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An SLP algorithm and its application to topology optimization

COMPUTATIONAL & APPLIED MATHEMATICS 2011年第1期30卷 53-89页

作者： Gomes, Francisco A. M. Senne, Thadeu A. Univ Estadual Campinas Dept Matemat Aplicada IMECC BR-13083859 Campinas SP Brazil

We introduce a globally convergent sequential linear programming method for nonlinear programming. The algorithm is applied to the solution of classic topology optimization problems, as well as to the design of compliant mechanisms. The numerical results suggest that the new algorithm is faster than the globally convergent version of the method of moving asymptotes, a popular method for mechanical engineering applications proposed by Svanberg.

关键词： topology optimization compliant mechanisms sequential linear programming global convergence theory

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A trust region interior point algorithm for truss structural optimization problems

A trust region interior point algorithm for truss structural...

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The Fourth International Joint Conference on Computational Science and Optimization(第四届计算科学与优化国际大会 CSO 2011)

作者： TaoXu Zhenglei Yu Wenjie Zuo Heng Li State Key Laboratory of Automotive Dynamic Simulation College of Mechanical Science and Engineering College of Mechanical Science and Engineering Jilin University Changchun 130025 China

The use of optimization in a simulation-based design of automotive, aerospace and consumer products has become a common trend today. Designers are faced with the continuous challenge of reducing manufacturing costs and design cycle times while improving the systems performance and reliability. In practical design, sequential linear programming (SLP) is very popular because of its inherent simplicity and easy availability. However, the inherent conceptual simplicity makes the SLP techniques not globally convergent. This research presents a new algorithm that uses a linearization error and an interior point trust-region method in SLP to truss structures that is both considered sizing and configuration problems. The algorithm may be suitable for large optimization problems where time is a constraint and the optimization may be stopped before convergence is achieved. Results of application studies are presented, illustrating the applicability of the proposed algorithm.

关键词： interior point methods structural optimization sequential linear programming linearization error trust region methods

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An SLP filter algorithm for probabilistic analytical target cascading

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STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2010年第6期41卷 935-945页

作者： Han, Jeongwoo Papalambros, Panos Y. Argonne Natl Lab Argonne IL 60439 USA Univ Michigan Dept Mech Engn Ann Arbor MI 48104 USA

Decision-making under uncertainty is particularly challenging in the case of multidisciplinary, multilevel system optimization problems. Subsystem interactions cause strong couplings, which may be amplified by uncertainty. Thus, effective coordination strategies can be particularly beneficial. Analytical target cascading (ATC) is a deterministic optimization method for multilevel hierarchical system design that has been extended to probabilistic formulations. Solving the probabilistic optimization problem requires propagation of uncertainty, namely, evaluating or estimating the output distributions, a task that is computationally expensive for highly nonlinear functions. This article presents the use of sequential linear programming (SLP) for probabilistic ATC. By linearizing and solving a problem successively, the strategy takes advantage of the simplicity and ease of uncertainty propagation for a linear system under the assumption that inputs are normally distributed or can be transformed into equivalent normal distributions. A suspension strategy, developed for a deterministic SLP coordination strategy for ATC, is applied to reduce computational cost by suspending the analyses of subsystems that do not need considerable redesign. The accuracy and effectiveness of the proposed coordination strategy is demonstrated with several numerical examples.

关键词： Probabilistic analytical target cascading sequential linear programming Complex system design under uncertainty Suspension strategy

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A linear programming-based optimization algorithm for solving nonlinear programming problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2010年第3期200卷 658-670页

作者： Still, Claus Westerlund, Tapio Abo Akad Univ Proc Design & Syst Engn Lab FIN-20500 Turku Finland

In this paper a linear programming-based optimization algorithm called the sequential Cutting Plane algorithm is presented. The main features of the algorithm are described, convergence to a Karush-Kuhn-Tucker stationary point is proved and numerical experience on some well-known test sets is showed. The algorithm is based on an earlier version for convex inequality constrained problems, but here the algorithm is extended to general continuously differentiable nonlinear programming problems containing both nonlinear inequality and equality constraints. A comparison with some existing solvers shows that the algorithm is competitive with these solvers. Thus, this new method based on solving linear programming subproblems is a good alternative method for solving nonlinear programming problems efficiently. The algorithm has been used as a subsolver in a mixed integer nonlinear programming algorithm where the linear problems provide lower bounds on the optimal solutions of the nonlinear programming subproblems in the branch and bound tree for convex, inequality constrained problems. (C) 2009 Elsevier B.V. All rights reserved.

