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Derivative-free optimization: a review of algorithms and comparison of software implementations,” (2013)

by L M Rios, N V Sahinidis
Venue:Journal of Global Optimization,
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Fish swimming optimization and exploiting multi-body hydrodynamic interactions for underwater navigation

by Audrey Maertens , 2015
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Autotuning of Isotropic Hardening Constitutive Models on Real Steel Buckling Data with Finite Element Based Multistart Global Optimisation on Parallel Computers

by Anton Shterenlikht , Mohammad M Kashani , Nicholas A Alexander , Gethin Williams , Adam J Crewe
"... An automatic framework for tuning plastic constitutive models is proposed. It is based on multistart global optimisation method, where the objective function is provided by the results of multiple elastoplastic finite element analyses, executed concurrently. Wrapper scripts were developed for fully ..."
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An automatic framework for tuning plastic constitutive models is proposed. It is based on multistart global optimisation method, where the objective function is provided by the results of multiple elastoplastic finite element analyses, executed concurrently. Wrapper scripts were developed for fully automatic preprocessing, including model and mesh generation, analysis, and postprocessing. The framework is applied to an isotropic power hardening plasticity using real load/displacement data from multiple steel buckling tests. M. J. D. Powell's BOBYQA constrained optimisation package was used for local optimisation. It is shown that using the real data presents multiple problems to the optimisation process because (1) the objective function can be discontinuous, yet (2) relatively flat around multiple local minima, with (3) similar values of the objective function for different local minima. As a consequence the estimate of the global minimum is sensitive to the amount of experimental data and experimental noise. The framework includes the verification step, where the estimate of the global minimum is verified on a different geometry and loading. A tensile test was used for verification in this work. The speed of the method critically depends on the ability to effectively parallelise the finite element solver. Three levels of parallelisation were exploited in this work. The ultimate limitation was the availability of the finite element commercial solver license tokens.
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... was used in this work for local optimisation. BOBYQA stands for bound optimisation by quadratic approximation. It does not require derivatives of ...

Copyright c○2011 by C. T. Kelley2 Implicit Filtering: Users ’ GuideContents

by C. T. Kelley , 2011
"... R ..."
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1Rotation Optimization on the Unit Quaternion Manifold and its Application for Robotic Grasping

by Hanchen Xiong, Justus Piater
"... In this paper we consider black-box optimization of objects ’ grasp density functions relative to a gripper’s orientation. For this, we introduce Monte-Carlo Tree Search on the unit quaternion manifold. Our experimental evaluation shows that our method is feasible and allows finding grasps of arbitr ..."
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In this paper we consider black-box optimization of objects ’ grasp density functions relative to a gripper’s orientation. For this, we introduce Monte-Carlo Tree Search on the unit quaternion manifold. Our experimental evaluation shows that our method is feasible and allows finding grasps of arbitrary quality with regard to a fixed budget of objective function evaluations. 1.

Task-Relevant Roadmaps: A Framework for Humanoid Motion Planning

by unknown authors
"... Abstract—To plan complex motions of robots with many degrees of freedom, our novel, very flexible framework builds task-relevant roadmaps (TRMs), using a new sampling-based optimizer called Natural Gradient Inverse Kinematics (NGIK) based on natural evolution strategies (NES). To build TRMs, NGIK it ..."
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Abstract—To plan complex motions of robots with many degrees of freedom, our novel, very flexible framework builds task-relevant roadmaps (TRMs), using a new sampling-based optimizer called Natural Gradient Inverse Kinematics (NGIK) based on natural evolution strategies (NES). To build TRMs, NGIK iteratively optimizes postures covering task-spaces expressed by arbitrary task-functions, subject to constraints expressed by arbitrary cost-functions, transparently dealing with both hard and soft constraints. TRMs are grown to maximally cover the task-space while minimizing costs. Unlike Jacobian methods, our algorithm does not rely on calculation of gradients, making application of the algorithm much simpler. We show how NGIK outperforms recent related sampling algo-rithms. A video demo
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...ral constraints often involves a non-convex and non-smooth search space, which makes it particularly relevant to use the right search algorithm. Comparing a range of optimization methods, Rios et. al =-=[21]-=- found that evolutionary strategies perform exceptionally well in non-convex non-smooth optimization problems. We use the NES, a principled method for real-valued evolutionary optimization [7], to min...

1On Computing Optimal Thresholds in Decentralized Sequential Hypothesis Testing

by Can Cui, Aditya Mahajan
"... Abstract—Decentralized sequential hypothesis testing refers to a generalization of Wald’s sequential hypothesis testing setup in which multiple decision makers make separate stopping decisions that are coupled through a common loss function. In the simplest such generalization, the stopping decision ..."
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Abstract—Decentralized sequential hypothesis testing refers to a generalization of Wald’s sequential hypothesis testing setup in which multiple decision makers make separate stopping decisions that are coupled through a common loss function. In the simplest such generalization, the stopping decisions are not seen by other decision makers. For this model, it is known that threshold-based stopping strategies are optimal. Two methods are presented for approximately computing the optimal thresholds. The first method, which is called orthogonal search, is an iterative method that approximately solves the coupled dynamic programs pro-posed in Teneketzis and Ho, Information and Computation, 1987. The second method, which is called direct search, approximates the performance of a threshold-based strategy and then searches over the thresholds using a derivative-free non-convex optimiza-tion algorithm. The approximations for both methods are based on discretizing the continuous-state information state process to a finite-state Markov chain and calculating the absorption probabilities and absorption stopping times for appropriately defined absorption sets. The performance of both the methods is compared numerically. Index Terms—Hypothesis testing, sequential analysis, decen-tralized systems, dynamic programming, derivative-free opti-mization. I.
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...parameters (↵1,1,↵2,2). For an example, see [15]. In principle, such non-convex optimization problems can be solved using derivative-free methods that do no use numerical or analytic gradients (see =-=[23]-=-). In the numerical results we use one of the simplest derivative-free algorithms—NelderMead simplex algorithm (see [24]). This step can be replaced by more sophisticated algorithms to obtain better r...

