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A REFORMULATION-LINEARIZATION BASED ALGORITHM FOR THE SMALLEST ENCLOSING CIRCLE PROBLEM

JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2021年第6期17卷 3633-3644页

作者： Jiang, Yi Cai, Yuan Sichuan Normal Univ Sch Math Sci Chengdu 610066 Sichuan Peoples R China Sichuan Normal Univ VC VR Key Lab Chengdu 610066 Sichuan Peoples R China

In this paper, an effective algorithm based on the reformulation linearization technique (RLT) is developed to solve the smallest enclosing circle problem. Extensive computational experiments demonstrate that the algo... 详细信息

关键词： The smallest enclosing circle second order cone programming linear programming

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Planning renewables in distribution system with electric vehicles to improve hosting capacity and energy losses: Two-stage stochastic optimization framework

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SUSTAINABLE ENERGY GRIDS & NETWORKS 2024年 39卷

作者： Rawat, Tanuj Singh, Jyotsna Pandey, Vipin Chandra Sharma, Sachin Newcastle Univ Sch Engn Newcastle Upon Tyne England Banasthali Vidyapith Sch Automat Vanasthali 304022 Rajasthan India King Abdullah Univ Sci & Technol KAUST Comp Elect & Math Sci & Engn CEMSE Divison Thuwal Saudi Arabia Graphic Era Deemed Be Univ Dept Elect Engn Dehra Dun India

Excessive penetration of renewables in distribution system can create several operational issues. One of the technologies that can maximize accommodation of renewables is electric vehicles (EVs). However, along with EVs additional measures are required while maximizing hosting capacity (HC) to avoid negative impact on system and account for uncertain parameters. In this regard, this paper proposes a two-stage stochastic optimization approach for planning of renewables in distribution system integrated with EVs. In the first stage, capacity of renewables is determined while maximizing HC whereas in the second stage operating strategy of EVs, renewables and grid power is evaluated to minimize expected energy losses. The proposed framework includes uncertainties in load demand, renewables and EVs characteristics through stochastic programming approach. The optimization problem is formulated as second order cone programming problem. The proposed model is tested on modified IEEE-33 bus and real-life 108-bus Indian distribution systems with different charging/discharging patterns and penetration rates of EVs. Moreover, an economic based cost analysis to compare planning cost and EV charging cost is also provided. Simulation results reveal that in 33-bus system with 500 EVs, the HC with vehicle-to-grid capability (V2G) is higher as compared to uncoordinated and coordinated charging by 29.86% and 6.36% respectively, while in 108-bus system with 1000 EVs, it is higher by 18.51% and 5.69% respectively. Further, the energy losses with V2G are 27.54% and 1.36% less in 33-bus system and 7.31% and 3.22% less in 108-bus system as compared to uncoordinated and coordinated charging respectively.

关键词： Two-stage stochastic programming second order cone programming Hosting capacity Renewables Electric vehicle

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Approximate Load Models for Conic OPF Solvers

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IEEE TRANSACTIONS ON POWER SYSTEMS 2021年第1期36卷 549-552页

作者： Nazir, Firdous Ul Pal, Bikash C. Jabr, Rabih A. Imperial Coll Elect & Elect Engn Dept London SW7 2AZ England Amer Univ Beirut Dept Elect & Comp Engn Beirut 11072020 Lebanon

The global optimum of the optimal power flow (OPF) problem can be sought in various practical settings by adopting the conic relaxations, such as the second order cone programs (SOCPs) and semi-definite programs (SDPs). However, the ZIP (constant impedance, constant current, constant power) and exponential load models are not directly amenable with these conic solvers. Thus, these are mostly treated as constant power loads in the literature. In this letter, we propose two simple methods to approximate these static loads with good accuracy. The proposed methods perform much better than the traditional constant power approximation.

关键词： Exponential load model optimal power flow second order cone programming semi-definite programming ZIP load model

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Covering problems with polyellipsoids: A location analysis perspective

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2021年第1期289卷 44-58页

作者： Blanco, Victor Puerto, Justo Univ Granada IEMath GR Granada Spain Univ Seville IMUS Seville Spain

In this paper we analyze the extension of the classical smallest enclosing disk problem to the case of the location of a polyellipsoid to fully cover a set of demand points in R-d. We prove that the problem is polynomially solvable in fixed dimension and analyze mathematical programming formulations for it. We also consider some geometric approaches for the problem in case the foci of the polyellipsoids are known. Extensions of the classical algorithm by Elzinga-Hearn are also derived for this new problem. Moreover, we address two extensions of the problem, as the case where the foci of the enclosing polyellipsoid are not given and have to be determined among a potential set of points or the induced covering problems when instead of polyellipsoids, one uses ordered median polyellipsoids. For these problems we also present Mixed Integer (Non) Linear programming strategies that lead to efficient ways to solve it. Extensive computational experiments on different datasets show the usefulness of our solution methods. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Polyellipsoids Covering location Minimum enclosing disk second order cone programming

