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An exact second order cone programming approach for traffic assignment problems

RAIRO-OPERATIONS RESEARCH 2024年第1期58卷 847-864页

作者： Bayram, Vedat TED Univ Dept Ind Engn Kolej Cankaya TR-06420 Ankara Turkiye Univ Kent Ctr Logist & Sustainabil Analyt Kent Business Sch Dept Analyt Operat & Syst Canterbury CT2 7NZ Kent England

Demographic changes, urbanization and increasing vehicle ownership at unprecedented rates put a lot of strain on cities particularly on urban mobility and transportation and overwhelm transportation network infrastructures and current transportation systems, which are not built to cope with such a fast increasing demand. Traffic congestion is considered as the most difficult challenge to tackle for sustainable urban mobility and is aggravated by the increased freight activity due to e-commerce and on-demand delivery and the explosive growth in transportation network companies and ride-hailing services. There is a need to implement a combination of policies to ensure that increased urban traffic congestion does not lower the quality of life and threaten global climate and human health and to prevent further economic losses. This study aims to contribute to the United Nations (UN) climate action and sustainable development goals in tackling recurring traffic congestion problem in urban areas to achieve a sustainable urban mobility in that it offers a solution methodology for traffic assignment problem. We introduce an exact generalized solution methodology based on reformulation of existing traffic assignment problems as a second order cone programming (SOCP) problem and propose column generation (CG) and cutting plane (CP) algorithms to solve the problem effectively for large scale road network instances. We conduct numerical experiments to test the performance of the proposed algorithms on realistic road networks.

关键词： Sustainable development goals traffic congestion traffic assignment column generation cutting plane second order cone programming

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A novel improved edge-based smoothed particle finite element method for elastoplastic contact analysis using second order cone programming

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2025年 441卷

作者： Zhou, Xi-Wen Jin, Yin-Fu Yin, Zhen-Yu Liu, Feng-Tao Chen, Xiangsheng Shenzhen Univ State Key Lab Intelligent Geotech & Tunnelling Shenzhen 518060 Guangdong Peoples R China Shenzhen Univ Natl Engn Res Ctr Deep Shaft Construct Shenzhen 518060 Guangdong Peoples R China Shenzhen Univ Coll Civil & Transportat Engn Shenzhen 518060 Guangdong Peoples R China Hong Kong Polytech Univ Dept Civil & Environm Engn Hung Hom Kowloon Hong Kong Peoples R China Guilin Univ Technol Guangxi Key Lab Geotech Mech Engn Guilin 541004 Peoples R China

Contact problems are of paramount importance in engineering but present significant challenges for numerical solutions due to their highly nonlinear nature. Recognizing that contact problems can be formulated as optimization problems with inequality constraints has paved the way for advanced techniques such as the Interior Point (IP) method. This study presents an Improved Edge-based Smoothed Particle Finite Element Method (IES-PFEM) with novel contact scheme for elastoplastic analysis involving large deformation using second-order cone programming (SOCP). Within the proposed framework, classical node-to-surface (NTS) and surface-to-surface (STS) contact discretization schemes in SOCP form are rigorously achieved. The governing equations of elastoplastic boundary value problems are formulated as a min-max problem via the mixed variation principle, and by applying the primal-dual theory of convex optimization, the problem is transformed into a dual formulation with stresses as optimization variables. The Mohr-Coulomb plastic yield criterion and the Coulomb friction law are naturally expressed as second-order cone constraints. A fixed-point iteration scheme is developed to address unphysical normal expansion arising from the natural derivation of an associated friction model within the SOCP formulation. Furthermore, the volumetric locking problem in nearly incompressible materials is alleviated by IES-PFEM formulation without requiring additional stabilization techniques. The proposed method is validated through a series of benchmark examples involving contact and elastoplastic deformations. Numerical results confirm the capability of the proposed approach to handle both contact and elastoplastic nonlinearities effectively, without the need for convergence control, highlighting the superiority of the proposed method.

关键词： second order cone programming Interior point method Contact Elastoplastic deformations Smoothed finite element method

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Green supply chain design with emission sensitive demand: second order cone programming formulation and case study

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OPTIMIZATION LETTERS 2021年第1期15卷 231-247页

作者： Elhedhli, Samir Gzara, Fatma Waltho, Cynthia Univ Waterloo Dept Management Sci Waterloo ON Canada

We propose a novel modeling framework for supply chain network design that models a prevailing trend in consumer choice in which demand is impacted by carbon footprint. To date, the literature lacks models that realistically account for and accurately calculate per unit emissions, i.e., carbon footprint. We develop a profit maximizing model that accounts for emissions at the different stages of the supply chain, locates facilities and selects their technology, and decides on the flow between echelons. To calculate the carbon footprint, fixed emissions are averaged over throughput, which results in a nonlinear optimization problem with fractional terms. To solve it, we provide a mixed integer second order cone programming reformulation. We perform extensive testing of the framework on a realistic case study and carry out detailed analysis. The proposed framework succeeds in capturing the trade-off between lost demand due to a high carbon footprint and investing in environmentally-friendly technology. The framework serves as a tool to induce organizations to invest in green technology and to allow regulating authorities to assess the impact of eco-labeling.