On

by unknown authors
"... computing optimal thresholds in decentralized sequential hypothesis testing ..."
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computing optimal thresholds in decentralized sequential hypothesis testing
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...rameters .˛1; ˇ1; ˛2; ˇ2/. For an example, see [7]. In principle, such non-convex optimization problems can be solved using derivative-free methods that do no use numerical or analytic gradients (see =-=[15]-=-). In the numerical results we use one of the simplest derivative-free algorithms— Nelder-Mead simplex algorithm (see [16]). This step can be replaced by more sophisticated algorithms to obtain better...

Moving Frames for Heart Fiber Reconstruction

by Emmanuel Piuzea, Jon Sporringb, Kaleem Siddiqia
"... Abstract. The method of moving frames provides powerful geometrical tools for the analysis of smoothly varying frame fields. However, in the face of missing measurements, a reconstruction problem arises, one that is largely unexplored for 3D frame fields. Here we consider the particular example of r ..."
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Abstract. The method of moving frames provides powerful geometrical tools for the analysis of smoothly varying frame fields. However, in the face of missing measurements, a reconstruction problem arises, one that is largely unexplored for 3D frame fields. Here we consider the particular example of reconstructing impaired cardiac diffusion magnetic resonance imaging (dMRI) data. We combine moving frame analysis with a diffu-sion inpainting scheme that incorporates rule-based priors. In contrast to previous reconstruction methods, this new approach uses comprehensive differential descriptors for cardiac fibers, and is able to fully recover their orientation. We demonstrate the superior performance of this approach in terms of error of fit when compared to alternate methods. We antic-ipate that these tools could find application in clinical settings, where damaged heart tissue needs to be replaced or repaired, and for generating dense fiber volumes in electromechanical modelling of the heart. 1
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...ken from [12], where f1 is the fiber direction, f3 is approximately normal to the heart wall, and f2 = f3 × f1. For the energy-minimizing approach we experimented with NelderMead (NM) and BOBYQA (BQ) =-=[10]-=- optimizers1 to solve the energy term in (7). Here, all connection forms are estimated in an isotropic neighborhood of size 33, seeds are obtained using (6), and λ = 0.0001. On an SSD quad-core 2.5GHz...

Construct Data Integrity Attacks Against Real-Time Electrical Market in Smart Grid

by unknown authors
"... Abstract—The normal operation of real-time electrical market requires accurate state estimation in Smart Grid. However, recent research shows that strategically designed data integrity attacks can easily introduce errors into state estimation without being detected. From the perspective of attackers ..."
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Abstract—The normal operation of real-time electrical market requires accurate state estimation in Smart Grid. However, recent research shows that strategically designed data integrity attacks can easily introduce errors into state estimation without being detected. From the perspective of attackers, this increases the chances of controlling real-time electrical market operations through manipulations of meter measurements. In this paper, we first reveal the intrinsic relations between data integrity attacks and real-time electrical market, and explicitly characterize their complex interactions as a process simulator. Then a simulation-based global optimization problem is formulated, from which an attacker could maximize financial incentives through constructed data integrity attacks. More importantly, we further consider the construction of data integrity attacks when power network topologies and parameters are unknown. A systematic construc-tion strategy is proposed based on recursive least square subspace estimation. As far as we know, our paper is the first attempt to attack real-time electrical market without network information. Finally, we evaluate the performance of the proposed attacking strategies through numerical simulations in IEEE test systems. I.
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... Figure 1. Only function values are available and there is no algebraic model to analyze differentiability and Lipschitz condition. Therefore, derivative-free optimization methods have to be employed =-=[12]-=-. The selection of optimization solvers is out of the scope of this paper. Second, as in (3) (4) (6) (11) (13), the attacker will need the following knowledge to solve P1 accurately: • 1) The meter me...

unknown title

by F. Rinaldi , 2013
"... A class of derivative-free nonmonotone optimization algorithms employing coordinate rotations and gradient approximations ..."
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A class of derivative-free nonmonotone optimization algorithms employing coordinate rotations and gradient approximations
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...on problems with n ∈ {10, 20}) from the CUTEr collection [13] gathered from papers on derivativefree optimization (see, e.g. [1,5]), and 49 nonsmooth problems from the collection of Lukšan and Vlček =-=[27,32]-=-. Since the problems in P have at most 50 variables, in our numerical experience we set the maximum computational budget to be 5000 and we investigate the behavior of the solvers within this computati...

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