Cooling Schedules for Optimal Annealing

Hajek, Bruce

doi:10.1007/978-1-4612-4808-8_42

Cited by 317 publications

(529 citation statements)

References 1 publication

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“…Let Ω be a measurable set with a measure m and let µ be a measure on Ω with a density (also denoted by µ) with respect to m. We aim to minimize some cost C. The S.A. involves a simulation of a non-homogeneous Markov chain whose invariant distribution at iteration n is µ n ∝ µ −C/Tn where (T n ) n≥0 is a temperature with T n → 0. Under classical conditions (see [H88,GG84] for instance), µ ∞ concentrates on the set of minima of C. The S.A. method with transition distribution q(I, I ′ ) works as follow:…”

Section: Reversible Jump Proposalmentioning

confidence: 99%

Adaptive sequential design for regression on multi-resolution bases

2011

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This work investigates the problem of construction of designs for estimation and discrimination between competing linear models. In our framework, the unknown signal is observed with the addition of a noise and only a few evaluations of the noisy signal are available. The model selection is performed in a multi-resolution setting. In this setting, the locations of discrete sequential D and A designs are precisely contraint in a small number of explicit points. Hence, an efficient stochastic algorithm can be constructed that alternately improves the design and the model. Several numerical experiments illustrate the efficiency of our method for regression. One can also use this algorithm as a preliminary step to build response surfaces for sensitivity analysis.

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Section: Reversible Jump Proposalmentioning

confidence: 99%

Adaptive sequential design for regression on multi-resolution bases

2011

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“…Early results show that this desirable property holds for suitably adjusted logarithmic schedules (23)(24)(25). However, it is demonstrated in (26) that exponential cooling must be preferred as soon as one deals with a finite amount of computing time.…”

Section: Optimization By Samentioning

confidence: 99%

A graph‐based approach for automatic cardiac tractography

Frindel

Robini

Schaerer

et al. 2010

Magnetic Resonance in Med

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A new automatic algorithm for assessing fiber-bundle organization in the human heart using diffusion-tensor magnetic resonance imaging is presented. The proposed approach distinguishes from the locally "greedy" paradigm, which uses voxel-wise seed initialization intrinsic to conventional tracking algorithms. It formulates the fiber tracking problem as the global problem of computing paths in a boolean-weighted undirected graph, where each voxel is a vertex and each pair of neighboring voxels is connected with an edge. This leads to a global optimization task that can be solved by iterated conditional modes-like algorithms or Metropolis-type annealing. A new deterministic optimization strategy, namely iterated conditional modes with α-relaxation using (t 2 )-and (t 4 )-moves, is also proposed; it has similar performance to annealing but offers a substantial computational gain. This approach offers some important benefits. The global nature of our tractography method reduces sensitivity to noise and modeling errors. The discrete framework allows an optimal balance between the density of fiber bundles and the amount of available data. Besides, seed points are no longer needed; fibers are predicted in one shot for the whole diffusion-tensor magnetic resonance imaging volume, in a completely automatic way. Magn Reson Med 64:1215-1229, 2010.

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“…Despite this very attractive characteristic such a schedule tends to converge too slowly. Other t schedules for optimality were also proposed by Geman and Geman (1984), Hajek (1988), and Siarry (1997). These however may not converge in an acceptable amount of time for many problems (Cohn and Fielding, 1999).…”

Section: Solving the Problem Of The Optimisation Function Modelmentioning

confidence: 99%

Optimal estuarine sediment monitoring network design with simulated annealing

Nunes

Caeiro²,

Cunha

et al. 2006

Journal of Environmental Management

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An objective function based on geostatistical variance reduction, constrained to the reproduction of the probability distribution functions of selected physical and chemical sediment variables, is applied to the selection of the best set of compliance monitoring stations in the Sado river estuary in Portugal. These stations were to be selected from a large set of sampling stations from a prior field campaign. Simulated annealing was chosen to solve the optimisation function model. Both the combinatorial problem structure and the resulting candidate sediment monitoring networks are discussed, and the optimal dimension and spatial distribution are proposed. An optimal network of sixty stations was obtained from an original 153-station sampling campaign. q

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Cooling Schedules for Optimal Annealing

Cited by 317 publications

References 1 publication

Adaptive sequential design for regression on multi-resolution bases

Adaptive sequential design for regression on multi-resolution bases

A graph‐based approach for automatic cardiac tractography

Optimal estuarine sediment monitoring network design with simulated annealing

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