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3rd Symposium on Piezoelectricity, Acoustic Waves and Device Applications

作者： Zhu, Hua Zhang, Jian-tao Zhao, Chun-sheng Nanjing Univ Aeronaut & Astronaut Precis Driving Lab Nanjing 210016 Jiangsu Peoples R China

ISBN: (纸本)9781424428915

The electromechanical coupled dynamic model of the stator of the bar-type ultrasonic motor is derived based on the finite element method. The dynamical behavior of the stator is analyzed via this model and the theoretical result agrees with the experimental result-of the stator of the prototype motor very well. Both the structural design principles and the approaches to meet the requirements for the mode of the stator are discussed. Based on the pattern search algorithm, an optimal model to meet the design requirements is established. The numerical simulation results show that this optimal model is effective for the structural design of the stator.

关键词： Ultrasonic motor optimal design pattern search algorithm electromechanical coupled dynamic model

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Solving economic machining models using quantum-pattern search-particle swarm hybrid optimization algorithm

Solving economic machining models using quantum-pattern sear...

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11th IASTED International Conference on Artificial Intelligence and Soft Computing

作者： Alfares, Fawzan S. Alenezi, Hussein Alajmi, Mahdi S. Department of Manufacturing Engineering PAAET Kaifan P.O. Box: 68425 Kuwait School of Engineering and Design Brunel University Uxbridge Middlesex UB8 3PH United Kingdom

ISBN: (纸本)9780889866935

This paper introduce novel hybrid optimization algorithm consists from elements of three optimization algorithms. The first algorithm is the particle swarm optimization, in which the element "velocity" is used. This element provides the distance to jump from the current position to the new position. The second element acquired from the pattern search algorithm in which the movement of the solution candidate in the neighborhood performed. This movement called compass movement where the direction of movement is to the up, down, right, or left. The last element obtained from the quantum-inspired algorithm. This element says that if no best solution found after perforining the compass movement then the solution candidate will move to one of these positions that have the highest probability. The formula of the probabilities based on quantum computing theory. To investigate the performance of the proposed algorithm, machining economic models are used. The results have showed promising application of this hybrid algorithm to the field of mechanical engineering.

关键词： optimization evolution algorithms quantum theory pattern search algorithm and particle swarm optimization

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Mixed variable optimization of a load-bearing thermal insulation system using a filter pattern search algorithm

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OPTIMIZATION AND ENGINEERING 2004年第2期5卷 157-177页

作者： Abramson, MA USAF Inst Technol Dept Math & Stat Wright Patterson AFB OH 45433 USA

This paper describes the optimization of a load-bearing thermal insulation system characterized by hot and cold surfaces with a series of heat intercepts and insulators between them. The optimization problem is represented as a mixed variable programming (MVP) problem with nonlinear constraints, in which the objective is to minimize the power required to maintain the heat intercepts at fixed temperatures so that one surface is kept sufficiently cold. MVP problems are more general than mixed integer nonlinear programming (MINLP) problems in that the discrete variables are categorical;i.e., they must always take on values from a predefined enumerable set or list. Thus, traditional approaches that use branch and bound techniques cannot be applied. In a previous paper, a linearly constrained version of this problem was solved numerically using the Audet-Dennis generalized pattern search (GPS) method for MVP problems. However, this algorithm may not work for problems with general nonlinear constraints. A new algorithm that extends that of Audet and Dennis by incorporating a filter to handle nonlinear constraints makes it possible to solve the more general problem. Additional nonlinear constraints on stress, mass, and thermal contraction are added to that of the previous work in an effort to find a more realistic feasible design. Several computational experiments show a substantial improvement in power required to maintain the system, as compared to the previous literature. The addition of the new constraints leads to a very different design without significantly changing the power required. The results demonstrate that the new algorithm can be applied to a very broad class of optimization problems, for which no previous algorithm with provable convergence results could be applied.

关键词： mixed variable programming categorical variables filter algorithm pattern search algorithm thermal insulation heat intercepts nonlinear constraints

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AN EFFICIENT APPROACH TO OPTIMIZE THE VIBRATION MODE OF ULTRASONIC MOTORS

AN EFFICIENT APPROACH TO OPTIMIZE THE VIBRATION MODE OF ULTR...

