Simulating annealing

Note The segmentation operation yields a near-optimal estimate x that may be used as initialization point for an optimization algoritlim that has to find out the global minimum of the criterion /(.). Because of its nonlinear nature, we prefer to minimize it by using a stochastic optimization algorithm (a version of the Simulated Annealing algorithm [3]). 

This criterion resumes all the a priori knowledge that we are able to convey concerning the physical aspect of the flawed region. Unfortunately, neither the weak membrane model (U2 (f)) nor the Beta law Ui (f)) energies are convex functions. Consequently, we need to implement a global optimization technique to reach the solution. Simulated annealing (SA) cannot be used here because it leads to a prohibitive cost for calculations [9]. We have adopted a continuation method like the GNC [2]. 

Kirkpatrick S, Gelatt C D Jr and Vecchi M P 1983 Optimization by simulated annealing Science 220 671... 

D. D. Humphreys, R. A. Friesner, and B. J. Berne. Simulated annealing of a protein in a continuum solvent by multiple-time-step molecular dynamics. J. Phys. Chem., 99 10674-10685, 1995. 

The time for classical simulated annealing increases exponentially as a function of the ratio of the energy scales /AU. However, for 5 > 1 the situation is qualitatively different. As a result of the weak temperature dependence in the barrier crossing times, the time for simulated annealing increases only weakly as a power law. 

S. Sun, Reduced representation approach to protein tertiary structure prediction statistical potential and simulated annealing, J. Theor. Biol. 172 (1995), 13-32. 

Other methods which are applied to conformational analysis and to generating multiple conformations and which can be regarded as random or stochastic techniques, since they explore the conformational space in a non-deterministic fashion, arc genetic algorithms (GA) [137, 1381 simulation methods, such as molecular dynamics (MD) and Monte Carlo (MC) simulations 1139], as well as simulated annealing [140], All of those approaches and their application to generate ensembles of conformations arc discussed in Chapter II, Section 7.2 in the Handbook. 

Simulated Annealing-based solutions [19] are conceptually the same as Genetic Algorithm-based approaches. However, the SA-based techniques, in our experience, are more sensitive to the initial settings of the parameters. Nevertheless, once the correct ones are found, the method can achieve the efficiency of GA-based solutions. We must point out that SA-based solutions have never outperformed the GA-based ones in our studies. Much of what has been mentioned regarding the GA-based solutions is also relevant for the SA technique, particularly, with respect to the cost functions. 

Variable and pattern selection in a dataset can be done by genetic algorithm, simulated annealing or PCA... 

J. Korst, E.H. Aarts, A. Korst, Simulated Annealing and Boltzmann Machines ... 

J. Kalivas, Adaption of Simulated Annealing to Chemical Optimization Problems. Elsevier Science, New York, 1995. 

Quenched dynamics is a combination of high temperature molecular dynamics and energy minimization. This process determines the energy distribution of con formational families produced during molecular dynamics trajectories. To provide a better estimate of conformations, you should combine quenched dynamics with simulated annealing. 

Otieriched dynam ics can trap structures in local minima. I o prevent this problem, you can cool the system slowly to room temperature or some appropriate lower temperature. I heu run room letTiperature m olecti lar dyn am ics sim ulation s to search for con formations that have lower energies, closer to the starting structure. Cooling a structure slowly is called simulated annealing. 

TlyperChern has a facility for a more systematic approach to the global min im urn than just choosing ran dom startin g poin ts. This facility is associated with the idea of simulated annealing. 

Humphreys D D, R A Friesner and B ] Berne 1995. Simulated Annealing of a Protein in a Continuu Solvent by Multiple Time-step Molecular Dynamics. Journal of Physical Chemistry 99 10674-1068... 

Je next introduce the basic algorithms and then describe some of the mmy variants upon lem. We then discuss two methods called evolutionary algorithms and simulated anneal-ig, which are generic methods for locating the globally optimal solution. Finally, we discuss jme of the ways in which one might cinalyse the data from a conformational malysis in rder to identify a representative set of conformations. 

Finding the Global Energy Minimum Evolutionary Algorithms and Simulated Annealing... 

A particularly important application of molecular dynamics, often in conjunction with the simulated annealing method, is in the refinement of X-ray and NMR data to determine the three-dimensional structures of large biological molecules such as proteins. The aim of such refinement is to determine the conformation (or conformations) that best explain the experimental data. A modified form of molecular dynamics called restrained moleculai dynarrdcs is usually used in which additional terms, called penalty functions, are added tc the potential energy function. These extra terms have the effect of penalising conformations... 

Gdanitz, R J 1992. Prediction of Molecular Crystal Stluctures by Monte Carlo Simulated Annealing Without Reference to Diffraction Data. Chemical Physics Letters 190 391-396. 

Kirkpatrick S, C D Gelatt and M P Vecchi 1983. Optimization by Simulated Annealing. Science 220 671-680. 

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