian decomposition method indicate that the proposed iterative convex relaxations yield solutions within 1% of the exact ℓ0-approach, and can tackle instances with up to 100,000 variables under one minute.

关键词： mixed-integer quadratic optimization conic quadratic optimization perspective formulation sparsity

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：