关键词： Green supply chain design second order cone programming Carbon footprint Emission sensitive demand Eco-labels

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A rigorous numerical formulation for upper bound analysis of reinforced soils using second order cone programming

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GEOTEXTILES AND GEOMEMBRANES 2021年第5期49卷 1294-1311页

作者： Yuan, Shuai Changan Univ Sch Highway Xian 710064 Peoples R China

A rigorous upper bound formulation is established for reinforced soils considering both the tensile rupture of the reinforcement and the relative slippage of the reinforcement-soil interface. To represent its finite tensile strength and negligible compressive strength, a novel strategy is proposed to calculate the plastic dissipation rate of the reinforcement without the incorporation of stress variables. Plastic dissipation rates of the soil, the reinforcement and their interfaces are obtained using only kinematic variables and all flow rules are expressed in terms of linear constraints and second order cones. The solution domain is then discretized using linear strain elements for the soil and constant strain elements for the reinforcement and the interface. Numerical examples are given to show the accuracy of the present formulation. The effect of design parameters such as the tensile strength, the length and the location of the reinforcement is discussed.

关键词： Reinforced soil Upper bound limit analysis second order cone programming

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FSOCP: feature selection via second-order cone programming

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CENTRAL EUROPEAN JOURNAL OF OPERATIONS RESEARCH 2025年第1期33卷 51-64页

作者： Guldogus, Buse Cisil Ozogur-Akyuz, Suereyya Bahcesehir Univ Dept Ind Engn Istanbul Turkiye Bahcesehir Univ Dept Math Istanbul Turkiye

Feature selection is an important factor of accurately classifying high dimensional data sets by identifying relevant features and improving classification accuracy. The use of feature selection in operations research allows for the identification of relevant features and the creation of optimal subsets of features for improved predictive performance. This paper proposes a novel feature selection algorithm inspired from ensemble pruning which involves the use of second-order conic programming modeled as an embedded feature selection technique with neural networks, named feature selection via second order cone programming (FSOCP). The proposed FSOCP algorithm trains features individually on a neural network and generates a probability class distribution and prediction, allowing the second-order conic programming model to determine the most important features for improved classification accuracies. The algorithm is evaluated on multiple synthetic data sets and compared with other feature selection techniques, demonstrating its promising potential as a feature selection approach.

关键词： Feature selection Feature extraction Neural networks Ensemble pruning second order cone programming

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Approximate and exact optimal designs for 2^k factorial experiments for generalized linear models via second order cone programming

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STATISTICAL PAPERS 2020年第6期61卷 2737-2767页

作者： Duarte, Belmiro P. M. Sagnol, Guillaume Inst Super Engn Coimbra Inst Politecn Coimbra Dept Chem & Biol Engn Rua Pedro Nunes P-3030199 Coimbra Portugal Univ Coimbra Dept Chem Engn CIEPQPF Coimbra Portugal Tech Univ Berlin Inst Math Berlin Germany

Model-based optimal designs of experiments (M-bODE) for nonlinear models are typically hard to compute. The literature on the computation of M-bODE for nonlinear models when the covariates are categorical variables, i.e. factorial experiments, is scarce. We propose second order cone programming (SOCP) and Mixed Integer second order programming (MISOCP) formulations to find, respectively, approximate and exact A- and D-optimal designs for 2(k) factorial experiments for Generalized Linear Models (GLMs). First, locally optimal (approximate and exact) designs for GLMs are addressed using the formulation of Sagnol (J Stat Plan Inference 141(5):1684-1708, 2011). Next, we consider the scenario where the parameters are uncertain, and new formulations are proposed to find Bayesian optimal designs using the A- and log detD-optimality criteria. A quasi Monte-Carlo sampling procedure based on the Hammersley sequence is used for computing the expectation in the parametric region of interest. We demonstrate the application of the algorithm with the logistic, probit and complementary log-log models and consider full and fractional factorial designs.

