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Displacement and equilibrium mesh-free formulation based on integrated radial basis functions for dual yield design

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2016年第0期71卷 92-100页

作者： Ho, Phuc L. H. Le, Canh V. Tran-Cong, T. Univ Tech Educ HCMC Fac Appl Mech & Civil Engn Hanoi Vietnam Inst Computat Sci & Technol Computat Engn Lab Ho Chi Minh City Vietnam Int Univ VNU HCM Dept Civil Engn Hanoi Vietnam Univ Southern Queensland Computat Engn & Sci Res Ctr Toowoomba Qld 4350 Australia

This paper presents displacement and equilibrium mesh-free formulation based on integrated radial basis functions (iRBF) for upper and lower bound yield design problems. In these approaches, displacement and stress fields are approximated by the integrated radial basis functions, and the equilibrium equations and boundary conditions are imposed directly at the collocation points. In this paper it has been shown that direct nodal integration of the iRBF approximation can prevent volumetric locking in the kinematic formulation, and instability problems can also be avoided. Moreover, with the use of the collocation method in the static problem, equilibrium equations and yield conditions only need to be enforced at the nodes, leading to the reduction in computational cost. The mean value of the approximated upper and lower bound is found to be in excellent agreement with the available analytical solution, and can be considered as the actual collapse load multiplier for most practical engineering problems, for which exact solution is unknown. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Limit analysis Yield design Integrated radial basis function Mesh-free method second order cone programming

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Some applications of polynomial optimization in operations research and real-time decision making

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OPTIMIZATION LETTERS 2016年第4期10卷 709-729页

作者： Ahmadi, Amir Ali Majumdar, Anirudha Princeton Univ Dept Operat Res & Financial Engn Princeton NJ 08544 USA MIT Dept Elect Engn & Comp Sci CSAIL Cambridge MA 02139 USA

We demonstrate applications of algebraic techniques that optimize and certify polynomial inequalities to problems of interest in the operations research and transportation engineering communities. Three problems are considered: (1) wireless coverage of targeted geographical regions with guaranteed signal quality and minimum transmission power, (2) computing real-time certificates of collision avoidance for a simple model of an unmanned vehicle (UV) navigating through a cluttered environment, and (3) designing a nonlinear hovering controller for a quadrotor UV, which has recently been used for load transportation. On our smaller-scale applications, we apply the sum of squares (SOS) relaxation and solve the underlying problems with semidefinite programming. On the larger-scale or real-time applications, we use our recently introduced "SDSOS Optimization" techniques which result in second order cone programs. To the best of our knowledge, this is the first study of real-time applications of sum of squares techniques in optimization and control. No knowledge in dynamics and control is assumed from the reader.

关键词： Polynomial optimization Semidefinite programming second order cone programming Algebraic techniques in optimization Lyapunov methods Real-time optimization

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Strong SOCP Relaxations for the Optimal Power Flow Problem

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OPERATIONS RESEARCH 2016年第6期64卷 1177-1196页

作者： Kocuk, Burak Dey, Santanu S. Sun, X. Andy Georgia Inst Technol H Milton Stewart Sch Ind & Syst Engn Atlanta GA 30332 USA

This paper proposes three strong second order cone programming (SOCP) relaxations for the AC optimal power flow (OPF) problem. These three relaxations are incomparable to each other and two of them are incomparable to the standard SDP relaxation of OPF. Extensive computational experiments show that these relaxations have numerous advantages over existing convex relaxations in the literature: (i) their solution quality is extremely close to that of the standard SDP relaxation (the best one is within 99. 96% of the SDP relaxation on average for all the IEEE test cases) and consistently outperforms previously proposed convex quadratic relaxations of the OPF problem, (ii) the solutions from the strong SOCP relaxations can be directly used as a warm start in a local solver such as IPOPT to obtain a high quality feasible OPF solution, and (iii) in terms of computation times, the strong SOCP relaxations can be solved an order of magnitude faster than the standard SDP relaxation. For example, one of the proposed SOCP relaxations together with IPOPT produces a feasible solution for the largest instance in the IEEE test cases (the 3375-bus system) and also certifies that this solution is within 0.13% of global optimality, all this computed within 157.20 seconds on a modest personal computer. Overall, the proposed strong SOCP relaxations provide a practical approach to obtain feasible OPF solutions with extremely good quality within a time framework that is compatible with the real-time operation in the current industry practice.