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第三届全国压电和声波理论及器件技术研讨会

作者： Hua ZHU,Jian-tao ZHANG,Chun-sheng ZHAO Precision Driving Laboratory,Nanjing University of Aeronautics and Astronautics, 29 Yudao Street,Nanjing,Jiangsu 210016,China

The electromechanical coupled dynamic model of the stator of the bar-type ultrasonic motor is derived based on the finite element *** dynamical behavior of the stator is analyzed via this model and the theoretical result agrees with the experimental result of the stator of the prototype motor very *** the structural design principles and the approaches to meet the requirements for the mode of the stator are *** on the pattern search algorithm,an optimal model to meet the design requirements is *** numerical simulation results show that this optimal model is effective for the structural design of the stator.

关键词： Ultrasonic motor optimal design pattern search algorithm electromechanical coupled dynamic model

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Controller design via nonsmooth multidirectional search

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 2006年第6期44卷 1923-1949页

作者： Apkarian, P Noll, D CERT ONERA Control Syst Dept F-31055 Toulouse France Univ Toulouse 3 CNRS UMR 5640 Toulouse France

We propose an algorithm which combines multidirectional search (MDS) with nonsmooth optimization techniques to solve difficult problems in automatic control. Applications include static and fixed-order output feedback controller design, simultaneous stabilization, H-2/H-infinity-synthesis, and much else. We show how to combine direct search techniques with nonsmooth descent steps in order to obtain convergence certificates in the presence of nonsmoothness. Our technique is efficient when small and medium size controllers for plants with large state dimension are sought. Our numerical testing includes several benchmark examples. For instance, our algorithm needs 0.41 s to compute a static output feedback stabilizing controller for the Boeing 767. utter benchmark problem [ E. E. J. Davison, IFAC Technical Committee Reports, Pergamon Press, Oxford, 1990], a system with 55 states. The first static controller without performance specifications for this system was obtained in [ J. Burke, A. Lewis, and M. Overton, SIAM J. Optim., 15 ( 2003), pp. 751 - 779].

关键词： NP-hard design problems static output feedback fixed-order synthesis simultaneous stabilization mixed H2/ H-infinity-synthesis pattern search algorithm moving polytope nonsmooth analysis spectral bundle method epsilon-subgradients bilinear matrix inequality (BMI)

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Second-order behavior of pattern search

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SIAM JOURNAL ON OPTIMIZATION 2005年第2期16卷 515-530页

作者： Abramson, MA USAF Inst Technol Dept Math & Stat AFIT ENC Wright Patterson AFB OH 45433 USA

Previous analyses of pattern search algorithms for unconstrained and linearly constrained minimization have focused on proving convergence of a subsequence of iterates to a limit point satisfying either directional or first-order necessary conditions for optimality, depending on the smoothness of the objective function in a neighborhood of the limit point. Even though pattern search methods require no derivative information, we are able to prove some limited directional second-order results. Although not as strong as classical second-order necessary conditions, these results are stronger than the first-order conditions that many gradient-based methods satisfy. Under fairly mild conditions, we can eliminate from consideration all strict local maximizers and an entire class of saddle points.

关键词： nonlinear programming pattern search algorithm derivative-free optimization convergence analysis second-order optimality conditions

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A pattern search filter method for nonlinear programming without derivatives

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SIAM JOURNAL ON OPTIMIZATION 2004年第4期14卷 980-1010页

作者： Audet, C Dennis, JE Ecole Polytech GERAD Montreal PQ H3C 3A7 Canada Ecole Polytech Dept Math & Genie Ind Montreal PQ H3C 3A7 Canada Rice Univ Dept Appl & Computat Math Houston TX 77005 USA

This paper formulates and analyzes a pattern search method for general constrained optimization based on filter methods for step acceptance. Roughly, a filter method accepts a step that improves either the objective function value or the value of some function that measures the constraint violation. The new algorithm does not compute or approximate any derivatives, penalty constants, or Lagrange multipliers. A key feature of the new algorithm is that it preserves the division into search and local poll steps, which allows the explicit use of inexpensive surrogates or random search heuristics in the search step. It is shown here that the algorithm identifies limit points at which optimality conditions depend on local smoothness of the functions and, to a greater extent, on the choice of a certain set of directions. Stronger optimality conditions are guaranteed for smoother functions and, in the constrained case, for a fortunate choice of the directions on which the algorithm depends. These directional conditions generalize those given previously for linear constraints, but they do not require a feasible starting point. In the absence of general constraints, the proposed algorithm and its convergence analysis generalize previous work on unconstrained, bound constrained, and linearly constrained generalized pattern search. The algorithm is illustrated on some test examples and on an industrial wing planform engineering design application.