关键词： Nonlinear programming Cutting plane algorithms sequential linear programming

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Recycling Krylov subspaces for efficient large-scale electrical impedance tomography

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2010年第49-52期199卷 3101-3110页

作者： Motta Mello, Luis Augusto de Sturler, Eric Paulino, Glaucio H. Nelli Silva, Emilio Carlos Univ Sao Paulo Dept Mechatron & Mech Syst Engn Sch Engn BR-05508 Sao Paulo Brazil Virginia Tech Dept Math Blacksburg VA 24061 USA Univ Illinois Dept Civil & Environm Engn Newmark Lab Urbana IL 61801 USA

Electrical impedance tomography (EIT) captures images of internal features of a body. Electrodes are attached to the boundary of the body, low intensity alternating currents are applied, and the resulting electric potentials are measured. Then, based on the measurements, an estimation algorithm obtains the three-dimensional internal admittivity distribution that corresponds to the image. One of the main goals of medical EIT is to achieve high resolution and an accurate result at low computational cost. However, when the finite element method (FEM) is employed and the corresponding mesh is refined to increase resolution and accuracy, the computational cost increases substantially, especially in the estimation of absolute admittivity distributions. Therefore, we consider in this work a fast iterative solver for the forward problem, which was previously reported in the context of structural optimization. We propose several improvements to this solver to increase its performance in the EIT context. The solver is based on the recycling of approximate invariant subspaces, and it is applied to reduce the EIT computation time for a constant and high resolution finite element mesh. In addition, we consider a powerful preconditioner and provide a detailed pseudocode for the improved iterative solver. The numerical results show the effectiveness of our approach: the proposed algorithm is faster than the preconditioned conjugate gradient (CG) algorithm. The results also show that even on a standard PC without parallelization, a high mesh resolution (more than 150,000 degrees of freedom) can be used for image estimation at a relatively low computational cost. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Iterative methods Preconditioning Krylov subspace recycling Three-dimensional electrical impedance tomography sequential linear programming

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Using a Filter-Based sequential Quadratic programming Algorithm in a Parallel Environment

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JOURNAL OF AEROSPACE COMPUTING INFORMATION AND COMMUNICATION 2009年第12期6卷 635-648页

作者： Venter, Gerhard Vanderplaats, Garret N. Univ Stellenbosch Dept Mech & Mech Engn ZA-7602 Stellenbosch South Africa Vanderplaats Res & Dev Inc Monterey CA 93940 USA

A parallel, filter-based, sequential quadratic programming algorithm is implemented and tested for typical general-purpose engineering applications. Constrained engineering test problems, including a finite element simulation, with up to 512 design variables are considered. The accuracy and serial performance of the filter-based algorithm are compared against that of a standard sequential quadratic programming algorithm. The parallel performance of the algorithm is evaluated, using up to 52 cores on a Linux Cluster. The results indicate that the filter-based algorithm competes favorably with a standard sequential quadratic programming algorithm in a serial environment. However, the filter-based algorithm exhibits much better parallel efficiency due to the lack of a one-dimensional search.

关键词： sequential Quadratic programming Parallel Computing Finite Element Analysis sequential linear programming High Performance Computing Particle Swarm Optimization Nonlinear programming Numerical Simulation Parallel Algorithm Young's Modulus

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General skew constrained clock network sizing based on sequential linear programming

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IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS 2005年第5期24卷 773-782页

作者： Wang, K Ran, YJ Jiang, HL Marek-Sadowska, M Univ Calif Santa Barbara Dept Elect & Comp Engn Santa Barbara CA 93106 USA

In this paper, we investigate the problem of clock network sizing subject to general skew constraints. A novel approach based on sequential linear programming is presented. The original nonlinear programming problem is transformed into a sequence of linear programs by taking the first-order Taylor's expansion of clock path delay with respect to buffer and/or wire widths. For each linear program, the sensitivities of clock path delay, with respect to buffer and/or wire widths, are efficiently updated by applying time-domain analysis to the clock network in a divide-and-conquer fashion. Our technique can take into account power supply and process variations. We demonstrate experimentally that the proposed technique is not only capable of optimizing effectively the skew and area of clock network, but also of providing more accurate delay and skew results compared to the traditional approaches.