关键词： optimal power flow semidefinite programming second order cone programming cutting planes

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An integrated approach for airline scheduling, aircraft fleeting and routing with cruise speed control

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TRANSPORTATION RESEARCH PART C-EMERGING TECHNOLOGIES 2016年 68卷 38-57页

作者： Gurkan, Huseyin Gurel, Sinan Akturk, M. Selim Duke Univ Fuqua Sch Business Decis Sci Durham NC 27706 USA Middle E Tech Univ Dept Ind Engn Ankara Turkey Bilkent Univ Dept Ind Engn Ankara Turkey

To place an emphasis on profound relations among airline schedule planning problems and to mitigate the effect of unexpected delays, we integrate schedule design, fleet assignment and aircraft routing problems Within a daily planning horizon while passengers' connection service levels are ensured via chance constraints. We propose a nonlinear mixed integer programming model due to the nonlinear fuel consumption and CO2 emission cost terms in the objective function, which is handled by second order conic reformulation. The key contribution of this study is to take into account the cruise time control for the first time in an integrated model of these three stages of airline operations. Changing cruise times of flights in an integrated model enables to construct a schedule to increase utilization of fuel efficient aircraft and even to decrease total number of aircraft needed while satisfying the same service level and maintenance requirements for aircraft fleeting and routing. There is a critical tradeoff between the number of aircraft needed to fulfill the required flights and overall operational expenses. We also propose two heuristic methods to solve larger size problems. Finally, computational results using real data obtained from a major U.S. carrier are presented to demonstrate potential profitability in applying the proposed solution methods. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Airline scheduling Aircraft fleeting and routing Cruise time controllability second order cone programming

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Continuous multifacility ordered median location problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2016年第1期250卷 56-64页

作者： Blanco, Victor Puerto, Justo Ben-Ali, Safae El-Haj Univ Granada Dept Quantitat Methods Econ & Business Granada 18011 Spain Univ Seville Dept Estadist & Invest Operat E-41012 Seville Spain USMBA Univ ENSA Fes Dept Genie Elect & Informat Fes Morocco

In this paper we propose a general methodology for solving abroad class of continuous, multifacility location problems, in any dimension and with l(tau)-norms proposing two different methodologies: (1) by a new second order cone mixed integer programming formulation and (2) by formulating a sequence of semidefinite programs that converges to the solution of the problem;each of these relaxed problems solvable with SDP solvers in polynomial time. (C) 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.

关键词： Continuous multifacility location ordered median problems Semidefinite programming second order cone programming

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Local linear smoothing for sparse high dimensional varying coefficient models

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ELECTRONIC JOURNAL OF STATISTICS 2016年第1期10卷 855-894页

作者： Lee, Eun Ryung Mammen, Enno Sungkyunkwan Univ Dept Stat Seoul 32419 South Korea Heidelberg Univ Inst Appl Math D-69120 Heidelberg Germany Natl Res Univ Higher Sch Econ Moscow 103012 Russia

Varying coefficient models are useful generalizations of parametric linear models. They allow for parameters that depend on a covariate or that develop in time. They have a wide range of applications in time series analysis and regression. In time series analysis they have turned out to be a powerful approach to infer on behavioral and structural changes over time. In this paper, we are concerned with high dimensional varying coefficient models including the time varying coefficient model. Most studies in high dimensional nonparametric models treat penalization of series estimators. On the other side, kernel smoothing is a well established, well understood and successful approach in nonparametric estimation, in particular in the time varying coefficient model. But not much has been done for kernel smoothing in high-dimensional models. In this paper we will close this gap and we develop a penalized kernel smoothing approach for sparse high-dimensional models. The proposed estimators make use of a novel penalization scheme working with kernel smoothing. We establish a general and systematic theoretical analysis in high dimensions. This complements recent alternative approaches that are based on basis approximations and that allow more direct arguments to carry over insights from high-dimensional linear models. Furthermore, we develop theory not only for regression with independent observations but also for local stationary time series in high-dimensional sparse varying coefficient models. The development of theory for local stationary processes in a high-dimensional setting creates technical challenges. We also address issues of numerical implementation and of data adaptive selection of tuning parameters for penalization. The finite sample performance of the proposed methods is studied by simulations and it is illustrated by an empirical analysis of NASDAQ composite index data.

关键词： Sparse estimation local stationary time series high-dimensional data local stationarity time varying coefficient models kernel method local linear method penalized methods BIC oracle in-equality oracle property partially linear varying coefficient model semi-parametric model consistent structural identification second order cone programming

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Sensitivity Analysis in Stochastic second order cone programming for Mobile Ad Hoc Networks

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Procedia - Social and Behavioral Sciences 2010年第6期2卷 7704-7705页

作者： Francesca Maggioni Stein W. Wallace Marida Bertocchi Elisabetta Allevi Departement of .Mathematics Statistics Computer Science and Applications University of. Bergamo Via dei Caniana n. 2 24127 Bergamo Ialy Department of Management Science Lancaster University Management School Lancaster LA1 4YX United Kingdom Department of Quantitative Methods. University of Brescia. Contrada S. Chiara 50 25122 Brescia Italy

In this paper sensitivity analysis is adopted in order to understand the randomness of a stochastic second order cone program for mobile ad hoc networks [3]. The algorithm looks for a destination node and sets up a route by means of the expected zone, the region where the sender node expects to find the destination node and the requested zone defined by the sender node for spreading the route request to the destination node. Sensitivity analysis is performed by considering different costs of flooding and latency penalty. Evaluation of EVPI and VSS [2]-[4] allows us to find the range of values in which it is safe to save time by using a deterministic approach instead of a stochastic one.

