On lumped models for thermodynamic properties of simulated annealing problems

Abstract

2014 Nous décrivons une nouvelle méthode pour estimer les propriétés thermodynamiques dans des problèmes de recuit simulé, méthode qui utilise des données acquises durant le recuit simulé. La méthode est basée sur l' estimation des probabilités de transition énergie-énergie et est bien adaptée à des simulations de type recuit simulé, dans lesquelles le système n'est jamais à l'équilibre. Abstract. 2014 The paper describes a new method for the estimation of thermodynamic properties for simulated annealing problems using data obtained during a simulated annealing run. The method works by estimating energy-to-energy transition probabilities and is well adapted to simulations such as simulated annealing, in which the system is never in equilibrium.

A SIMULATED ANNEALING APPROACH TO SEISMIC MODEL OPTIMIZATION WITH SPARSE PRIOR INFORMATION1

“…The aim of our work has been to investigate the efficiency and accuracy of a recently developed implementation of simulated annealing applied to a realistic, seismic trace inversion problem. This method, which is called 'simulated annealing at constant thermodynamic speed' Andresen et al 1988), replaces the random experimental approach with a systematic approach that takes advantage of statistical information about the model-algorithm system, acquired during the annealing. As a standard of reference in our investigation, we have used a more primitive, stochastic model optimization method, the so-called iterative improvement, when investigating the efficiency and accuracy of the implementation of simulated annealing.…”

A Feedback Algorithm for Determining Search Parameters for Monte Carlo Optimization

“…Some of these factors have to do with the cooling schedule, and some with the neighborhood structure [1]. To reduce the time required to reach a good (although not necessarily optimal) solution, cooling schedules have received much attention [1,3,4,10,13,20,28].…”

“…The lumping in [4] is a lumping by energies, i.e., states with similar energies are aggregated in the lumped model. We conclude this section with notation and some of the assumptions that we use throughout the remainder of this paper.…”

“…In general, working with the underlying Markov matrix is unrealistic given its |S| × |S| dimension. In [4] a lumped model of the SA Markov chain is developed using theory that can be found in [15]. Their criterion for designing an annealing schedule is based on thermodynamic considerations; the temperature is decreased in such a way as to minimize entropy production.…”

Combining pressure and temperature control in dynamics on energy landscapes

“…Finally we design optimal schedules that maximize the probability to reach a particular basin of the energy landscape. For the last step, we employed similar techniques as have been used for the optimization of relaxation schedules on lumped complex energy landscapes in the past; examples are optimal schedules for global optimization algorithms [22,[43][44][45][46], or the dynamics on minimum+saddle point landscape models derived for atom clusters, with the goal to design an optimal simulated annealing schedule to reach the global minimum [47].…”