关键词： pattern search algorithm filter algorithm surrogate-based optimization derivative-free convergence analysis constrained optimization nonlinear programming

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Generalized pattern searches with derivative information

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MATHEMATICAL PROGRAMMING 2004年第1期100卷 3-25页

作者： Abramson, MA Audet, C Dennis, JE Air Force Inst Technol Wright Patterson AFB OH 45433 USA Ecole Polytech Dept Math & Genie Ind Montreal PQ H3C 3A7 Canada GERAD Dept Math & Genie Ind Montreal PQ H3C 3A7 Canada Rice Univ Dept Comp & Applied Math Seattle WA 98136 USA

A common question asked by users of direct search algorithms is how to use derivative information at iterates where it is available. This paper addresses that question with respect to Generalized pattern search (GPS) methods for unconstrained and linearly constrained optimization. Specifically, this paper concentrates on the GPS POLLstep. Polling is done to certify the need to refine the current mesh, and it requires O(n) function evaluations in the worst case. We show that the use of derivative information significantly reduces the maximum number of function evaluations necessary for POLLsteps, even to a worst case of a single function evaluation with certain algorithmic choices given here. Furthermore, we show that rather rough approximations to the gradient are sufficient to reduce the POLLstep to a single function evaluation. We prove that using these less expensive POLLsteps does not weaken the known convergence properties of the method, all of which depend only on the POLLstep.

关键词： pattern search algorithm linearly constrained optimization surrogate-based optimization nonsmooth optimization gradient-based optimization

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Controller Design via Nonsmooth Multi-Directional search

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IFAC Proceedings Volumes 2004年第21期37卷 351-356页

作者： Pierre Apkarian Dominikus Noll Daniel Alazard ONERA-CERT Centre d'études et de recherche de Toulouse Control System Department 2 av. Edouard Belin 31055 Toulouse France Mathématiques pour l'Industrie et la Physique Université Paul Sabatier Toulouse France Université Paul Sabatier Supaero

We propose an algorithm which combines multi-directional search (MDS) with nonsmooth techniques such as bundling to solve several difficult synthesis problems in automatic control. Applications include static and fixed-order output feedback controller design, simultaneous stabilization, H2/H ∞ synthesis to cite just a few. We show in which way direct search techniques may be safeguarded by nonsmooth oracles in order to maintain convergence certificates in the presence of nonsmoothness. Our numerical testing includes numerous benchmark examples. For instance, our algorithm needs 0.41 seconds to compute a static output feedback stabilizing controller for the Boeing 767 flutter benchmark problem (E.J. Davison, 1990), a system with 55 states.

关键词： pattern search algorithm nonsmooth analysis bundle method BMI

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Analysis of generalized pattern searches

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SIAM JOURNAL ON OPTIMIZATION 2003年第3期13卷 889-903页

作者： Audet, C Dennis, JE Ecole Polytech Dept Math & Genie Ind Montreal PQ H3C 3A7 Canada Rice Univ Dept Computat & Appl Math Houston TX 77005 USA

This paper contains a new convergence analysis for the Lewis and Torczon generalized pattern search (GPS) class of methods for unconstrained and linearly constrained optimization. This analysis is motivated by a desire to understand the successful behavior of the algorithm under hypotheses that are satisfied by many practical problems. Specifically, even if the objective function is discontinuous or extended-valued, the methods find a limit point with some minimizing properties. Simple examples show that the strength of the optimality conditions at a limit point depends not only on the algorithm, but also on the directions it uses and on the smoothness of the objective at the limit point in question. The contribution of this paper is to provide a simple convergence analysis that supplies detail about the relation of optimality conditions to objective smoothness properties and to the de ning directions for the algorithm, and it gives previous results as corollaries.

关键词： pattern search algorithm linearly constrained optimization surrogate-based optimization nonsmooth optimization derivative-free convergence analysis

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