关键词： sensitivity analysis stochastic programming mobile ad hoc network second order cone programming evaluation of deterministic solution

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Upper and lower bound limit analysis of plates using FEM and second-order cone programming

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COMPUTERS & STRUCTURES 2010年第1-2期88卷 65-73页

作者： Le, Canh V. Nguyen-Xuan, H. Nguyen-Dang, H. Univ Sheffield Dept Civil & Struct Engn Sheffield S1 3JD S Yorkshire England Univ Sci Dept Mech Fac Math & Comp Sci VNU HCM Ho Chi Minh City Vietnam Univ Liege LTAS Div Fracture Mech B-4000 Liege Belgium

This paper presents two novel numerical procedures to determine upper and lower bounds on the actual collapse load multiplier for plates in bending. The conforming Hsieh-Clough-Tocher (HCT) and enhanced Morley (EM) elements are used to discrete the problem fields. A Morley element with enhanced moment fields is used. The constant moment fields is added a quadratic mode in which the pressure is equilibrated by corner loads only, ensuring that exact equilibrium relations associated with a uniform pressure can be obtained. Once the displacement or moment fields are approximated and the bound theorems applied, limit analysis becomes a problem of optimization. In this paper, the optimization problems are formulated in the form of a standard second-order cone programming which can be solved using highly efficient interior point solvers. The procedures are tested by applying it to several benchmark plate problems and are found good agreement between the present upper and lower bound solutions and results in the literature. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Limit analysis Upper and lower bounds Displacement and equilibrium models Criterion of mean second order cone programming

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A New Minimax Probabilistic Approach and Its Application in Recognition the Purity of Hybrid Seeds

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CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES 2015年第6期104卷 493-506页

作者： Yang, Liming Gao, Yongping Sun, Qun China Agr Univ Coll Sci Beijing 100083 Peoples R China Capital Normal Univ Beijing 100048 Peoples R China China Agr Univ Coll Agr & Biotechnol Beijing 100193 Peoples R China

Minimax probability machine (MPM) has been recently proposed and shown its advantage in pattern recognition. In this paper, we present a new minimax probabilistic approach (MPA),which can provide an explicit lower bound on prediction accuracy. Applying the Chebyshev-Cantelli inequality, the MPA is posed as a second order cone program formulation and solved effectively. Following that, this method is exploited directly to recognize the purity of hybrid seeds using near-infrared spectroscopic data. Experimental results in different spectral regions show that the proposed MPA is competitive with the existing minimax probability machine and support vector machine in generalization, while requires less computational time than them. These results illustrate the feasibility and effectiveness of the proposed approach in recognition the purity of hybrid seeds.

关键词： Sample moments Minimax probability machine second order cone programming Maize seeds classification

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Compromising system and user interests in shelter location and evacuation planning

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TRANSPORTATION RESEARCH PART B-METHODOLOGICAL 2015年 72卷 146-163页

作者： Bayram, Vedat Tansel, Barbaros C. Yaman, Hande Bilkent Univ Dept Ind Engn TR-06800 Ankara Turkey

Traffic management during an evacuation and the decision of where to locate the shelters are of critical importance to the performance of an evacuation plan. From the evacuation management authority's point of view, the desirable goal is to minimize the total evacuation time by computing a system optimum (SO). However, evacuees may not be willing to take long routes enforced on them by a SO solution;but they may consent to taking routes with lengths not longer than the shortest path to the nearest shelter site by more than a tolerable factor. We develop a model that optimally locates shelters and assigns evacuees to the nearest shelter sites by assigning them to shortest paths, shortest and nearest with a given degree of tolerance, so that the total evacuation time is minimized. As the travel time on a road segment is often modeled as a nonlinear function of the flow on the segment, the resulting model is a nonlinear mixed integer programming model. We develop a solution method that can handle practical size problems using second order cone programming techniques. Using our model, we investigate the importance of the number and locations of shelter sites and the trade-off between efficiency and fairness. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Evacuation traffic management Shelter location Traffic assignment System optimal Constrained system optimal second order cone programming

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