Mesh Adaptive Direct Search Algorithms for Constrained Optimization

Audet, Charles; Dennis, John E.

doi:10.1137/040603371

Cited by 1,027 publications

(1,020 citation statements)

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“…Robustness of the solution to noise and experimental uncertainty is enforced by allowing the ellipses to contain a specified small percentage of pixels that lie outside the specified image level set. The optimization problem is solved numerically by applying a mesh adaptive direct search (MADS) algorithm [6] with a filter [5]. The filter allows intermediate solutions that violate constraints in order to provide a more robust global search of the parameter space.…”

Section: Performing Organization Name(s) and Address(es)mentioning

confidence: 99%

“…Because of the weaknesses inherent to filter-GPS, Audet and Dennis [6] more recently introduced the class of MADS algorithms. Instead of limiting local exploration to a finite number of directions (as GPS does), MADS systematically generates an asymptotically dense set of directions in the limit.…”

Section: Mesh Adaptive Direct Search (Mads)mentioning

confidence: 99%

“…Instead of limiting local exploration to a finite number of directions (as GPS does), MADS systematically generates an asymptotically dense set of directions in the limit. Because of this property, convergence to both first-order [6] and second-order [2] stationary points is guaranteed under reasonable assumptions without the need for a filter but with the requirement that the starting point be feasible.…”

Section: Mesh Adaptive Direct Search (Mads)mentioning

confidence: 99%

“…Under this construction, GPS is the specific implementation of MADS for which ∆ m k = ∆ p k for all k. Figures 2 and 3 give examples of a GPS and MADS frame, respectively [6]. As shown Figure 2: Example of GPS frames…”

Section: Mesh Adaptive Direct Search (Mads)mentioning

confidence: 99%

“…In fact, the total of all poll directions can be chosen to become asymptotically dense. A specific implementation of MADS was devised in [6] in which the sets D k are limited in size but chosen randomly at each iteration. This preserves the denseness of poll directions, but does so only with probability one.…”

Section: Mesh Adaptive Direct Search (Mads)mentioning

confidence: 99%

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Characteristic Shape Sequences for Measures on Images

Pinge¹,

Abramson²,

Asaki³

et al. 2006

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Researchers in many fields often need to quantify the similarity between images using metrics that measure qualities of interest in a robust quantitative manner. We present here the concept of image dimension reduction through characteristic shape sequences. We formulate the problem as a nonlinear optimization program and demonstrate the solution on a test problem of extracting maximal area ellipses from twodimensional image data. To solve the problem numerically, we augment the class of mesh adaptive direct search (MADS) algorithms with a filter, so as to allow infeasible starting points and to achieve better local solutions. Results here show that the MADS filter algorithm is successful in the test problem of finding good characteristic ellipse solutions from simple but noisy images.

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Section: Performing Organization Name(s) and Address(es)mentioning

confidence: 99%

Section: Mesh Adaptive Direct Search (Mads)mentioning

confidence: 99%

Section: Mesh Adaptive Direct Search (Mads)mentioning

confidence: 99%

Section: Mesh Adaptive Direct Search (Mads)mentioning

confidence: 99%

Section: Mesh Adaptive Direct Search (Mads)mentioning

confidence: 99%

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Characteristic Shape Sequences for Measures on Images

Pinge¹,

Abramson²,

Asaki³

et al. 2006

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Improving process representation in conceptual hydrological model calibration using climate simulations

Minville

Cartier

Guay

et al. 2014

Water Resources Research

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Different sets of calibrated model parameters can yield divergent hydrological simulations which in turn can lead to different operational decisions or scientific conclusions. In order to obtain reliable hydrological results, proper calibration is therefore fundamental. This article proposes a new calibration approach for conceptual hydrological models based on the paradigm that hydrological process representation, along with the reproduction of observed streamflows, need to be taken into account when assessing the performance of a hydrological model. Several studies have shown that complementary data can be used to improve hydrological process representation and make hydrological modeling more robust. In the current study, the process of interest is actual evapotranspiration (AET). In order to obtain a more realistic representation of AET, meteorological variables and the AET mean annual cycle simulated by a regional climate model (RCM) driven by reanalysis are used to impose constraints during the optimization procedure. This calibration strategy is compared to a second strategy which relies on AET derived from reference data and to the classical approach based solely on the reproduction of observed discharges. The different methodologies are applied to calibrate the lumped conceptual model HSAMI, used operationally at HydroQuebec, for six Canadian snow-dominated basins with various hydrometeorological and physiographical characteristics.

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Optimal Design for Placements of Tsunami Observing Systems to Accurately Characterize the Inducing Earthquake

Mulia

Gusman

Satake

2017

Geophysical Research Letters

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Recently, there are numerous tsunami observation networks deployed in several major tsunamigenic regions. However, guidance on where to optimally place the measurement devices is limited. This study presents a methodological approach to select strategic observation locations for the purpose of tsunami source characterizations, particularly in terms of the fault slip distribution. Initially, we identify favorable locations and determine the initial number of observations. These locations are selected based on extrema of empirical orthogonal function (EOF) spatial modes. To further improve the accuracy, we apply an optimization algorithm called a mesh adaptive direct search to remove redundant measurement locations from the EOF-generated points. We test the proposed approach using multiple hypothetical tsunami sources around the Nankai Trough, Japan. The results suggest that the optimized observation points can produce more accurate fault slip estimates with considerably less number of observations compared to the existing tsunami observation networks.

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Mesh Adaptive Direct Search Algorithms for Constrained Optimization

Cited by 1,027 publications

References 25 publications

Characteristic Shape Sequences for Measures on Images

Characteristic Shape Sequences for Measures on Images

Improving process representation in conceptual hydrological model calibration using climate simulations

Optimal Design for Placements of Tsunami Observing Systems to Accurately Characterize the Inducing Earthquake

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