APPSPACK 4.0 : asynchronous parallel pattern search for derivative-free optimization.

Gray, Genetha Anne.; Kolda, Tamara G.

doi:10.2172/974891

Cited by 57 publications

(64 citation statements)

References 17 publications

(18 reference statements)

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“…We compared the results obtained for SID-PSM using MFN models against three solvers: NEWUOA [13], a trust-region code based on interpolation by MFN models; NMSMAX [3] an implementation of the Nelder-Mead simplex method; and APPSPACK [8], an implementation of an asynchronous generating set search method mainly derived for parallel computing, but considered here in the serial mode and with a random ordering of directions.…”

Section: Numerical Experiments and Conclusionmentioning

confidence: 99%

Incorporating minimum Frobenius norm models in direct search

Custódio¹,

2009

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The goal of this paper is to show that the use of minimum Frobenius norm quadratic models can improve the performance of direct-search methods. The approach taken here is to maintain the structure of directional direct-search methods, organized around a search and a poll step, and to use the set of previously evaluated points generated during a direct-search run to build the models. The minimization of the models within a trust region provides an enhanced search step. Our numerical results show that such a procedure can lead to a signicant improvement of direct search for smooth, piecewise smooth, and stochastic and nonstochastic noisy problems.

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Section: Numerical Experiments and Conclusionmentioning

confidence: 99%

Incorporating minimum Frobenius norm models in direct search

Custódio¹,

2009

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“…The minimization problem (1) is solved with APPSPACK 5.0.1 [22,23], which is an open-source, asynchronous, parallel, derivative-free optimization code. APPSPACK uses a pattern search method to obtain the optimal solution by iteratively searching for updates to the current design (which is parameterized by the quantities in d) that are within a positive spanning set of p .…”

Section: Numerical Optimizationmentioning

confidence: 99%

Design Optimization of Vena Cava Filters: An Application to Dual Filtration Devices

Singer

Wang

Diachin³

2010

Journal of Biomechanical Engineering

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Background: Pulmonary embolism (PE) is a significant medical problem that results in over 300,000 fatalities per year. A common preventative treatment for PE is the insertion of a metallic filter into the inferior vena cava that traps thrombi before they reach the lungs. The goal of this work is to use methods of mathematical modeling and design optimization to determine the configuration of trapped thrombi that minimizes the hemodynamic disruption. The resulting configuration has implications for constructing an optimally designed vena cava filter.Approach: Computational fluid dynamics is coupled with a nonlinear optimization algorithm to determine the optimal configuration of trapped model thrombus in the inferior vena cava. The location and shape of the thrombus are parameterized, and an objective function, based on wall shear stresses, determines the worthiness of a given configuration. The methods are fully automated and demonstrate the capabilities of a design optimization framework that is broadly applicable.Results: Changes to thrombus location and shape alter the velocity contours and wall shear stress profiles significantly. For vena cava filters that trap two thrombi simultaneously, the undesirable flow dynamics past one thrombus can be mitigated by leveraging the flow past the other thrombus. Streamlining the shape of thrombus trapped along the cava wall reduces the disruption to the flow, but increases the area exposed to abnormal wall shear stress. Conclusions:Computer-based design optimization is a useful tool for developing vena cava filters. Characterizing and parameterizing the design requirements and constraints is essential for constructing devices that address clinical complications. In addition, formulating a well-defined objective function that quantifies clinical risks and benefits is needed for designing devices that are clinically viable.

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“…Therefore, a search method like pattern search can make use of this function to search for a maximum of the function in this region. The basic pattern search algorithm is explained fully in [13]. However, for this case, it need not be run asynchronously.…”

Section: A Robust Algorithm For Optimum Utilitymentioning

confidence: 99%

A Robust Algorithm for Optimum Utility

Guenther¹,

Lee²

2017

JAAM

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The black box functions found in computer experiments often have multiple optima. When there are multiple optima, the goal of a computer experiment should be to determine the best optimum for the purposes of the experiment. This brings up the concept of the utility of an optimum: The degree to which the optimum fulfills the purposes of the experiment. The utility of an optima is based on measures of the variability of the surface in the tolerance region (region of interest around the optima) defined by the accuracy with which influential variables can be specified. This tolerance region can be symmetric or asymmetric. For symmetric optima the tolerance region that provides maximum utility is centered at the optimum point. For asymmetric optima, it may be advantageous to displace the center of the tolerance region from the optimum point. For example, a very skewed optimum (minimum in this case) can increase significantly in one direction but only slightly in the opposite direction from the minimum point. For such an optimum the center point of the tolerance region that provides maximum utility for the optimum is displaced from the optimum point along the direction that only slightly increases. The algorithm discussed in this paper locates the center point for the tolerance region to achieve the best utility for any optimum, symmetric or asymmetric. Making use of the surface predictions of the emulator around the minimum point, it employs pattern search to find the best center point for any optimum and for any dimensionality.

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APPSPACK 4.0 : asynchronous parallel pattern search for derivative-free optimization.

Cited by 57 publications

References 17 publications

Incorporating minimum Frobenius norm models in direct search

Incorporating minimum Frobenius norm models in direct search

Design Optimization of Vena Cava Filters: An Application to Dual Filtration Devices

A Robust Algorithm for Optimum Utility

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