Simulated annealing: A review of the thermodynamic approach

Harland, John R.; Salamon, Peter

doi:10.1016/0920-5632(88)90023-0

Cited by 13 publications

(4 citation statements)

References 16 publications

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“…(Note that there also exist more complex forms of simulated annealing where an ensemble of random walkers share or exchange statistical information about the misfit surface. See, for example, Harland and Salamon [1988], Hoffmann et al . [1990], Mosegaard and Vestergaard [1991], and Ruppeiner et al ., [1991]).…”

Section: Monte Carlo Methods: the Technology Of Informationmentioning

confidence: 99%

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Monte Carlo Methods in Geophysical Inverse Problems

Sambridge

Mosegaard

2002

Reviews of Geophysics

649

395

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[1] Monte Carlo inversion techniques were first used by Earth scientists more than 30 years ago. Since that time they have been applied to a wide range of problems, from the inversion of free oscillation data for whole Earth seismic structure to studies at the meter-scale lengths encountered in exploration seismology. This paper traces the development and application of Monte Carlo methods for inverse problems in the Earth sciences and in particular geophysics. The major developments in theory and application are traced from the earliest work of the Russian school and the pioneering studies in the west by Press [1968] to modern importance sampling and ensemble inference methods. The paper is divided into two parts. The first is a literature review, and the second is a summary of Monte Carlo techniques that are currently popular in geophysics. These include simulated annealing, genetic algorithms, and other importance sampling approaches. The objective is to act as both an introduction for newcomers to the field and a comprehensive reference source for researchers already familiar with Monte Carlo inversion. It is our hope that the paper will serve as a timely summary of an expanding and versatile methodology and also encourage applications to new areas of the Earth sciences. INDEX TERMS:3260

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Section: Monte Carlo Methods: the Technology Of Informationmentioning

confidence: 99%

“…40, 3 / REVIEWS OF GEOPHYSICS the misfit surface. See, for example, Harland andSalamon [1988], Hoffmann et al [1990], Mosegaard and Vestergaard [1991], and Ruppeiner et al, [1991]). The early history of GAs in the Earth sciences has been traced above.…”

Section: Genetic Algorithmsmentioning

confidence: 99%

Monte Carlo Methods in Geophysical Inverse Problems

Sambridge

Mosegaard

2002

Reviews of Geophysics

649

395

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“…The value of the amplitudes ψ 0,n and the stripe momentum k 1 can be obtained by minimizing the mean-field energy. We do that using the Simulated Annealing algorithm [19]. The effect of quantum fluctuations can be included following the Bogoliubov scheme.…”

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confidence: 99%

Supersolid stripes enhanced by correlations in a Raman spin-orbit-coupled system

2020

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A Bose gas under the effect of Raman Spin-Orbit Coupling (SOC) is analyzed using the Discrete Spin T-moves Diffusion Monte Carlo method [1,2]. By computing the energy as well as the static structure factor and the superfluid fraction of the system, the emergence of an energetically favorable supersolid stripe state is observed, which is in agreement with recent observations. A significant enhancement of the stability of the stripe phase with respect to the mean-field prediction is observed when the strength of the inter-atomic correlations is increased. We also quantify and characterize the degree of superfluidity of the stripes and show that this quantity is mostly determined by the ratio between the Raman coupling and the square of the momentum difference between the pair of SOC inducing laser beams.Spin-Orbit Coupling (SOC), which denotes the interplay between a particle's momentum and its spin, has been a subject of interest in the recent years, both theoretically and experimentally. This is due to the wide variety of exotic quantum states induced by this kind of interaction, which include topological insulators [3], topological superconductors [4], and Majorana fermions [5]. SOC is a relativistic effect that emerges naturally in electronic systems, and that is also synthetically engineered [6] in ultracold atomic gases. These recent realizations in dilute gases represent an important achievement in the study of the physics of SOC due to the high controllability and tunability of these systems. In the particular case of Raman SOC, its implementation was first achieved experimentally by inducing a Raman coupling via two laser beams on an atomic Lambda type configuration. SOC is then generated by the simultaneous driving of a spin flip transition and transferring of momentum [7][8][9][10][11]. Under this scheme, Raman SOC has been realized with 87 Rb bosons, both in the continuum [7] and in a lattice [12,13], and also with other species: 6 Li [14], 40 K [15], 87 Sr [16], 173 Yb [17, 18], and 161 Dy [19]. In this context, two hyperfine states of the atom are labeled as the spin states.In this Letter, we focus in Raman SOC, which couples the linear momentum of an atom with its spin according toŴwith m the mass of the particle,P x the x-component of the momentum,σ x andσ z the Pauli matrices, Ω the Raman coupling, and k 0 the magnitude of the wave vector difference between the two laser beams. Some striking features induced by the SOC interaction can be observed already at the single particle level. The coupling between momentum and spin implies that the minimum of the energy dispersion relation is in a non-zero momentum, degenerate state for a given range of values of the Raman coupling [20]. This degeneracy involves states of equal magnitude but opposite sign in momentum space, enabling the possibility of a stripe phase ground state. Supersolid stripes arise from the breaking of two symmetries: a gauge symmetry, giving rise to off-diagonal long-range order, and spatial symmetry, seen as a periodic density modula...

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“…SA is a local search-based algorithm able to bypass local optima because it searches not only for trial solutions that may reduce the cost function, but also allows moves leading to increase the objective function value. This mechanism may avoid the optimization search being trapped prematurely in a local minimum [10].…”

Section: Introductionmentioning

confidence: 99%

Reliability Based Optimization with Metaheuristic Algorithms and Latin Hypercube Sampling Based Surrogate Models

Chu

Cursi²,

Hami³

et al. 2015

ACM

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Reliability based optimization (RBO) is one of the most appropriate methods for structural design under uncertainties. It searches for the best compromise between cost and safety while considering system uncertainties by incorporating reliability measures within the optimization. Despite the advantages of RBO, its application to practical engineering problem is still quite challenging. In this paper, we propose an effective method to decouple the loops of reliability assessment analysis and optimization by creating surrogate models. The Latin Hypercube sampling approach is applied to a structural finite element model to obtain an effective database for building surrogate models. In order to avoid premature convergence of the optimization process, the RBO problem is solved with metaheuristic methods such as genetic algorithm and simulated annealing. The relative efficiency of surrogate models and their relationship with metaheuristic search engine are discussed in the article.

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Simulated annealing: A review of the thermodynamic approach

Cited by 13 publications

References 16 publications

Monte Carlo Methods in Geophysical Inverse Problems

Monte Carlo Methods in Geophysical Inverse Problems

Supersolid stripes enhanced by correlations in a Raman spin-orbit-coupled system

Reliability Based Optimization with Metaheuristic Algorithms and Latin Hypercube Sampling Based Surrogate Models

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