关键词： clock slew power supply noise sequential linear programming

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Enhanced multiobjective particle swarm optimization in combination with adaptive weighted gradient-based searching

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ENGINEERING OPTIMIZATION 2008年第9期40卷 789-804页

作者： Izui, Kazuhiro Nishiwaki, Shinji Yoshimura, Masataka Nakamura, Masahiko Renaud, John E. Kyoto Univ Dept Aeronaut & Astronaut Kyoto Japan Univ Notre Dame Aerosp & Mech Engn Notre Dame IN 46556 USA

This article proposes a new multiobjective optimization method for structural problems based on multiobjective particle swarm optimization (MOPSO). A gradient-based optimization method is combined with MOPSO to alleviate constraint-handling difficulties. In this method, a group of particles is divided into two groups - a dominated solution group and a non-dominated solution group. The gradient-based method, utilizing a weighting coefficient method, is applied to the latter to conduct local searching that yields superior non-dominated solutions. In order to enhance the efficiency of exploration in a multiple objective function space, the weighting coefficients are adaptively assigned considering the distribution of non-dominated solutions. A linear optimization problem is solved to determine the optimal weighting coefficients for each non-dominated solution at each iteration. Finally, numerical and structural optimization problems are solved by the proposed method to verify the optimization efficiency.

关键词： structural optimization particle swarm optimization multiobjective optimization hybrid technique sequential linear programming adaptive weighting coefficient

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Design optimization of a controllable camber rotor airfoil

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AIAA JOURNAL 2008年第1期46卷 142-153页

作者： Gandhi, Farhan Frecker, Mary Nissly, Andrew Penn State Univ Dept Aerosp Engn University Pk PA 16802 USA Penn State Univ Dept Mech & Nucl Engn University Pk PA 16802 USA

A conformable airfoil is proposed as an alternative to trailing-edge flaps used for active helicopter vibration reduction through high-frequency changes in camber. The design consists of several compliant mechanisms of predetermined topology that are placed serially within the airfoil along the chord, aft of the leading-edge spar. A shape optimization approach is used to design the compliant mechanisms, in which the objective is to maximize trailing-edge deflection while minimizing airfoil deflections due to aerodynamic loads. Solutions were obtained using a sequential linear programming method coupled with a finite element analysis. An optimized shape is predicted to achieve a trailing-edge deflection of +/- 6.0 mm or a +/- 4.6-deg equivalent flap deflection angle using the tip deflection objective. Results indicate that the deflection is dependent on the amount of passive material allowed and the objective function used. The aerodynamic loads are found to cause only small deformations in comparison with those caused by the actuation. Prototype fabrication and bench-top tests demonstrated that rotor airfoil camber is controllable using the proposed concept.

关键词： Airfoil Profiles Airfoil Geometry Aerodynamic Properties Lift to Drag Ratio Finite Element Analysis Trailing Edge Flap Shape Optimization sequential linear programming Helicopter Vibration Reduction Aspect Ratio

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Active/reactive bid based dispatch models to be used in electricity markets

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ELECTRIC POWER SYSTEMS RESEARCH 2008年第1期78卷 106-121页

作者： Gomes, M. H. R. Saraiva, J. T. [a]Departamento de Engenharia Electrotécnica Escola Superior de Tecnologia de Tomar Quinta do Contador Estrada da Serra 2300 Tomar Portugal [b]INESC Porto and Departamento de Engenharia Electrotécnica e Computadores Faculdade de Engenharia da Universidade do Porto Campus da FEUP Rua Dr. Roberto Frias 4200 - 465 Porto Portugal

This paper describes two new active/reactive dispatch models to be used by System Operators in order to assign reactive power and to validate the economic schedules prepared by Market Operators together with the injections related with Bilateral Contracts. When talking about electricity markets one usually refers to active power markets paying less attention to ancillary services, namely to reactive power/voltage control. This usually leads to a chronological sequence of activities that may lead to inefficiencies because active and reactive powers are coupled given the capability diagram of synchronous generators, the ac power flow equations and the branch thermal limits. In this paper, we propose new models to remarry active and reactive allocation procedures based on a market approach as a way to ensure operation transparency. The resulting optimization problems are solved by a sequential linear programming, SLP, approach that allows one to compute active and reactive nodal marginal prices at its final iteration. The paper includes a case study based on the IEEE 24 Bus Test System to illustrate the application of the developed models and demonstrate their interest in the scope of restructured power systems.

关键词： Integrated active/reactive dispatch Electricity markets System Operator Active/reactive nodal marginal prices sequential linear programming

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