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Russell Graph efficiency measures in Data Envelopment Analysis: The multiplicative approach

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2021年第2期292卷 663-674页

作者： Alcaraz, Javier Anton-Sanchez, Laura Aparicio, Juan Monge, Juan F. Ramon, Nuria Miguel Hernandez Univ Elche Ctr Operat Res Avda Univ S-N Elche 03202 Alicante Spain

The measurement of technical efficiency is a topic of great interest. Since the beginning, many researchers have developed new approaches to gauge technical efficiency, mainly in the non-parametric area of Data Envelopment Analysis (DEA). However, the first measures in DEA, the well-known radial models, only accounted for radial inefficiency, which motivated the introduction in the literature of the so-called Global Efficiency Measures (GEMs);non-oriented and non-radial in nature. Two famous GEMs are the Russell Graph Measure and the Enhanced Russell Graph Measure, also known as the Slacks-Based Measure. These approaches aggregate input and output specific efficiencies through the arithmetic mean, which may not be the most appropriate aggregator function when input and output efficiency ratios are considered, as will be shown. In this paper, in contrast, we propose aggregating input and output specific inefficiencies by applying the geometric average, which will allow us to define new multiplicative versions of the Russell Graph Measures. We also prove some theoretical results and introduce an iterative algorithm, based upon second order cone programming, to solve the new models. Finally, the implementation of the introduced approaches is empirically illustrated through a data set taken from the literature. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Data envelopment analysis Russell Graph Measures Properties second order cone programming

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An integrated efficiency evaluation of China stock market

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2021年第4期72卷 950-969页

作者： Kuo, Kuo-Cheng Lu, Wen-Min Dinh, Thanh Nhan Chinese Culture Univ Program Global Business Taipei Taiwan Natl Def Univ Natl Management Coll Taipei Taiwan Chinese Culture Univ Dept Int Business Adm Taipei 11114 Taiwan

Several studies employ data envelopment analysis (DEA) in the area of portfolio optimization or stock market efficiency evaluation, however, they have not extended two-stage network DEA to further decompose the efficiency of firms on the stock market and understand the origin of performance. Because of China's rising role in global stock market, the current research utilizes the sample of 140 firms extracted from China CSI 300 Index from 2012 to 2016 and proposes an additive two-stage network DEA model to evaluate the performance of China listed firms derived from production and financial production process with fundamental and technical analysis approaches. Analytic hierarchy process and second order cone programming are developed to determine the weights and to solve the nonlinear problem in the additive efficiency decomposition model. In addition to, future data estimated from regression analysis is applied in the DEA model to predict the performance. The main findings are as follows: The production process is more important in defining the overall efficiency of a firm on the stock market;There are significant differences in the distribution of efficiencies among various group industries;The health care, information technology or energy industry has a predicted outstanding performance in general.

关键词： Data envelopment analysis additive efficiency decomposition second order cone programming China stock market

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Exact solution approaches for the workload smoothing in assembly lines

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ENGINEERING SCIENCE AND TECHNOLOGY-AN INTERNATIONAL JOURNAL-JESTECH 2021年第6期24卷 1318-1328页

作者： Dinler, Derya Tural, Mustafa Kemal Hacettepe Univ Dept Ind Engn Ankara Turkey Middle East Tech Univ Dept Ind Engn Ankara Turkey

In this paper, the problem of minimizing the smoothness index for an assembly line given a fixed cycle time and the number of workstations is studied. This problem which is known as the workload smoothing line balancing problem (WSLBP) is a mixed-integer quadratic programming problem. Until recently, this problem has only been tackled using heuristic approaches. Recently, there have been some attempts to solve this problem exactly using mixed-integer linear programming (MILP). The MILP formulations, however, are not usually capable of solving large size problem instances. In this paper, the aim is to solve the WSLBP using mathematical programming formulations by using off-the-shelf solvers. Differently from the literature some non-MILP formulations are also considered for the problem. For this purpose, three MILP formulations, one from the literature, and two non-MILP formulations are compared. The two non-MILP formulations include a mixed-integer second order cone programming formulation and a constraint programming model. The superiority of the non-MILP formulations over the considered MILP formulations is experimentally shown. (C) 2021 Karabuk University. Publishing services by Elsevier B.V.