关键词： D-optimal designs 2(k) Factorial experiments Exact designs second order cone programming Generalized linear models Quasi-Monte Carlo sampling

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Free isotropic material optimization via second order cone programming

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COMPUTER-AIDED DESIGN 2019年 115卷 52-63页

作者： Yang, Xingtong Li, Ming Zhejiang Univ State Key Lab CAD & CG Hangzhou Zhejiang Peoples R China

Designing an engineered structure of optimal performance is the ultimate goal of engineering design, and various structural optimization approaches have been proposed. However, previous studies on the topic mainly rely on the single design variable of Young's modulus or density without considering its Poisson's ratio as another key isotropic material parameter, and thus may limit the best design ultimately reached. In the study, the problem of free isotropic material optimization (FIMO) is studied that takes as design variables both Young's modulus and Poisson's ratio at each point of the design domain without constraints on its manufacturability;certain necessary conditions on the material attainability are the only imposed requirements. Global optimum to the FIMO is achieved via rigorously reformulating it as a second order cone programming, to which a global optimum is theoretically verified and numerically trackable;the novel formulation also avoids the challenging singularity issue on void elements. The material dimension of the resulted design can also be reduced to any prescribed number of high fidelity via a hierarchical material clustering algorithm. The generated structure can be taken as benchmark solutions with which other optimized designs can be compared, and to propose novel new product design. Performance of the approach is tested on various 2D examples, in comparison with structures generated via classical topology optimization. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Free isotropic material optimization (FIMO) second order cone programming Poisson's ratio Multi-material Topology optimization

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A logarithmic barrier interior-point method based on majorant functions for second-order cone programming

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OPTIMIZATION LETTERS 2020年第3期14卷 729-746页

作者： Alzalg, Baha Univ Jordan Dept Math Amman 11942 Jordan

We present a logarithmic barrier interior-point method for solving a second-order cone programming problem. Newton's method is used to compute the descent direction. The main contribution of this paper is that it uniquely uses the so-called majorant functions as an efficient alternative to line search methods to determine the displacement step along the direction while solving second-order cone programs. The efficiency of our method is shown by presenting numerical experiments.

关键词： second order cone programming Interior-point methods Logarithmic barrier methods Majorant functions Jordan algebras

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A second-order cone programming Model for Planning PEV Fast-Charging Stations

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IEEE TRANSACTIONS ON POWER SYSTEMS 2018年第3期33卷 2763-2777页

作者： Zhang, Hongcai Moura, Scott J. Hu, Zechun Qi, Wei Song, Yonghua Tsinghua Univ Dept Elect Engn Beijing 100084 Peoples R China Univ Calif Berkeley Dept Civil & Environm Engn Berkeley CA 94720 USA Tsinghua Berkeley Shenzhen Inst Smart Grid & Renewable Energy Lab Shenzhen 518055 Peoples R China McGill Univ Desautels Fac Management Montreal PQ H3A 1G5 Canada

This paper studies siting and sizing of plug-in electric vehicle (PEV) fast-charging stations on coupled transportation and power networks. We develop a closed-form model for PEV fast-charging stations' service abilities, which considers heterogeneous PEV driving ranges and charging demands. We utilize a modified capacitated flow refueling location model based on subpaths (CFRLM_SP) to explicitly capture time-varying PEV charging demands on the transportation network under driving range constraints. We explore extra constraints of the CFRLM_SP to enhance model accuracy and computational efficiency. We then propose a stochastic mixed-integer second-order cone programming model for PEV fast-charging station planning. The model considers the transportation network constraints of CFRLM_SP and the power network constraints with ac power flow. Numerical experiments are conducted to illustrate the effectiveness of the proposed method.

关键词： Plug-in electric vehicle charging station planning heterogeneous driving ranges transportation power system second order cone programming

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second order cone programming approach to two-stage network data envelopment analysis

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2017年第1期262卷 231-238页

作者： Chen, Kun Zhu, Joe Nanjing Audit Univ Coll Auditing & Evaluat Nanjing 211815 Jiangsu Peoples R China Worcester Polytech Inst Foisie Business Sch Worcester MA 01609 USA

Efficiency aggregation and efficiency decomposition are two techniques used in modeling decision making units (DMUs) with two-stage network structures under network data envelopment analysis (DEA). Multiplicative efficiency decomposition (MED) is usually used in a very specialized two-stage structure when constant returns to scale (CRS) is assumed. MED-based network DEA retains the property of the conventional DEA in the sense that input- and output-oriented models yield the same efficiency scores. Compared with the additive efficiency decomposition (AED), MED does not require predetermined weights to combine individual stage efficiencies. However, if there are external inputs to the second stage, and/or some outputs leave the first stage and do not become inputs to the second stage, or if we assume variable returns to scale (VRS), MED has limited capability to address these extensions. Alternatively, multiplicative efficiency aggregation (MEA), which is highly nonlinear and is impossible to be transformed into a linear programming problem, defines the overall efficiency as a product of stage efficiency scores and can be easily applied to general two-stage network structures. The current study discovers that MEA DEA model for general two-stage networks corresponds to a cone structure in disguise, and can be transformed into the form of second order cone programming (SOCP). Therefore, MEA in two-stage network DEA can be effectively and efficiently solved, regardless of the network structures. We show that AED can also be solved using SOCP and demonstrate that input and output-oriented AED models may not yield the same efficiency scores under CRS. The current research enables us to solve both MEA and AED using SOCP which is considered as effective as linear programming. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Data envelopment analysis (DEA) Multiplicative efficiency aggregation Two-stage second order cone programming

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