Simulated Annealing Techniques

Several variants of the basic SA algorithm have been developed, which differ in the choice of the CF, in the design of the annealing schedule or in the procedure for the generation of the trial configurations. For example, Andreev et al. reduce T at a preset rate and, for each T, perform several moves which increase as the acceptance ratio decreases David et introduced the following relevant novelties, included in the computer program DASH  

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Another interesting implementation of simulated annealing for continuous minimization (like a typical parameter estimation problem) utilizes a modification of the downhill simplex method. Press et al. (1992) provide a brief overview of simulated annealing techniques accompanied with listings of computer programs that cover all the above cases. 

A detailed presentation of the simulated annealing techniques can be found in The Annealing Algorithm by Often and Ginneken (1989). 

This article will describe the successful use of simulated annealing techniques to overcome two difficult types of massive search problems in modem X-ray crystallographic studies of large biomolecules. This in mind, a brief but sufficient overview of the current practice of biological X-ray crystallography will be first presented. Then two separate search problems will be discussed. Next, a simulated annealing solution to these problems vriU be described. Finally, the successful application of the developed methodology will be demonstrated with the help of real-life examples. 

The particular iterative technique chosen by Car and Parrinello to iteratively solve the electronic structure problem in concert with nuclear motion was simulated annealing [11]. Specifically, variational parameters for the electronic wave function, in addition to nuclear positions, were treated like dynamical variables in a molecular dynamics simulation. When electronic parameters are kept near absolute zero in temperature, they describe the Bom-Oppenheimer electronic wave function. One advantage of the Car-Parrinello procedure is rather subtle. Taking the parameters as dynamical variables leads to robust prediction of values at a new time step from previous values, and cancellation in errors in the value of the nuclear forces. Another advantage is that the procedure, as is generally true of simulated annealing techniques, is equally suited to both linear and non-linear optimization. If desired, both linear coefficients of basis functions and non-linear functional parameters can be optimized, and arbitrary electronic models employed, so long as derivatives with respect to electronic wave function parameters can be calculated. 

The S4 peptide and the IS2, IS4, IS34, IVS4 and Islink56 peptides of the rat brain sodium channel have been synthesized and studied in aqueous trifluoroethanol and DPC micelles using the NOE distance restraint/simulated annealing technique. All of the peptides were found to have predominantly a-helical structures in both types of environment. There was some evidence for bending of the longer helices but no discernible evidence for a well-defined tertiary structure. ... 

It is noteworthy that the JG operator has also been successfully incorporated into a Multi-objective Simulated Annealing technique (Sankararao and Gupta, 2007 see Chapter 4 in this book). The performance assessment of this algorithm was done on three well-known test (benchmark) problems commonly used in the evolutionary MOO field. This algorithm was then employed for the MOO of an industrial fluidized-bed catalytic cracking unit. 

Several molecular dynamics simulation approaches are available, including regular simulation, constrained simulation, and simulated annealing techniques. In addition, the simulated annealing dynamics simulation also was popular in computational chemistry studies of proteins and drug molecules (34.44.45). A common experimental protocol has been widely used in molecular dynamics simulation as following (34.46.47) ... 

T. Burger, MOCCA A Conformational Analysis Tool Combining Monte Carlo and Simulated Annealing Techniques., unpublished results. 

The calculation of the ground-state geometry and electronic structure proceeds by an interlaced iteration of the Kohn-Sham equations and the ionic stationary conditions. The Kohn-Sham equations were solved by a damped gradient iteration method and the ionic configuration was iterated with a simulated annealing technique, using a Metropolis algorithm. 

It is possible to use an alternative approach, regarding the minimization of the functional as an optimization problem, which can be solved by means of the simulated annealing procedure. A simulated annealing technique based on MD can be efficiently applied to minimize the KS functional the resulting technique, called dynamical simulated annealing allows the study of finite temperature properties. 

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