关键词： Smoothness index Assembly line balancing Workload smoothing Mixed-integer linear programming second order cone programming Constraint programming

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A random optimization strategy of microgrid dispatching based on stochastic response surface method considering uncertainty of renewable energy supplies and load demands

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2023年第1期154卷

作者： Liang, Yuansheng Xu, Zhenli Li, Haifeng Wang, Gang Huang, Zejie Li, Zhikeng South China Univ Technol Sch Elect Power Engn Guangzhou 510640 Peoples R China China Energy Engn Grp Guangdong Elect Power Design Guangzhou 510663 Peoples R China

The stochastic response of microgrid regulation under the influence of uncertainty should be considered in the day-ahead optimal dispatching. This paper focuses on the Stochastic Response Surface Method (SRSM) modelling and second-order cone programming (SOCP) optimal solution for the stochastic optimization strategy of microgrid dispatching considering the random fluctuations of renewable energy supplies and load demands. Based on the SRSM theory, the random distributions of uncertainty are converted into independent standard normal distributions by Nataf transformation, then by means of a small amount of standardized SRSM samples of random fluctuations, the Hermite Chaotic Polynomials can be formulated to describe the random response process of microgrid adjustment. And the Hermite Chaotic Matrix establishes the linear constraint functions for the probability distribution characteristics of stochastic response process of microgrid adjustment considering uncertainty. On this basis, the SRSM based stochastic optimization (SO) model with multi-objective functions are constructed for the optimal economic operation, control of cost fluctuation and lower carbon emissions. In addition, to reduce operation risk, the constraints of extreme power shortage are introduced into the model. To ensure the convexity of the optimization model, the second-order cone Relaxation is applied to all the quadratic terms in the model. Thus, the proposed SO model of microgrid dispatching can be transformed into an SOCP optimization problem. And the Yalmip-Gurobi solver is adopted for the solution of the proposed SO model, which has an efficient operation speed and stability. The effectiveness of the proposed scheme is demonstrated by the case studies using Monte Carlo sampling simulation.

关键词： Microgrid dispatching Stochastic optimization scheme Stochastic Response Surface Method second order cone programming

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Exactness Conditions for Semidefinite programming Relaxations of Generalization of the Extended Trust Region Subproblem

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MATHEMATICS OF OPERATIONS RESEARCH 2023年第3期48卷 1235-1253页

作者： Jiang, Rujun Li, Duan Fudan Univ Sch Data Sci Shanghai 200433 Peoples R China City Univ Hong Kong Sch Data Sci Hong Kong Peoples R China

The extended trust region subproblem (ETRS) of minimizing a quadratic objective over the unit ball with additional linear constraints has attracted a lot of attention in the last few years because of its theoretical significance and wide spectra of applications. Several sufficient conditions to guarantee the exactness of its semidefinite programming (SDP) relaxation have been recently developed in the literature. In this paper, we consider a generalization of the extended trust region subproblem (GETRS), in which the unit ball constraint in the ETRS is replaced by a general, possibly nonconvex, quadratic constraint, and the linear constraints are replaced by a conic linear constraint. We derive sufficient conditions for guaranteeing the exactness of the SDI' relaxation of the GETRS under mild assumptions. Our main tools are two clacses of convex relaxations for the GETRS based on either a simultaneous diagonalization transformation of the quadratic forms or linear combinations of the quadratic forms. We also compare our results to the existing sufficient conditions in the literature. Finally, we extend our results to derive a new sufficient condition for the exactness of the SDP relaxation of general diagonal quadratically constrained quadratic programs, where each quadratic function is associated with a diagonal matrix.

关键词： quadratically constrained quadratic programming extended trust region subproblem semidefinite programming second order cone programming

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Nodal integration-based particle finite element method (N-PFEM) for poro-elastoplastic modelling of saturated soils under large deformation

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COMPUTERS AND GEOTECHNICS 2023年第1期161卷

作者： Wang, Liang Zhang, Xue Geng, Xueyu Lei, Qinghua Swiss Fed Inst Technol Dept Earth Sci Zurich Switzerland Univ Liverpool Dept Civil Engn & Ind Design Liverpool England Univ Warwick Sch Engn Coventry England Uppsala Univ Dept Earth Sci Uppsala Sweden

This paper presents the nodal integration-based particle finite element method (N-PFEM) for poro-elastoplastic analysis of saturated soils subject to large deformation, utilising the generalised Hellinger-Reissner variational principle to reformulate the governing equations for saturated soil dynamics into a min-max optimisation problem. With finite element discretisation and nodal integration over cells, the problem is transformed into a standard second-order cone programming problem, efficiently resolved using the advanced primal-dual interior point method. The N-PFEM method has several advantages, including the use of linear triangular elements without volumetric locking issues, the avoidance of regularisation techniques, and the elimination of tedious variable mapping after remeshing. The numerical model is validated for large deformation analysis of saturated soils with a series of benchmarks against available analytical and numerical solutions, with a case study of the deformation of an embankment considering stone column reinforcement also carried out. This N-PFEM framework offers an effective and efficient simulation approach for the evolutionary behaviour of saturated soils with large deformation in complex geotechnical configurations of practical relevance.

关键词： Saturated soils N-PFEM second order cone programming Effective stress analysis

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